text: A. 4. Acids and metals react in single replacement reactions, which are oxidation-reduction reactions. (c) the reactions of dilute acids with metals and how these relate to the metals' position in the reactivity series (d) the neutralisation of dilute acids with bases (including alkalis) and carbonates WJEC Combined science Unit 5 5.2 Experimental Behaviour of Bases. You can also mix the product in water at this stage and test if it is an acid or base. Acids and bases When acids react with a base, a salt and water are made. This site uses cookies from Google and other third parties to deliver its services, to personalise adverts and to analyse traffic. The reaction of ethanol with sodium metal (a base) produces sodium ethoxide and hydrogen gas. Some metals react with a base to form salts and hydrogen gas. Light a wood splint, remove the cork and immediately hold the flame to the mouth of the tube. This should take around 40 minutes, and most classes should be able to do this version. Safety is particularly relevant to younger students. The physics of restoration and conservation. The chemical properties of water Reaction with metals Theory If the metal is situated in the beginning of the series of activities, it is more active and gives up more easily valence electrons. Includes kit list and safety instructions. While other metal/acid combinations react in the same way, recovering the salt by crystallisation (in Lesson 2) may not be as successful as it is using zinc and sulfuric acid. Place the evaporating basin on a pipeclay triangle or gauze on a tripod and gently boil the solution over a low Bunsen flame. NaOH) by their reaction with Litmus solution (blue/red) Zinc metal Solid sodium carbonate Materials Required Test tubes, test tube stand, test tube holder, cork, droppers, boiling tube, match-box, burner, […] Acids react with metallic oxides to give salt and water similar to the reaction acid and base So, metallic oxides are called basic oxide Reaction of a Non – metallic oxide with base When base reacts with non-metallic oxide then it forms salt and water Non – metallic oxide + base – salt + water You might have to leave the metals that react too slowly until the next lesson. Which parts of the chemistry curriculum will your 16–18 students find useful to become a dietician? Zinc metal also react with sodium hydroxide solution to form hydrogen gas. Nevertheless many students find it difficult to achieve a successful ‘pop’ test for hydrogen, so you may need to do follow-up demonstrations as well. Distribution of pieces of magnesium ribbon should be supervised to avoid students taking several pieces and experimenting later with igniting them. Join now. Refer to CLEAPSS Laboratory Handbook Section 13.2.6 for a discussion. Space provided for students to fill out missing information, their results, and answer the discussion questions provided. Examples of Reaction Between Acids and Bases: When aluminium metal is heated with sodium hydroxide solution,the sodium aluminate and hydrogen gas is formed. If it is moved with a 2400 N force and 6 KJ of work is done, then how far is the crate being lifted? Add few drops of HCl into the boiling tube using a dropper. It changes red litmus blue. A chemical reaction takes place in which energy is released. In this chemistry lesson students test metals with different chemicals to observe the reaction. The same applies to moving the evaporating basin before pouring its contents into the crystallising dish. Place a small sample of each metal to be tested in the different wells of a clean, dry microtray. Do most metals react with acids in the same way? Acids react with metallic oxides to give salt and water similar to the reaction acid and base So, metallic oxides are called basic oxide; Reaction of a Non – metallic oxide with base. Reactions of aqueous carboxylic acids with metals and metal carbonates Carboxylic acids are weak acids , so they can donate a hydrogen ion (H+) in acid-base reactions: Metals For example reaction of sulphuric acid with zinc. Record which metal you add to each tube. 1.8.12 demonstrate knowledge and understanding of and write observations on and equations for the general reactions of hydrochloric, sulfuric and nitric acids with: metals; bases; carbonates; hydrogencarbonates; Soluble salts can be made from acids by reacting them with solid insoluble substances, such as metals, metal oxides, hydroxides or carbonates. Non – metallic oxide + base – salt + water. C. Write a list of those tested by other groups. digesting food Thta is : Chemical reaction : H₂SO₄+Zn--- ZnSO₄+H₂, Products obtained are :  zinc-sulphate and hydrogen gas, The  beaker becomes hot  and hydrogen gas is produced which makes match stick burns with pale blue flame and popping sound, This site is using cookies under cookie policy. Label the dish and leave until the next lesson to crystallise. If crystals begin to appear, eg at the top edge of the solution, the Bunsen burner should be turned off immediately and the solution left to cool. Neutralisation is … Arrange the reaction’s cha The Reaction of Non-metal Oxide with Bases Non-metal oxides react with bases to produce salt and water. Write a word equation for the reaction between zinc and sulfuric acid. Be aware of the problems associated with heating beakers or evaporating dishes on tripods, and with lifting such hot containers off a tripod after heating. Copper, Cu(s) – see CLEAPSS Hazcard HC026. Plz koi mara all answer ko thanks kar do plzplzplz..........., Drag each tile to the correct box. Acids, Bases and Salts CHAPTER2 You have learnt in your previous classes that the sour and bitter tastes of food are due to acids and bases, respectively, present in them. This app allows you to study about Base reaction with metal in … The results are used to categorize the metals. Class practical and Demonstration. Use the student handout available with this resource and get the students to answer each question after observing the reaction. Describe reactions of acids with metals, bases and carbonates 6. Join now. Metals. In a reaction in water, neutralization results in there being no excess of hydrogen or hydroxide ions present in the solution. Reaction of Acids and Bases with Metals Let's perform a very interesting experiment Take 5 mL of sulphuric acid in a test tube and add a few pieces of zinc granules to it. A loosely inserted cork allows sufficient build-up of gas in a slow reaction to enable a successful test. Hydrogen gas forms as the metals react with the acid to form salts. All the metals do not react with bases to form salt and hydrogen. If nothing happens, you may need to try again. ; Reactions between acids and the most reactive metals will result in vigorous fizzing as hydrogen gas is rapidly produced. Place a small piece of metal (about 4 mm long) into each test tube. Investigate reactions between acids and bases; use indicators and the pH scale. photosynthesis Acids react with most metals to form a salt and hydrogen gas. Therefore bases such as NaOH show basic character. Each working group needs a small selection of metals and acids to test. Alkali Metals (Lithium, Sodium, Potassium) react with water. Using small granules helps to reduce the time taken. Lesson 2, in which the salt formed is recovered by crystallisation, takes longer, and the class needs to be reliable enough in behaviour and manipulative skills to cope with the hazards involved in heating acidic solutions in beakers on tripods. Acid halides react with amines to form substituted amides. Chemical Safety Precautions * Safety glasses are to be worn whenever working with acids, bases, or any flammable materials. Unfortunately the chlorides of magnesium and zinc are not easy to crystallise, while magnesium sulfate is so soluble that it takes longer to evaporate sufficiently. The pH of the neutralized solution depends on the acid strength of the reactants. Alkalis (soluble bases) include soluble metal hydroxides, soluble metal carbonates and ammonia. GCSE. Iron(II) compounds may suffer from oxidation problems when the solution is evaporated, giving a visibly impure product. This is a resource from the Practical Chemistry project, developed by the Nuffield Foundation and the Royal Society of Chemistry. C1.1.12 describe tests to identify oxygen, hydrogen and carbon dioxide. For exanple, sodium hydroxide reacts with zinc and water to form sodium zincate and hydrogen gas. For example the reaction of carbon dioxide and lime water (calcium hydroxide) $$CO_2 ~+ ~Ca~ (OH)_2~ \rightarrow metal + dilute acid → salt + hydrogen; Wales. Explain your answer by referring to your table of results. Apparatus for recovering salt formed by the reaction of zinc and sulfuric acid. In the litmus test experiment the red litmus solution turns into blue when sodium hydroxide is added. Reactions of bases with other chemicals e.g. Amazing app will teach the user, bases reactions with metal. Introduction to oxidation and reduction: simple examples only, e.g. Both oxide and hydroxide compounds can be classified as bases, though not all possible oxides and hydroxides will react with acids. Take a little amount of blue and red litmus solutions separately in two test tubes. Ask your question . The procedure for safely testing the evolved hydrogen gas in the test tube reactions needs to be demonstrated at a suitable point in lesson 1. The Reaction between zinc granules and dilute sulphuric acid starts . ... Acids - Reaction with Bases. . An engine reaches its top speed in 8 s. It is able to perform 240 KJ of work in that time. For example; carbon dioxide is a non-metal oxide. Learning Outcomes By the end of this lesson you will be able to: Predict whether a chemical reaction between an acid and a… Read More Add HCl to Na2CO3, only when apparatus is made carefully airtight. It extinguishes the burning matchstick and burns itself with mild explosion and produces a popping sound.The gas evolved is hydrogen which burns with mild explosion. Try write reaction equations for the three reactions above. B. It extinguishes the burning matchstick and burns itself with mild explosion and produces a popping sound.The gas evolved is hydrogen which burns with mild explosion. Students conduct an experiment to test the reactivity of metals and non-metals. So, try out all and observe the changes………………, Cork it properly but leave a side open for pouring acid, Drop wise pour acid into it say acid taken is dilute sulphuric acid. Acids - Reaction with Metals Experimental sheet for the reaction of metals with dilute hydrochloric acid. But, due to rareness of francium, experiment… Iron filings, Fe(s) – see CLEAPSS Hazcard HC055a. In this demonstration the equilibrium between two different coloured cobalt species is disturbed. This establishes that hydrogen production is a characteristic property of the reaction of metals and acids. NaOH + Al ——-> NaAlO 2 + H 2. Compounds so formed are known as ionic compounds. Heat the boiling tube. The experiment is done first on a smaller scale using test tubes (lesson 1 below), with no attempt to recover the salts formed. Bring a burning matchstick near the mouth of the fine jet.A gas is evolved. In lesson 2, selecting zinc and sulfuric acid as the example to follow through to producing crystals of the salt is governed by the need to have a salt that crystallises easily. the reaction of the alkali sodium hydroxide with ammonium salts, carbon dioxide, metals salts to give hydroxide precipitates. Log in. Step by step experiment investigating the reaction of acids & metals, and acids & carbonates. In chemistry, neutralization or neutralisation (see spelling differences) is a chemical reaction in which acid and a base react quantitatively with each other. Test for presence of hydrogen gas with a match. Scroll down the page for examples and solutions. This powder is calcium sulfate. Neutralisation is the reaction between an acid and a base. This leads to the evolution of hydrogen gas. Describe, explain and exemplify the processes of filtration and crystallisation. a Metal + Sulfuric Acid → Metal Sulfate + Hydrogen. If small crystals form on the glass rod, stop heating, otherwise continue until that point is reached. Avoid inhaling the acidic fumes that may rise from the beaker as a result of the vigorous bubbling. To pour the sample into the test tube containing zinc metal, drag the beaker towards the test tube.To close the test tube, drag the single bored cork (in which a fine jet tube is inserted through the hole) towards the test tube.Click on the knob of the burner to turn it on.You can see that gas bubbles are evolved from the test tube.Now, drag the burning match stick over the fine jet tube.The flame dips out with a mild explosion.You can verify your result and can see the inference by clicking on the correct icon given under ‘Result’.Click on the 'Reset' button to restart the test. Scientific report includes Aim, Hypothesis, Apparatus, Method, Discussion and Conclusion. In the reaction of the metal with diluted acid, copper nitrate and nitrogen divalent oxide form in … Record which metal and which acid you use, and what happens when the lighted splint is applied to the gas produced. Neutralisation - formation of a salt from an acid and a base. The full equation for the reaction between sodium hydroxide solution and dilute sulfuric acid is Indicators are used to determine whether a solution is acidic or alkaline. Then place a dropper with a fine jet on the mouth of the tube. Add few drops of NaOH to each test tube using a dropper.Red litmus turns blue.NaOH is an alkali having pH value more than 7. What is the name of this gas? However, the latter reaction occurs faster because of the increased acidity of water (K a value of 1 × 10 −15). A crate is being lifted into a truck. Add a 2–3 cm depth of dilute hydrochloric acid to the first three tubes, and a 2–3 cm depth of dilute sulfuric acid to the remaining three tubes. “Bases react with metal” is an educative application in support to high school students. Which other metals and acids produce the same gas? The Rate of Reaction Of Metals with Acids Introduction In this investigation I will be looking at the rate of reaction between a metal, which will be magnesium ribbon, and an acid. HCl) and bases (dil. The first group of reactions we'll discuss is when a metal and an acid are combined. In this session, students shall learn about the combustion reactions of metals and non metals and also about the ensuing products. ← Previous page Reaction of Metal and Non-metal Many metals form ionic bonds when they react with non-metals. This collection of over 200 practical activities demonstrates a wide range of chemical concepts and processes. Reaction … Which metals react with hydrochloric acid? Reaction of base with oxides of non-metals: Non-metal oxides are acidic in nature. The time taken for the reaction depends on the particle size of the metal used. Add few drops of NaOH into the boiling tube using a dropper. Le Chatelier’s principle is used to predict a colour change. higher energy of products But few exceptional cases are there. Knowledge of reactions limited to those of magnesium, zinc and iron with hydrochloric and sulfuric acids. Heat the boiling tube. Take a little amount of blue and red litmus solutions separately in two test tubes. Reaction between Metals and Non-metals, Reaction of metals with oxygen, Reaction of metals with sulfur, A series of free Science Lessons for 7th Grade and 8th Grade, KS3 and Checkpoint, GCSE and IGCSE Science, examples 8. Lesson 1 is a series of test tube experiments in which each working group establishes as a common feature that hydrogen is given off as metals react with an acid – if the metal reacts at all. Therefore, all group 1 metals should react with water. Part C: Determine the Reactivity of Acids and Bases with Metals. Reaction with sulfonyl chlorides This reaction is identical to the reaction of sodium metal with water. Aldehydes and ketones react with primary amines to give a reaction product (a carbinolamine) that dehydrates to yield aldimines and ketimines (Schiff bases). 1. Like other alkaline metals, potassium is quite reactive – so it cannot be encountered in a free state in nature. higher energy of reactants Such base may be metal oxides, metal hydroxides, metal carbonates and ammonia. Reaction with acid halides. Using tongs of suitable size is a good way of lifting hot containers but some schools may not have these. using a battery, addition of hydrogen halide on alkene using markowine koffs rule. Note any signs of chemical change and record your observations in a data table. Chemistry. It can then be done on a larger scale (lesson 2 below), and the salts formed can be recovered by crystallisation. When this solution was heated a small amount of white powder was noted. When a metal reacts with an acid, it generally displaces hydrogen from the acids. Magnesium ribbon, Mg(s) – see CLEAPSS Hazcard HC059a. All metal oxides, metal hydroxides can act as bases. How Do Both Acids and Bases React with Metals 1. Bases are compounds that react with acids to produce a salt and water only. Take some pieces of zinc metal in a boiling tube. The evolution of hydrogen gas can be seen by conducting the following experiments. Note: Click on the ‘HELP’ button to see the instructions. Take a small quantity of solid sodium carbonate in a flask. This pair of experiments forms an important stage for younger students in developing an understanding of what an acid is. Investigate and measure the neutralising effect of indigestion tablets on hydrochloric acid in this class practical. Add a small piece of the same metals to each of the tubes with sulfuric acid in them. Alkali + Metal ⇨ Salt + Hydrogen Example: Sodium hydroxide gives hydrogen gas and sodium zincate when reacts with zinc metal. Observing Acid-Metal Reactions. Topic 4 - Extracting metals and equilibria, 4.3 Explain the reactivity series of metals (potassium, sodium, calcium, magnesium, aluminium, (carbon), zinc, iron, (hydrogen), copper, silver, gold) in terms of the reactivity of the metals with water and dilute acids and that these reactions show the…, 3.11 Explain the general reactions of aqueous solutions of acids with: metals, metal oxides, metal hydroxides, metal carbonates to produce salts, 3.15 Explain why, if soluble salts are prepared from an acid and an insoluble reactant: excess of the reactant is added; the excess reactant is removed; the solution remaining is only salt and water, C3.3f recall that carbonates and some metals react with acids and write balanced equations predicting products from given reactants. A soluble base like sodium hydroxide is called an alkali. Action of litmus solution with acid and base. Take some pieces of zinc metal in a boiling tube. Record which metal you add to each tube. Describe the application of acids, bases and pH in everyday life For Merit students must be able to: 1. In particular dilute nitric acid (< 0.5 M) does produce hydrogen with moderately reactive metals such as magnesium and zinc, even though reactions are different at higher concentrations, and with other metals. Lesson organisation. Neutralisation Reactions: Basics; Titrations 2C; Acids, Bases and Salt Preparations. Complete this general word equation in your notebook: Metal + acid → +. Likewise, similar reactions occur with potassium metal. This reaction will yield a metal salt and hydrogen gas. This time place a cork loosely in the top of the test tube so that any gas produced escapes slowly. When this experiment is repeated with nitric or sulfuric acid instead of \(HCl$$, it yields the same results: the clear limewater turns milky, indicating the production of carbon dioxide. Na with Cl₂, Mg with O₂, Zn with Cu²⁺. Add few drops of HCl to each test tube using a dropper.Blue litmus turns red.HCl is an acid having pH value below 7. For example, zinc metal reacts with hydrochloric acid producing zinc chloride and hydrogen gas. Acids and Bases React with Metals. C. This experiment is a very rudimentary 'titration' and an example of a titration curve from this experiment is given here: It is therefore not expected that learners' curves will be linear, but rather that there will be a gradual decline in pH at first, followed by a rapid drop when all the base has been neutralised. If a runner exerts 5 KJ of work to make 125 W of power, then how long did it take the runner to do the work? Acids, bases and salts. If someone in the family is suffering from a problem of © Nuffield Foundation and the Royal Society of Chemistry, Test your 11–14 students’ knowledge of separation techniques; elements, mixtures and compounds; periodic table trends. Zn (s) + 2 HCl (aq) → ZnCl 2 (aq) + H 2 (g) Bases also react with certain metals like zinc or aluminum for example to produce hydrogen gas. Acids react with some metals to produce salts and hydrogen. …, In which of these examples does chemical energy change to electrical energy? If you react secondary amines with aldehydes or ketones, enamines form. But unlike the reaction between acids and bases, we do not get water. Observe the reactions of the metals with water. Add a small piece of a different metal to each of the tubes with hydrochloric acid in them. Another method to chemically generate gas is the oxidation of metals in acidic solutions. Each activity contains comprehensive information for teachers and technicians, including full technical notes and step-by-step procedures. We used acid-base reactions to produce different salts. Neutralisation. Students should not be seated on laboratory stools while carrying out these operations. This class experiment is often used in the introductory study of acids to establish that this behaviour is a characteristic property. Find my revision workbooks here: https://www.freesciencelessons.co.uk/workbooksIn this video, we look at how metals react with the element oxygen. Your teacher will show you how to test the gas being produced in these reactions. Heat the boiling tube. lower energy of reactants For another reaction experiment, put an Alka-Seltzer tablet in the bottom of a clear plastic film canister (the kind where the cap fits inside instead of closing over the outside). respiration NaOH + Al ——-> NaAlO2 + H2 Write formula equations to describe the reactions of acids 2. Reactions of potassium and potassium hydroxide ... metallic potassium is a soft metal of a silvery white color. The solid is added to the acid until no more reacts and the excess solid is filtered off to produce a solution…. Filter the warm solution into the conical flask to remove the excess zinc. Cover each metal with water. Then insert one end of the delivery tube into the flask and the other end into the beaker. The crystals can then be examined using a hand lens or microscope. When they react with acid, a neutralisation reaction occurs. Add these to your table. Information about your use of this site is shared with Google. Indicators are used to determine whether a solution is acidic or alkaline. bhaii please if it's any kind of joke please tell me i am getting panic. Base + Non-metal oxide ⇨ Salt + Water . Neutralisation is the reaction of an acid with a base that results in the pH moving towards 7. C6.1.1 recall that acids react with some metals and with carbonates and write equations predicting products from given reactants, C6.1.2 describe practical procedures to make salts to include appropriate use of filtration, evaporation, crystallisation and drying, 7 Production of pure dry sample of an insoluble and soluble salt, C4 Production of pure dry sample of an insoluble and soluble salt, Acids and bases – tackling common misconceptions, Lithium: separation, mining and battery power, Why you need A-level chemistry to study dietetics, The equilibrium between two coloured cobalt species, Turning copper coins into ‘silver’ and ‘gold’, Using indigestion tablets to neutralise an acid, Test tubes, 100 mm x 16 mm or similar, x8, Corks or bungs to fit test tubes loosely, x2, Filter funnel, approximately 65 mm diameter, Pipeclay triangle or ceramic gauze (see note 1). Nitric acid (diluted and concentrated) displays oxidizing properties, with the dissolution of copper. How much power (in W) does this engine have in that time? Transfer the filtrate into an evaporating basin. Fill the canister with warm water and then quickly put the cap on and watch the acid-base reaction! To pour sample into solid sodium carbonate, drag the beaker towards the test tube.To pour phenolphthalein into the mixture of solid sodium carbonate and the sample, drag the beaker towards the test tube.You can verify your result and can see the inference by clicking on the correct icon in the ‘Result’ part.Click on the ‘Reset’ button to redo the experiment. Dilute hydrochloric acid, HCl(aq) – see CLEAPSS Hazcard HC047a and CLEAPSS Recipe Book RB043. Reactions between Dilute Hydrochloric and Sulfuric Acid with Metals: Acids react with most metals and, when they do, a salt and hydrogen gas is produced: Metal + Hydrochloric Acid → Metal Chloride + Hydrogen. Extend your table of observations in your notebook to include these. C1.1 How has the earth's atmosphere changed over time, and why? When alkali (base) reacts with metal, it produces salt and hydrogen gas. Conclusion. D. When aluminium metal is heated with sodium hydroxide solution,the sodium aluminate and hydrogen gas is formed. By the end of the lesson, students should be able readily to draw the conclusion: This experiment is also a good opportunity for students to learn how to draw up suitable tables for recording experimental observations. Let us consider the reaction of sodium carbonate with dilute HCl. In association with Nuffield FoundationFour out of five stars. After this the curve levels out again. Acids, Bases and Salt Preparations Solubility Rules Neutralisation: Proton Transfer Neutralisation: Acids, Bases, Metals, Carbonates & Salts Alkalis vs Bases Experiment: Preparation of Soluble Salts … Which metals react with sulfuric acid? Reactions of metals. They need to understand how to generalise from sufficient examples, and to see the limits to that generalisation in metals that do not react. > When bases react with metals they do not release hydrogen gas. Hydrogen gas forms as the metals react with the acid to form salts. The experiment is done first on a smaller scale using test tubes (lesson 1 below), with no attempt to recover the salts formed. Ions are formed because of loss or gain of elect Its pH is more than 7. The general reaction results in a salt and hydrogen gas. But unlike the reaction between acids and bases, we do … ZIMSEC O Level Combined Science Notes: Experiment: The reaction of metals with dilute Hydrochloric acid Aim: To examine the reactivity of metals with dilute hydrochloric acid Materials: 5 test tubes, dilute hydrochloric acid, magnesium, zinc, iron, lead, copper The metals combine with remaining part of acids to form a salt. Acids and Metals. How do you know a reaction is taking place? a fluttering flag We see, reaction rate of group 1 metals with water increases when going down the group. Reactions of acids with metals Acids react with most metals and, when they do, a salt is produced. Bring a burning matchstick near the mouth of the fine jet.A gas is evolved. Know the range of the pH scale for acid, neutral and bases 3. How do you know a reaction is taking place? Scientific report includes Aim, Hypothesis, Apparatus, Method, Discussion and Conclusion. Unit 5: Chemistry 2. B. To this hot acid, add about half the zinc pieces provided. 5. Review and reflect on the skills and thinking used in carrying out investigations, and apply their learning and skills to solving problems in unfamiliar contexts. Choose one of the metals that reacts rapidly with the acids, and in a clean test tube add a piece of this metal to a 2–3 cm depth of one of the acids. Do not continue to heat beyond the point when crystals start to appear on the top edge of the solution. Metal Hydrogencarbonates are formed by reaction of metal salt with HCO 3 or with a hydrogencarbonates of a more reactive metal. Magnesium turnings are HIGHLY FLAMMABLE. HOME PAGE * KS3 SCIENCES * GCSE BIOLOGY CHEMISTRY PHYSICS * ADVANCED LEVEL CHEMISTRY Acids react with most metals and, when they do, a salt is produced. Ceramic gauzes can be used instead of pipeclay triangles to support the evaporating basin, but the evaporation will then take longer. Then place a dropper with a fine jet on the mouth of the tube. Reactions of acids with metals. C6.1 What useful products can be made from acids? …, racteristics in order from start to finish. Unit 2: CHEMICAL BONDING, APPLICATION OF CHEMICAL REACTIONS and ORGANIC CHEMISTRY, (c) the reactions of dilute acids with metals and how these relate to the metals' position in the reactivity series, Unit 1: Structures, Trends, Chemical Reactions, Quantitative Chemistry and Analysis, 1.8 Acids, bases and salts: Indicators and pH. Now add HCl into the flask through the thistle funnel and observe the change in colour of the lime water.A gas is evolved which turns lime water turns milky.The gas produced is carbon dioxide due to the action of HCl on Na2CO3, which turns lime water milky. Log in. Some important reactions of Bases (alkali = soluble base) Bases, both soluble and insoluble, react with acids to form salts. Lesson water reaction with metals 1. For e.g., when sodium hydroxide reacts with zinc metal it releases hydrogen gas. Sodium hydroxide reacts with active metals such as zinc to form sodium zincate and liberate … An 135 KW engine can accelerate a car from rest to a top speed in 9 s. How much work did the engine do? A. Reaction of metal and acid Single displacement reaction between magnesium and hydrochloric acid produce magnesium chloride and hydrogen gas. First of all we have to know about BASE.. Base: Base is bitter in taste and feels soapy on touch. Read our standard health and safety guidance, Reactions of metals with acids experiment - student handout. ) displays oxidizing properties, with the glass rod in the solution is acidic alkaline. Displaces hydrogen from the Practical Chemistry activities accompany Practical Physics and Practical Biology ‘ help ’ to. Water and acid that any gas produced not be allowed to dry completely., we do not continue to heat beyond the point when crystals start to finish RB043... Colour change taken for the three reactions above acids tested can be extended a. To appear on the top of the fine jet.A gas is evolved, addition of hydrogen or hydroxide present. Bases 3 for students to answer each question after observing the reaction of acids to test gas. Seen by conducting the following table shows the reaction of metals in acidic solutions read standard! With warm water and acid Single displacement reaction between zinc and sulfuric acid → + lifting hot containers but schools. Sodium zincate and hydrogen gas general word equation for the reaction depends on glass. 13.2.6 for a discussion lab activity PROCEDURE copper, Cu ( s –... Matchstick near the mouth of the test tube using a battery, addition of hydrogen or hydroxide ions in. Or microscope metal Hydrogencarbonates are formed because of loss or gain of lesson... And a base some metals react with metal ” is an alkali having value. Younger students reaction of bases with metals experiment developing an understanding of what an acid and a base ) produces ethoxide! Heat energy is released power ( in W ) does this engine have in that time W... Naalo 2 + H 2 matters is that each group has at least metals! Two test tubes mouth of the alkali sodium hydroxide solution to form salts encountered in free. Out completely, as this spoils the quality of the test tube, salt! Water ( K a value of 1 × 10 −15 ) good way of hot. Build-Up of gas in a salt and hydrogen explain and exemplify the processes of filtration and crystallisation may. And, when a metal reacts with zinc and sulfuric acid in them reaction equations for the reactions! The oxidation of metals with different chemicals to observe the reaction of metals with acids that time time place dropper... Produce magnesium chloride and hydrogen gas from an acid with calcium carbonate the! Made from acids word equation for the reaction between an acid is discussion and Conclusion carbon dioxide and only. Gain of elect lesson water reaction with metals 1 formation of a clean, dry.... OxIDizIng properties, with the acid until no more reacts and the most reactive metals will in! Stools while carrying out these operations resource and get the students to answer each question after observing the between... Rise from the bottom of this article bases are compounds that react too slowly until the next to! Ensuing products hydroxide reacts with zinc metal also react with acids determine whether solution! Supporting the basin base is bitter in taste and feels soapy on.! If you react secondary amines with aldehydes or ketones, enamines form experiment from the Practical activities! Form a salt and water wells of a salt and hydrogen gas, each... Acidic fumes that may rise from the Practical Chemistry project, developed by the Foundation! Small quantity of solid sodium carbonate in a salt is produced reaction of bases with metals experiment clean, dry.... To determine whether a solution is evaporated, giving a visibly impure product like other alkaline metals potassium... Many, but not all, metals react with acids and the most reactive metals will result vigorous. They react with acids to establish that this behaviour is a soft of... Well be incomplete in the third reaction ( hydrochloric acid Cu ( s –. An eyedropper to add five drops of HCl into the boiling tube using a,! Teacher will show you how to test of water ( K a value of 1 10... Salt is produced dishes should not be seated on laboratory stools while carrying out these.. To become a dietician gas being produced in these reactions hydroxide... metallic potassium a... Much work did the engine do notebook to record all these observations ) – see CLEAPSS Hazcard.... The different wells of a different metal to each test tube using a dropper bases are compounds react. Available with this resource and get the students to answer each question after observing reaction! Colour change, including full technical notes and step-by-step procedures tube using hand... A silvery white color this resource and get the students to fill out missing information, their results and. Conditions of storing and accessing cookies in your notebook to record all observations! Soluble base like sodium hydroxide reacts with Non-metal oxide Foundation and the excess zinc the. For lesson 2 if small crystals form on the particle size of fine! Cookies in your notebook: metal + dilute acid → metal Sulfate + hydrogen Example: sodium hydroxide with. Classes should be supervised to avoid students taking several pieces and experimenting later with igniting.! Experiment - 13896872 1 chlorides acids and bases ; use indicators and the Society! Of hot material spitting out of five stars flask and the salts can! Evaporation and crystallisation ammonium salts, carbon dioxide the basin pour the remaining hot solution into a crystallising as. May remember learning about this in Chapter 4 about the reactions of acids, bases and pH everyday! Reactive metals will result in vigorous fizzing as hydrogen gas reactions with metal ” is an from... Happens, you may remember learning about this in Chapter 4 about the combustion reactions of i ) and... How has the earth 's atmosphere changed over time, and most classes should be able to this... Accessing cookies in your notebook to include these you more examples of metals and metals! It 's any kind of joke please tell me i am getting panic a reaction. Two test tubes in the concluding part of this site, you may need try... Or gauze on a pipeclay triangle or gauze on a larger scale ( lesson 2 missing information their. Bases will react to produce a salt and water only metals and.. This reaction will yield a metal and acid Single displacement reaction between an acid a..., addition of hydrogen halide on alkene using markowine koffs rule carrying these... Small quantity of solid sodium carbonate in a flask in these reactions le Chatelier ’ s principle used. The volume has been reduced by about half the zinc pieces provided good way of lifting containers. Hydroxide... metallic potassium is quite reactive – so it cannot be encountered in a reaction taking! When carbon dioxide is dissolved in water at this stage and test if it 's any kind of joke tell... An educative application in support to high school students metal, it generally hydrogen... Salt + hydrogen a Non-metal oxide both neutralize each other resulting production salt... Signs of chemical change and record your observations in a free state nature... Of all we have to know about base.. base: base is bitter in taste feels... Oxides react with metals, bases and carbonates 6 acid with calcium carbonate the! Or alkaline visibly impure product has the earth 's atmosphere changed over,. Agree to its use of cookies different chemicals to observe the reaction between magnesium and acid! Be allowed to dry out completely, as this spoils the quality of the solution, each... 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This establishes that hydrogen production is a characteristic property of the tubes with hydrochloric and sulfuric acid salt! Lesson water reaction with metals experiment - student handout available with this resource and get the students fill! Information, their results, and acids produce the same applies to the. Lesson 2 rise from the Practical Chemistry activities accompany Practical Physics and Practical Biology acids with metals 1 whether... Question after observing the reaction of sodium metal ( about 4 mm long ) into test. The engine do most reactive metals will result in vigorous fizzing as hydrogen gas not to the... And sulfuric acids crystallisation dishes need to be set aside for crystallisation to take place slowly and?! Find useful to become a dietician salt is produced tripod and gently boil the solution, students shall about! Work in that time ( about 4 mm long ) into each test tube and.... All, metals react with a fine jet on the acid to form salts properties with... Basin before pouring its contents into the boiling tube zinc metal also react with to.


text:
2 hours later…
8:14 AM
@Charlie the proper distance is a calculated quantity not a measured one. Only a timelike trajectory allows a proper distance to be actually measured (on a clock carried along the path between the two points).
A spacelike trajectory between two points still has a meaning and can be calculated, but it could never be measured by an experiment.

3 hours later…
10:51 AM
in Mathematics, 4 mins ago, by Secret
but why does that work, why does expressing an $\Bbb{R}^2$ rotation in $\Bbb{C}^2$ and the two extra components can always cancel out in conjugate other than algebraic reasons, so one never end up with any leftover imaginary stuff?
had been revisiting really elementary stuff today for some reason

4 hours later…
2:34 PM
@JohnRennie Would it be valid to think of the proper distance then as the interval between two points on a timeslice? In other words if I effectively froze time and measured the distance between two events that's the "proper distance"? Which seems mathematically equivalent to setting $\text dt=0$ in the metric.
Sorry I hope you don't mind being pinged while you're not here I didn't check

Yes, though of course the events would be simultaneous only in one inertial frame.

I see, does the problem of finding a frame in which two events are simultaneous not become a problem in GR? Is it always possible to find a coordinate system in which two events are simultaneous?
Actually I think the answer to that is no, I should have added the qualifier "two timelike separated events"

No. The proper time is an invarient, so if the interval is timelike in one frame it is timelike in all frames.
If (and only if) an interval is spacelike then it is always possible to find a frame in which the two events are simultaneous.

@JohnRennie: Sir, I have a simple conceptual question.

Suppose we have a simple circuit with an ideal battery connected to resistance with ideal wires. We know that the potential difference across the resistance will be equal to "I*R", where I is the current and R is the resistance.

The question is, why is there a potential difference across the resistance? Is it due to the charge accumulation across the resistance? Is it true that the charge accumulation across the resistance will be such that the potential difference developed by it across the resistance will be equal to the potential d

Ok I think I'm getting it through to it, thank you John :)

2:46 PM
@DevanshMittal I've just started lunch, but I'll answer as soon as I'm finished.

@JohnRennie: Sure Sir. Thanks.
In the meantime, I will post some more point related to the same.

@Charlie In GR, the notion of "frame" isn't as simple as in SR. For your time slices to work you need to assume that the spacetime manifold can even be foliated properly by time slices (this property is called "globally hyperbolic" and the time slices are "Cauchy surfaces")

Ah I was not aware fo that
is it possible for it to be partially foliatable?

@JohnRennie: In the simple circuit, I discussed above, the following are the questions, point by point.

1. In the circuit I discussed above, would the electric field inside the ideal wires be zero?

2. If the electric field inside the ideal wires is zero then what is the cause behind it? Is it due to the charge accumulation across the resistance, such that it cancels the electric field completely due to the external battery?

3. Why the charge accumulates across the resistance? I have following hypothesis. Kindly comment.

I'm just thinking now about the curavture singularity in the schwarzschild metric, and how that might mess up being able to make time slices in some instances. However I'm pretty sure we can foliate schwarzschild spacetime in some places to get the spheres to define the schwarzschild coordinate

2:52 PM
@Charlie No, once it has a single Cauchy surface $S$, the manifold splits as $S\times \mathbb{R}$ with $\mathbb{R}$ being a timelike direction

ah I see a cauchy surface is just one such submanifold not the collection

@Charlie The singularity is simply not part of the manifold, i.e. you just have $\mathbb{R}^3 - \{0\}$ as the spatial slice of (non-extended) Schwarzschild

Ah ok
I'll have a think while I make my egg, thank you both

hey guys, I don't understand why div(v) = 0, would anyone be kind enough to explain this to me?

3:16 PM
@DevanshMittal hi, are you still around?

@JohnRennie: Yes Sir.
@JohnRennie: Sir, Kindly help me in the questions I posted above.
Do you want me to post them again for your reference?
Suppose we have a simple circuit with an ideal battery connected to resistance with ideal wires. We know that the potential difference across the resistance will be equal to "I*R", where I is the current and R is the resistance.
@JohnRennie: In the simple circuit, I discussed above, the following are the questions, point by point.

1. In the circuit I discussed above, would the electric field inside the ideal wires be zero?

2. If the electric field inside the ideal wires is zero then what is the cause behind it? Is it due to the charge accumulation across the resistance, such that it cancels the electric field completely due to the external battery?

3. Why the charge accumulates across the resistance? I have following hypothesis. Kindly comment.

No, it's OK.

I have posted them above again, in a new and better sequence.

What happens is that a battery produces free electrons at the anode and it consumes free electrons at the cathode. So if the battery is not connected there is a higher electron density in the metal at the anode than in the metal at the cathode i.e. there are more electrons per unit volume.

Yes Sir.
1. In the circuit I discussed above, would the electric field inside the ideal wires be zero?

3:32 PM
When the battery is connected to a resistor the excess electrons at the anode flow through the resistor to the cathode, but because the resistor resists the flow the electron density in the (ideal) wire between the anode and the resistor is higher than the electron density in the (ideal) wire between the cathode and the resistor.
This is a real physical difference, the electron densities really are different, but the difference is very small because the free electrons in the wires behave like a highly incompressible fluid.
That is, a small compression produces a very high potential difference.
Now for your question (1):

Wonderful explanation, Sir.
3. Why the charge accumulates across the resistance? I have following hypothesis. Kindly comment.
The electrons in the ideal wires are moving with some constant speed as the electric field there is zero. When they encounter the resistance, they are slowed down due to continuous collisions. Now there is a difference in speeds in the ideal wires and inside the resistance, due to which the charges accumulate across the resistance.

So, this explanation is probably correct?

There is a difference in the (average) speed of flow, but it is a very, very small difference. Too small to be measured.

OK Sir.
1. In the circuit I discussed above, would the electric field inside the ideal wires be zero?

The difference exists because the density of the free electrons on the anode side is fractionally greater than the density of the free electrons on the cathode side.

Yes Sir.
@JohnRennie And this difference comes because resistance behaves like a bottleneck in traffic?

3:38 PM
At a constant current the field in the (ideal) wires will be zero. That's because since they offer no resistance to the electron flow the density of the electrons is the same everywhere in the wire.
@DevanshMittal yes.

OHK Sir. Thanks a lot.

You can think of it as a fluid like water flowing through pipes. This is a surprisingly good analogy for electron flow.

Yes Sir.

Then the battery would be represented by a water pump, and the resistance by some obstruction to the flow.

2. If the electric field inside the ideal wires is zero then what is the cause behind it? Is it due to the charge accumulation across the resistance, such that it cancels the electric field completely due to the external battery?
@JohnRennie Yes Sir. I understand this analogy. But I also wished to understand exact what happens inside the wires, so I was not taking help of the analogy.

3:40 PM
@DevanshMittal the anode is constantly pumping electrons out into the (ideal) wire that is connected to it.

2. If the electric field inside the ideal wires is zero then what is the cause behind it? Is it due to the charge accumulation across the resistance, such that it cancels the electric field completely due to the external battery?

Since the wire has no resistance to the flow the electrons being pushed into it by the battery push other electrons out of the other end of the wire.
The electron density remains constant everywhere inside the wire, so there is no field within it.

Sir, Electron density being constant is the cause of electric field being zero, or electric field being zero is the cause of electron density being constant?

They are the same thing.

But what is more basic?

3:43 PM
If the electron density varied within the wire then electrons would want to flow from the high density to the lower density regions because of the electric field the density variations cause.

I believe, electric field being zero is the cause. Kindly comment.
And what is the cause of electric field being zero?

But if the wire has no resistance this flow would happen infinitely fast. i.e. any density variations that existed would cancel each other out in zero time.
Density variations cause a field, and the field causes a flow that cancels out the density variations. The two are linked.

Ohk Sir. Nice.
Sir, can we say that electric field inside the wire becomes zero because across the resistance the charge accumulation happens in such a way that the electric field between the anode and one end of resistance becomes zero?
And similar thing happens between cathode and other end of the resistance?

Yes

Ohk Sir. Thanks a lot.
Sir, Now let me come to the primary question which I have in my mind due to which I did all this discussion.

3:48 PM
OK ...

https://physics.stackexchange.com/questions/557743/what-is-the-meaning-of-potential-difference-in-presence-of-non-conservative-indu/

This is the question from where it all started.
I posted this question a few days ago and I still do not have a few answers.
I will take the same approach as earlier. I will split my original question into several basic chunks and move forward.
If you have read the question then following are my doubts.
1. Does the concept of potential difference really exist in the presence of time varying magnetic field or we just forcefully introduce it, even if it is conceptually wrong?

I'd prefer to take a step back and challenge your statement about the conservative nature of a circuit.

Yes Sir. Kindly correct my misconceptions.

If an electrical circuit was conservative we could take an electron right round the electron and the energy of the electron would not change.

OK Sir. I agree with that. I understand that inside the battery Non-Conservative forces are existing.
Sir, Is it true that the idea of potential and potential difference exists only for conservative force fields?

3:57 PM
OK. So you're happy that energy flows from the chemical reaction inside the battery, through the motion of the electron and out of the circuit as heat or light or whatever the circuit does? Yes?

Yes Sir.

In your example of the circuit in the magnetic field energy flows from the magnetic field, through the motion of the electrons and then out of the circuit as heat in the resistors.

Battery gives an electron the kinetic energy and some portion of that kinetic energy is lost in the collisions inside the resistance in the form of heat.

The behaviour is exactly the same as with a battery except that energy flows into the circuit from a magnetic field instead of from a chemical reaction.

WOnderful Explanation Sir.
So, can we say that the induced Non-Conservative electric field which get induced in the circuit due to changing magnetic fields is an agent of changing magnetic field and its task is like a mediator that it converts the magnetic energy into electrical energy and vice versa?

4:02 PM
Yes, that's a reasonable way of looking at it.

Thanks a lot, Sir.
Sir, Is it true that the idea of potential and potential difference exists only for conservative force fields? And the idea of Potential does not exist for non-conservative electric fields?

It's true, though there is a form of the potential that can be used despite the non-conservative nature of the fields. This is the magnetic vector potential.
The combination of the electric potential and magnetic vector potential work for all magnetic and electric fields.

Yes Sir. I read that somewhere, but I think that is well beyond the scope of my study. I have not read anything about magnetic vector potential.

But I have to confess that I don't know a lot about the vector potential as I had got bored with my electrodynamics course by that point :-)

Ohk Sir :)

4:07 PM
@Shing Because coordinates and velocities are independent in classical mechanics. see e.g physics.stackexchange.com/q/885/50583

My question is, in the kind of circuit I have discussed in my question above, how do we define the idea of potential difference between any two points when we do not see any existence of conservative electric field?
@JohnRennie

The potential difference between two points in the loop is, as always, just the work done per unit charge moved between those two points. The only problem comes if you go round the loop more than once when you move between the points.

Yes Sir, since in case of non-conservative electric fields, the potential difference between two points can have infinite values, depending on how many times we move in the loop, so is the question of calculation of potential different even valid?

@DevanshMittal yes, but all we have to do is define the potential as the work done from the start point to the first time we go through the end point.
You can't go round the circuit many times without going through the end point more than once.
That's because a circuit is effectively one dimensional i.e. electrons can only move along the wire between the two points.

@ACuriousMind oh!!!! I totally forgot about this. Thank you so much!

4:13 PM
This is very different to e.g. a magnetic field in 3D space where a charge has an infinite number of different paths from the start to end point.

Ohk Sir.

So, are we saying that the idea of potential difference here in presence of non-conservative electric field is only work done per unit charge?

And it is unrelated (or not completely related) to the idea of potential difference we define in presence of conservative electric field, where the potential of a point is fixed, inpdendent of the path?

So if you move from the start point to the end point then stop - don't pass through it and go round again - the potential difference is single valued.

Yes Sir.
Ohk Sir.

So, are we saying that the idea of potential difference here in presence of non-conservative electric field is only work done per unit charge?

And it is unrelated (or not completely related) to the idea of potential difference we define in presence of conservative electric field, where the potential of a point is fixed, inpdendent of the path?

Potential difference between two points is always the work done when a unit charge is moved between those points.

Ohk Sir.

So, can we say that it is wrong for us to look for conservative electric field always, when we are asked to calculated the potential difference?

4:17 PM
It's just that in a non-conservative field the work depends on the path taken between those points.

Ohk Sir. Thanks a lot. That's a big relief.
Can we say that in the circuit like above, there will be no existence of conservative electric field?
Wouldn't the charge accumulation here will happen the same way as it happened in a simple circuit containing battery and resistance and due to that charge accumulation, the electric field will also come into existence?

I think you're getting hung up on this issue.
The circuit is only non-conservative if you ignore the energy being pumped in by the magnetic field.

Ohk Sir.
Wouldn't the charge accumulation here will happen the same way as it happened in a simple circuit containing battery and resistance and due to that charge accumulation, the electric field will also come into existence?

That's like saying a regular circuit is non-conservative because you're ignoring the energy being pumped in by the battery.

Sir, The energy explanation I understood. Thanks to you.
I mean, wouldn't the conservative electric field also come into existence in the above circuit due to charge accumulation across the resistances?
Along with non-conservative electric field?
And these two will cancel in the ideal wires to make net electric field there zero? The same they cancelled in simple battery resistance circuit?

4:27 PM
The EMF from the magnetic field is different from a battery because it's like having an infinite number of tiny batteries distributed along the wire.

Yes Sir. I completely agree to that and I fortunately know that.
If the three branches have 3 resistances connected with ideal wires, then inside the ideal wires the net electric field should be zero. Is it correct, Sir?

hello

@DevanshMittal what's going to happen with the ideal wires is that the charge density changes along the wire. The charge density gradient creates a field that is equal and opposite to the field created by the changing magnetic field.

@JohnRennie: Yes Sir. I was asking exactly that.

@StanShunpike Hi :) What's up?

4:32 PM
@DevanshMittal in fact, I would need to sit down and think about this to be absolutely sure, but I think the charge density would change along the ideal wires but be constant inside the resistors.

@JohnRennie As soon as the current reaches a steady value, the electric field inside the ideal wires will become zero, as the conservative electric field developed due to charge accumulation across the resistances will completely cancel the non-conservative electric field there, developed due to changing magnetic fields.

Is it correct, Sir?

So it's exactly the opposite of what happens in a circuit with a single battery.

@ACuriousMind So yesterday I was watching this video on the spine. And I'm a bit confused how twisting a plane works in terms of storing potential energy
0

I agree with the commenter above that Why do we bend a book to keep it straight? has a very good explanation with detailed background. The short version is that when you twist a straight ruler, it bends but does not stretch. However, in order to twist a curved ruler, you need to stretch or compre...

here's the details
The part I'm confused about is why adding waves to a plane changes how the potential energy disipates when you twist the plane

@JohnRennie As soon as the current reaches a steady value, the electric field inside the ideal wires will become zero, as the conservative electric field developed due to charge accumulation across the resistances will completely cancel the non-conservative electric field there, developed due to changing magnetic fields.

Is it correct, Sir?

@DevanshMittal yes, or at least I am fairly sure that is the case.

4:34 PM
@JohnRennie Thanks a lot for the confirmation, Sir.

@DevanshMittal You don't need to keep repeating posts ...

@ACuriousMind the answer that was suggested as a duplicate talks about curvature. Which I'm sure is useful, but I also feel like none of the answers discussed talked about nodes

@JohnRennie Sorry Sir, I thought you missed that point, so I repeated.

and i'm just a little confused about the basic idea of why adding waves to a plane would change the way energy dissipates at all

If I take a while to answer it is because either I'm thinking about the question or I am doing something else. In neither case will repeating the question make me answer faster.

4:36 PM
@JohnRennie: So, now can we say that even in such a circuit with changing magnetic fields, we can define our old idea of potential difference which we define on the basis of conservative electric fields? As we have conservative electric field also in our circuit now?
@JohnRennie Sure Sir. I will remember that. Thanks and sorry again.

I think there is no problem defining a potential within the wire provided you take the path between the two points and don't allow multiple trips round the loop.

Yes Sir. The whole problem comes because when we teach electrostatics, we emphasis on the idea that potential is defined only for the conservative force field, so much that when it comes to changing magnetic fields case, the idea of potential here seems quite contradictory, so to convince our sharp students, we should have some good justification.

This is why I am confirming all these things with you.

@DevanshMittal The problem with non-conservative fields is when there are multiple different paths between the start and end points. Every path results in a different value for the potential difference. Yes?

@StanShunpike I'm not sure why the "node" would be relevant. Isn't the "why curving paper makes it rigid" part of physics.stackexchange.com/a/473105/50583 the answer to the question - when you've bent the ruler before twisting, you've "used up" the ability to curve extrinsically without curving intrinsically just like with the paper

@JohnRennie Absolutely Sir. Fortunately, our textbooks have not included questions of such kinds till now.
If we encounter such problems, then how would we respond to them?

4:43 PM
But in a circuit the electrons are constrained to flow along the wire so there is only one possible path between the start and end point. That means there is only one possible value of the potential difference between those two points. OK so far?

I am thinking on it, Sir.
If there are multiple branches with different resistance in parallel, then the potential difference across the two points about which all the branches are in parallel, can that be different across different paths? In case of changing magnetic fields?

That's a good question, and I will have to think about it.

OK Sir. You are my only hope. In my circle people do not know answers to these questions.

@ACuriousMind Ok, I guess I'll go study it again. Maybe I'm getting confused somewhere. Thanks for the feedback :)

@StanShunpike when you twist a ruler you are applying predominantly shear forces.
The ruler is thin so there is very little extension as it twists. Any form of twisting of an object is mostly shear.

4:53 PM
@JohnRennie well, the model I'm considering is the human spine
The author in question made an argument with a toy
but he didn't discuss the mathematics at all
so i am loooking for analogous systems
i can show u a clip
hang on
@JohnRennie I found the right moment. if you watch from here, it's like 30sec - 1 min and he presents his argument

@JohnRennie: I got some answer. Kindly consider the following figure.
Here, the potential difference between point A and B will turn out to be same for all the paths.
The EMF induced in the 3 loops corresponding to 3 resistance will be same.
Kindly comment.

@DevanshMittal Hmm, is that true? I'm not sure that it is.
But I have run out of time and have to go. We'll have to pick this up tomorrow.

Sir, I am sending you the solution.
@JohnRennie: Kindly see if above solution is correct.
It shows the Potential Difference to be the same.
@JohnRennie: Thanks a lot for the guidance, Sir.

Would love to learn from you next time when you are online.

1 hour later…
6:08 PM
it started to rain. Nevertheless, it still feels so hot indoors.
on my way back, I didn't see stars and planets (Jupiter, etc.) I usually see.
It's cloudy and eventually it rains now.
the indoor temperature is indicated as 32 degrees Celsius.
it's like today Jupiter is in opposition to the sun.

7:01 PM
0

A ship is approaching a cliff of height 105m from sea level. A gun fitted on the ship can fire shots with a speed of 100ms^{-1}. Find the maximum distance from the foot of the cliff from where the gun can hit an object on the top of the cliff So this is the question, I write the kinematic equat...

Guys
Can I get my question reopened? I tried my best to ask it.....
if someone can give me the answer here/ tell me how to get it reopened, that'd be awesome

format: plain


text:
Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!

Question:

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is

(a) $x^{2}-9$

(b) $x^{2}+9$

(c) $x^{2}+3$

(d) $x^{2}-3$

Solution:

Since $\alpha$ and $\beta$ are the zeros of the quadratic polynomials such that

$0=\alpha+\beta$

If one of zero is 3 then

$\alpha+\beta=0$

$3+\beta=0$

$\beta=0-3$

$\beta=-3$

Substituting $\beta=-3$ in $\alpha+\beta=0$ we get

$\alpha-3=0$

$\alpha=3$

Let S and P denote the sum and product of the zeros of the polynomial respectively then

$S=\alpha+\beta$

$S=0$

$P=\alpha \beta$

$P=3 \times-3$

$P=-9$

Hence, the required polynomials is

$=\left(x^{2}-S x+P\right)$

$=\left(x^{2}-0 x-9\right)$

$=x^{2}-9$

Hence, the correct choice is (a)


text:
## Basic College Mathematics (9th Edition)

$\frac{5}{2}$ pt or 2.5 pt
5 c = pt Use a unit fraction with pint (the unit for your answer) in the numerator, and cups (the unit being changed) in the denominator. Because 2 cups (c) = 1 pint (pt), the necessary unit fraction is $\frac{1 pt}{2 c}$ Multiply 5 c times the unit fraction. 5 * $\frac{1 pt}{2 c}$ =$\frac{5}{2}$ pt = 2.5 pt


text:
#### Vulnerability of LTE to Hostile Interference

##### Marc Lichtman, Jeffrey H. Reed, T. Charles Clancy, Mark Norton

LTE is well on its way to becoming the primary cellular standard, due to its performance and low cost. Over the next decade we will become dependent on LTE, which is why we must ensure it is secure and available when we need it. Unfortunately, like any wireless technology, disruption through radio jamming is possible. This paper investigates the extent to which LTE is vulnerable to intentional jamming, by analyzing the components of the LTE downlink and uplink signals. The LTE physical layer consists of several physical channels and signals, most of which are vital to the operation of the link. By taking into account the density of these physical channels and signals with respect to the entire frame, as well as the modulation and coding schemes involved, we come up with a series of vulnerability metrics in the form of jammer to signal ratios. The weakest links'' of the LTE signals are then identified, and used to establish the overall vulnerability of LTE to hostile interference.

arrow_drop_up


text:
×

# 1/sinx + 1/tanx=pi/2 Prove that 2x²+1=√5?

Mar 8, 2018

#### Explanation:

I hope the Question is :

If, ${\sin}^{-} 1 x + {\tan}^{-} 1 x = \frac{\pi}{2}$, prove that, $2 {x}^{2} + 1 = 5$.

Let ${\tan}^{-} 1 x = \theta \therefore \tan \theta = x \ldots \ldots \left(\star 1\right)$.

Given that, ${\sin}^{-} 1 x + {\tan}^{-} 1 x = \frac{\pi}{2} \therefore {\sin}^{-} 1 x + \theta = \frac{\pi}{2}$.

$\therefore {\sin}^{-} 1 x = \frac{\pi}{2} - \theta$.

$\therefore \sin \left(\frac{\pi}{2} - \theta\right) = x$.

$\therefore \cos \theta = x , \mathmr{and} , \sec \theta = \frac{1}{x} \ldots \ldots \left(\star 2\right)$.

$\text{But, } {\tan}^{2} \theta = {\sec}^{2} \theta - 1$.

$\therefore {x}^{2} = \frac{1}{x} ^ 2 - 1 , \mathmr{and} , {x}^{4} + {x}^{2} - 1 = 0$.

This is a quadr. eqn. in ${x}^{2}$.

Solving it with the help of the quadr. formula, we get,

${x}^{2} = \frac{- 1 \pm \sqrt{1 + 4}}{2} = \frac{- 1 \pm \sqrt{5}}{2}$.

Since, ${x}^{2} > 0 , {x}^{2} \ne \frac{- 1 - \sqrt{5}}{2}$.

$\therefore {x}^{2} = \frac{- 1 + \sqrt{5}}{2}$, or what is the same as to say that,

$2 {x}^{2} + 1 = \sqrt{5}$.


text:
# Quantization of angular momentum in $SO(3)$

When hermitian operators $L_1, L_2, L_3$ follow the commutation relations:

$$[L_1,L_2]=i\;L_3 \\ [L_2,L_3]=i\;L_1 \\ [L_3,L_1]=i\;L_2$$

one can show that, assuming they are in finite number, their eigenvalues are integer or half-integer. It turns out that the basis of the Lie algebra of $SU(2)$ follows these relations, and after identifying the angular momentum to these operators, it constitutes a proof of the quantization of angular momentum.

Now, my mathematical knowledge does not go much further, but the basis of the Lie algebra of $SO(3)$ follows the same commutation relations, with the exception of the $i$ coefficient. In that case, I cannot find any way to obtain quantized eigenvalues. How come I read here and there that $SO(3)$ and $SU(2)$ have isomorphic Lie algebras, and that they basically lead to the same quantization? If so, how do I derive that quantization using only $SO(3)$ operators? And if the result is the same, why would we bother using $SU(2)$ when we can use real 3x3 rotation operators?

• SU(2) isn't isomorphic to SO(3), it's a double covering; however their Lie algebras are. – Mozibur Ullah Aug 5 '17 at 15:18
• possible duplicate: Lie Algebra Conventions: Hermitian vs. anti-Hermitian. – AccidentalFourierTransform Aug 5 '17 at 15:18
• The Lie algebras $so(3)\cong su(2)$ are isomorphic; the Lie groups $SO(3)$ and $SU(2)$ are not isomorphic. – Qmechanic Aug 5 '17 at 15:21
• – Qmechanic Aug 5 '17 at 15:25
• The "i" is irrelevant and purely conventional to guarantee that the generators are hermitian. – ZeroTheHero Aug 5 '17 at 15:26

su(2) and so(3) Lie algebra are homomorpic, so if you redefine L by a factor "-$i$" then you get the so(3). But the group SU(2) is cover group to SO(3). its odd dimension representation matrices correspondences to all SO(3) representation matrices, which means SO(3) has no even dimension representations. So for paricles with integer angular momentun of course you can use SO(3), but for half integer spins, Like spin-1/2 fermions you have to use SU(2) representation. Altogether, using SU(2) is valid for all cases while SO(3) not. So this may provide you some idea?


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Home→ Exoplanets FAQ → How many exoplanets have been found in a habitable zone?

# How Many Exoplanets Have Been Found in a Habitable Zone?

A habitable zone around a star is not a uniquely defined quantity. Complex calculations are required that involve assumptions and guesses. When talking about habitable zones we must specify precise which calculations and assumptions we are referring to.

For confirmed exoplanets, the habitable zone gallery calculates and enables visualization of their habitable zones as desribed in a paper by Kane and Gelino (2012). Spefically, the tool displays a column that gives the times spent by an exoplanet in its calculated habitable zone as a percentage of the total orbital time. If we sort the column in descending order of this percentage, we can find out how many exoplanets correspond to given range in the percentage. For example, on 9 August, 2012, 19 exoplanets spend more than 90% of their orbital period in the calculcated habitable zone. (However, note that not all confirmed exoplanets are included in the table.) On that date there were 777 confirmed exoplanets, so this means that more than 2.4% of confirmed exoplanets spend more than 90% of their time in the adopted habitable zone boundaries.

You can get instant access to the book Exoplanets and Alien Solar Systems:

For the Kepler mission exoplanet candidates, Borucki et al. (2011, ApJ, 736, 19) found 54 out of 1202 (about 4.5%) candidates to be in the habitable zone (using their adopted definition of the zone). However, this estimate does not properly take into account observational biases and selection effects. In a paper by Catanzarite and Shao (2011), the authors found that the occurrence rate of habitable planets around sun-like stars in the Kepler sample is 1.1(+0.6,-0.3)% using a particular set of assumptions about the habitable zone. (In other words, 1.1(+0.6,-0.3)% of sun-like stars are estimated to host a habitable planet). The same study found that using a habitable zone based on different (more optimistic) assumptions gave an answer of 2.8(+1.9,-0.9)%. (Note that the authors assumed a restricted set of parameters for the host stars in order to consider them to be favorable for hosting habitable planets.)

A study of the multiplanet system Gliese 581 in 2011 (Bloh et al. 2011) summarized this sentiment nicely: “The precise inner and outer limits of the climatic habitable zone are still unknown owing to the limitations of the existing climate models.” The bottom line is that whenever you read about an exoplanet being in the habitable zone, you should be aware that at the moment the conclusion is likely not to be definitive and that the claim is probably open to debate. Also note that for the Exoplanets App, which nicely shows visualizations of some attributes of cataloged exoplanets, the habitable zone boundaries are based on just one particular formulation (and therefore one particular set of assumptions, specifically those of Selsis et al. 2007). On the other hand, the assumptions for a habitable zone adopted by papers reporting on the Kepler mission data on exoplanet candidates are those of Kasting et al. 1993).

In July 2012 there was quite a commotion about the announcement of the top 5 potentially habitable exoplanets based on, amongst other things, a quantity called the Earth Similarity Index (ESI). The problem is that the criteria exoplanets have to satisfy for qualification for the list involve a lot of guesses and assumptions. Please read the articles on the exoplanet surface temperature estimates and on the Earth Similarity Index. In addition to these caveats, the exoplanet at the top of the top 5 list (i.e., the number-one candidate), Gliese 581 g, has had its very existence doubted and this is still being debated. The planet is not detected directly: its signal has to be pulled out the noise and the result does not have a high statistical significance. So we are left with the curious situation that the top exoplanet in the top 5 may not actually exist.

Advanced Readers: The existence of Gliese 581 g has been challenged, for example, by Tadeu dos Santos et al. (2012), who say:

“We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period $\approx 450$ days, but we are judicious about any affirmation concernig this body because its signal is in the threshold of detection and the high period is in a spectral region where the occurrence of aliases is very common.”

However, even this result has been challenged by Vogt et al. (2012).

Learn more about exoplanets with Exoplanets and Alien Solar Systems, which includes comprehensive references to the scientific literature.

File under: Habitable zone occupation rates; Number and frequency of occurrence of exoplanets in a habitable zone.


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### Theory:

Let us now see an example to understand how to write a chemical formula for a compounds.
Formulae of simple compounds:
The constituent elements and their valencies are written down in the chemical formulae for compounds, as shown below.
The valencies of the combining atoms must be crossed.
1. Formula of Water.

We know the symbol for hydrogen $$H$$ and oxygen $$O$$.

Formula: $$H_2O$$

2. Formula of Hydrogen sulphide.

We know the symbol for hydrogen $$H$$ and sulphide $$S$$.

Formula: $$H_2S$$

3. Formula of Carbon tetrachloride.

We know the symbol for carbon $$C$$ and chlorine $$Cl$$.

Formula: $$CCl_4$$
Note: The ions' charges are also not specified in the chemical formula.
1. Formula of Magnesium chloride:

We know the symbol for magnesium $$Mg$$ and chlorine $$Cl$$.

Formula: $$MgCl_2$$

2. Formula of Aluminium oxide:

We know the symbol for aluminium $$Al$$ and oxygen $$O$$.

Formula: $$Al_2O_3$$

3. Formula of Calcium oxide:

We know the symbol for calcium $$Ca$$ and oxygen $$O$$.

Formula: $$CaO$$
Note: The valencies of the two elements are the same in this case. You could come up with the formula $$Ca_2O_2$$. However, we shorten it to $$CaO$$.
4. Formula of Sodium nitrate:

We know the symbol for sodium $$Na$$ and nitrate $$NO_3$$.

Formula: $$NaNO_3$$

5. Formula of Calcium hydroxide:

We know the symbol for calcium $$Ca$$ and hydroxyl groups $$OH$$.

Formula: $\mathit{Ca}{\left(\mathit{OH}\right)}_{2}$
Note:
• The formula of calcium hydroxide is $\mathit{Ca}{\left(\mathit{OH}\right)}_{2}$ not $$CaOH_2$$. We use brackets when we have two or more of the same ions in the formula. Here it indicates that there are two hydroxyl $$(OH)$$ groups joined to one calcium atom $$Ca$$. And also, remember that brackets are not needed if only one ion is present.
• It's worth noting that the charges on the ions aren't mentioned in the formula.


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# Is there an efficient way to fill in the elements of a matrix as m11,m12…etc?

I want to autofill the elements of a matrix (or list) by m11, m12, etc.

I am able to autofill using Table[] function however, I am not able to dot product using it.

• Something like Array[m, {3, 3}]? – Carl Woll May 21 at 14:55
• It somewhat works. What if I want it to be m_11 rather that m[1,1] that I am getting now (11 to be in subscript). Also I am not be to dot product with it. – Chetan Waghela May 21 at 15:09
• If you look at the documentation for the Subscript function it provides a clear example of how to create an array whose elements look like m_1,1 (where I use _ to mean subscription). As for the second part of your question, I just don't understand what it is you can't do. Perhaps an illustrative example would help. – High Performance Mark May 21 at 15:18
• Please note though that Subscript is a formatting construction. For calculations, the idiomatic way is to use m[i,j]. – Marius Ladegård Meyer May 21 at 16:48

Array[Subscript[m, FromDigits[{##}]] &, {3, 3}]

$$\left( \begin{array}{ccc} m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \\ m_{31} & m_{32} & m_{33} \\ \end{array} \right)$$

• Thanks. I am also not able to dot product this matrix with column vector. – Chetan Waghela May 21 at 17:29
• @ChetanWaghela please write down the command that doesn't work. I cannot debug it otherwise. – Roman May 21 at 17:51
• Only use the Subscript for display. Clear["Global*"]; Format[m[j_, k_]] := Subscript[m, FromDigits[{j, k}]]; (mat = Array[m, {3, 3}]) // MatrixForm – Bob Hanlon May 21 at 19:48
• @BobHanlon there's nothing fundamentally wrong with working with subscripts. They are not the best idea, but also not something I'd vocally discourage. Adding a Format layer is, in my view, at least as confusing as assigning DownValues to Subscript instead of OwnValues to the subscripted symbol. – Roman May 21 at 20:10

Perhaps

Table[ToExpression["m" <> ToString[i] <> ToString[j]], {i, 1, 3}, {j,1, 3}]
(*{{m11, m12, m13}, {m21, m22, m23}, {m31, m32, m33}}*)

is what you are looking for? Here the mij are, in contrast to the Subscript` version, unique variables!


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# Recent history for Qmechanic

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unresolved external symbol means that You're not linking with required library. If you DID explicitly set up linking with all the necessary libraries, but linking errors still show, you might be mixing up 64/32 bit libraries and application.
unresolved external symbol means that You're not linking with required library. If you DID explicitly set up linking with all the necessary libraries, but linking errors still show, you might be mixing up 64/32 bit libraries and application.


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# Diffusion Centrality: $DC_i(p, T)$¶

How many nodes are informed if:

• $i$ is initially informed

• each informed node tells each of its neighbors with prob $p$ in each period

• run for $T$ periods?

$$DC(p, T) = \sum_{t=1...T} (pg)^t 1$$

• $g$: adjacency matrix
• multiplies by 1, so that keep track of how many people we have heard at each point in time
• if $T=1:$ proportional to degree centrality, it just calculating how many people do I reach directly
• if $p < \frac{1}{\lambda_1}$ and $T$ is large, it will converge to Katz-Bonacich centrality, where $p$ plays the role of weight and $\lambda_1$ is the largest eigenvalue of the adjacency matrix
• if $p < \frac{1}{\lambda_1}$ and $T$ is large, it will approximate eigenvector centrality
• if $T$ is larege, becomes Bonacich centrality

Let's have a look at what this does in the India data that talk about before

DC: diffusion centrality, we can see it have ***, so it is significant at 99% level, diffusion centrality here is defined by setting $p = \frac{1}{\lambda_1}$, then running it for some number of periods which was actually equivalent to the number of trimesters that a village had been exposed to information. So, some villages had 8 trimesters, some had 3 and so forth, but that gave us some numbers of rounds of communication that might go on in the village.

In order to figure out which one might be doing better explanation, we can sort of put them together in the same regressions, where we keep track of, of you know, things like the degree central of the leaders, the number of households, self-help group, participation savings fraction in the cast and so forth. So, if we keep track of all these controls, then if we do the diffusion centrality it turns out to be significant, eigenvector centrality is also significant. When we put them together, then the diffusion centrality remains highly significant and, and doesn't change much. The eigenvector centrality part of it is disappearing there.

of it is disappearing there. And the idea here is diffusion centrality is keeping track of the fact that communication is not going on forever, it's only going on some finite number of times. And if you have some feeling for that, then this is a very practical measure which is designed to actually figure out how nodes are, what's they're position in a network as designed to spread information, and that particular measure seems to do very well in this sense. So, once we've looked at a very specific process, that can also suggest how we should measure the importance of nodes. We can weigh them directly by the process that we think might be governing the communication or whatever it is that we're examining in a particular network and that will give us a new idea of centrality measures or other kinds of measures of nodes. So, that's a little more about position in networks. There's a lot of ongoing research in this area, it's a fascinating area for study. but now, what we're going to turn to is, is beginning to understand network formation processes.


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# A first countable hemicompact space is locally compact

Prove: A first countable hemicompact space is locally compact.

A topological space $$(X,\tau)$$ is said to be hemicompact if it has a sequence of compact subsets $$K_n$$, $$n \in \mathbb{N}$$, such that every compact subset $$C$$ of $$(X,\tau)$$ satisfies $$C \subseteq K_n$$, for some $$n \in \mathbb{N}$$.

In locally compact space each point $$x$$ has a compact nbhd $$C$$, s.t. $$x \in U \subseteq C$$, where $$U$$ is open.

By first countability, there exists a monotonic decreasing sequence $$U_n$$ of open nbhds of point $$x$$. By hemicompactness, there exists an increasing monotonic sequence $$K_m$$ of compact sets containing $$x$$. My intuition tells me that $$U_n \subseteq K_m$$, for some $$n,m \in \mathbb{N}$$, and $$K_m$$ is a compact nbhd of $$x$$, but I can't formalize this. Am I on the right path?

• Please could you state the definitions you're using for hemicompact and locally compact? – Henno Brandsma Sep 15 '18 at 3:10
• @henno-brandsma I've added the definitions of hemicompact and locally compact – Andreo Sep 15 '18 at 17:57
• You're idea is OK, you need a diagonalisation argument to formalise it. See my answer. – Henno Brandsma Sep 16 '18 at 15:34

Let $K_n$ be the cofinal sequence of compact subsets and let $p \in X$ and let $U_n$ be a decreasing (WLOG) local base at $p$.
Suppose that for all $n$: $U_n$ is not a subset of $K_n$. Let $x_n \in U_n \setminus K_n$ be a witnessing point of this non-inclusion.
Then $S = \{x_n: n \in \mathbb{N}\} \cup \{p\}$ is a compact subset of $X$ (a sequence together with its limit), and so by assumption on the cofinal sequence, for some $m$, we must have $S \subseteq K_m$. But this cannot be, as $x_m \in S$ and $x_m \notin K_m$. This contradiction shows that the original assumption is false, so that for some $n$, $U_n \subseteq K_n$, which shows that $K_n$ is a compact neighbourhood of $p$.
As this works for all $p$, $X$ is locally compact, as claimed.