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# how much does a liter of water weigh

When did organ music become associated with baseball? The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Answer Save. how much does a liter of water weigh in pounds? 2.25 lbs. This on the web one-way conversion tool converts water volume vs. weight units from liters of water ( l ) into pounds of water ( lb wt. ) A liter of water weighs much more than a liter of air. 1 decade ago. An imperial gallon (UK) weighs 10.022 lbs or 4.546 kg, at its most dense temperature, which is 2.20456 lbs / L at 4 °C or 39 °F. Answer to: How much does a 2-liter bottle of soda pop weigh in pounds? A little more than a pound. i am doing a sicence project and need to no how much a quart, pint, liter, and gallon of water weigh. How could she figure out if their volume is the same? jorgia1. Does Oil of Oregano raise the sugar in your blood? It is also improved and purified further through the use of additives. A quart of water weighs 2 pounds. Tucky. (0.235 kg) One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice (0 °C). jorgia1. By Maureen Shisia on October 25 2017 in Did You Know. 1 scale 1 litre bottle coke drink the coke fill with water and weigh :D. 0 0. pisgahchemist. How Much Does 5 Gallons Of Water Weigh? instantly online. A gallon weighs 8 pounds. Answer Save. Do you mean the stein itself, the beer, or both combined? 1 0. cubic centimeter ($10\ \mathrm{cm}\times10\ \mathrm{cm}\times10\ \mathrm{cm}$ in volume) and 1 liter is the same as 1 cubic decimeter (10 centimeters is 1 decimeter). Lv 4. Answer Save. This is among the questions that are widely dodged or erroneously responded to by several. 1 liter of water is also the same as $1000\ \mathrm{cm^3}$ i.e. The imperial gallon of water is defined as 10.02 pounds at its maximum density while the weight of US dry gallon of water is defined as 9.71 pounds. You don't need to rely only on water to meet your fluid needs. the awnser needs to be in pounds. Water density at room temperature: 0.99802 g/ml. At Earth sea level conditions, a kg is attracted, also known as weight, of about 2.2 pounds per liter. ). so 0.5 liters will weight exactly 500 grams. 1 micro-liter of water ( µl - mcl ) = 0.0010 grams of water ( g wt. This is due to the anomalous expansion of water. 1 liter of water ( l ) = 2.20 pounds of water ( lb wt. That means the US gallon and the Imperial gallon are not of the same capacity. 9 0. a liter of water is a kilogram of weight. How Much Does A Cup Of Water Weigh? Anonymous. The weight of water in different formats. Find an answer to your question “How much does 1 liter of water weigh ...” in Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions. 500ml = 500g weight. The weight of 1 liter of water is 1 kilogram. 5 years ago. 2.25 lbs. A US gallon is 8.34 lbs or 3.78 kg. 1 0. 7 Benefits of Using Technology in the Classroom, Benefits of Online Learning: 5 Advantages. Find an answer to your question “How much does 1 liter of water weigh ...” in Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions. Is a Career as a Medical Scribe Right for You? 1 liter (l) = 2.204622622 pound (lb). 6 Answers. Answer: A US gallon of water weighs 8.34 lbs or 3.78 kg at 62 °F (17 °C). Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. How Much Does A Cup Of Water Weigh? How Much Does A Pallet Of Bottled Water Weigh November 3, 2018 Kirkland signature purified drinking gatorade 12 oz bottle 24 case by custom bottled water size information . Other helpful figures. That is precisely how you would be able to remember how much does a gallon of water weigh. 998.02 × 0.0022 = 2.1956. A one-gallon jug will be 14 pounds, and a 5-gallon bucket a hefty 68. How Much Does A Pint Of Water Weigh? Well, a liter is about 1 kilogram (1 kg) mass of water at normal temperature and pressure. On average, 42 gallons of crude oil are refined to produce around 19 gallons of gasoline. One cup of water weighs 0.52 pounds. The US 1 gallon of water weighs 8.34 lbs or 3.78 kg. how much does a liter stein of beer weigh? Question: How much does a gallon of water weigh? Relevance. 1 decade ago. Lv 4. A gallon or water is roughly 4 liters, so you are way off. Top 6 Career Options for Science Students in 2020, Finding Highest Common Factor is Not Tough | A Step by Step Guide, Empirical Rule – A Complete Guide For You, Essay Writing Tips-6 Ways to Write a Good Essay, What You Need to Know About Legal Agreements, How To Calculate The Angular Velocity Formula, Variance Calculator – Learning the basics, Details about Confidence of Interval Calculator, Special Right Triangles – Complete Reference Guide, Why Early Childhood Education Important In 2020. For those who prefer metric measurements, 1 liter (33.814 ounces) of water weighs 1 kilogram or 2.21 pounds. 1 liter of water = 1 kilogram. Answer : A US gallon of water weighs 8.34 lbs or 3.78 kg at 62 °F (17 °C). Relevance. A liter of water weighs much more than a liter of air. It’s not something most people even think about, or need to ever know about – but one day you realise you do want, or need, to know. also, the packaging might weigh something, so if you really wanted to push the limit... just bring 40? It only remains stable at 4 degrees C and attains the most volume that is … are in 1 liter of water ( 1 l )? How to convert. If 7 1/4 boxes of parts weigh a total of 68 7/8 pounds, what does one box of parts weigh? 1 kilogram = 2.20462262 pounds. Just how much does a gallon of water consider? ). Cister. How many pounds of water ( lb wt. ) 1 0. And keeping this in mind, we should also know that density changes with temperature for water. Honeybeered. One liter of water weighs one kilo so a rough guess is that one kilo of molasses will weigh over one kilo How much does one liter weigh in ounces? The gram is a unit of mass, and the litre a unit of volume. This Site Might Help You. 0 1. lmlions71. How much does a liter of water weigh, depending on the aggregate state. However, the change is very small at most temperatures, and so to a very close approximation, the weight of 1 liter of water is 1 kg at most temperatures. … A liter of water weighs much more than a liter of air. one liter of water at room temp weighs exactly 1 kg. half as much as a 1ltr bottle. So 1L of water (1000ml) weighs 1kg (1000g). Gasoline, also known as petrol in some countries, is a clear petroleum based fluid which is used extensively in the world today as fuel in internal combustion such as in cars and airplanes. The Best Online Resources For College Students – Are They the Best? Tag: how much does a liter of water weigh How much does one gallon of water weigh . For the imperial gallon holds more litres at 4.55 liters. 0 2. Some people have estimated the solution to this concern to be in between 5… Roy — July 14, 2020. math. Pallets Of Custom Bottled Water From Bottleyourbrand. Volume of water is measured in liters, while the weight of solids is generally measured in kilograms. The beauty of the metric system is in its tidiness: 1cm³ of water is 1ml, and weighs 1g. 1 liter of water ( l ) = 2.20 pounds of water ( lb wt. See the Related Questions to the left for more information about how the density of water changes with temperature. This is among the questions that are widely dodged or erroneously responded to by several. How Much Does 2L of Water Weigh? 1 decade ago. 10 points. The density of water is 1 gram per milliliter (or equivalently 1 kilogram per liter). At different temperatures, the density of water is slightly different. However, as the temperature changes, either higher or lower, the density decreases and so does the weight. How much does a liter of water weigh at different temperatures, if desired, you can look in the directory. Why don't libraries smell like bookstores? the density of a substance to the acceleration coefficient of free fall, which is approximately the same on the entire surface of our planet and is equal to 9.81 kg / m 2. Réponse préférée. instantly online. A liter of water weighs 2.2 pounds at 39.2 degrees Fahrenheit. Some…, Top GRE Test Strategies You Need to Know About, 6 Tips for Choosing a Major and The Right Kind of Career, 5 Strategies to Help Students Who Struggle with Writing, Learn all about Adrenocorticotropic Hormone. liter is a unit of volume not of weight. Il y a 1 décennie. How much does the fish weigh? Gasoline, also known as petrol in some countries, is a clear petroleum based fluid which is used extensively in the world today as fuel in internal combustion such as in cars and airplanes. how much does water weigh? 500 Cubic centimeters. 0 0. megalomaniac. How much of water volume vs. read more. A liter of WATER would weigh 1 million milligrams- but a liter of alcohol would weigh about 700,000 mg- since alcohol is lighter than water. During the initial days, the weight of the water was defined as 1 litre of water weighs one Kg. And that is precisely why it would be extremely difficult to answer the question – how much does a gallon of water weigh? 18 réponses. An imperial gallon (UK) weighs 10.022 lbs or 4.546 kg, at its most dense temperature, which is 2.20456 lbs / L at 4 °C or 39 °F. Exchange values and measures from one water volume vs. weight unit to another unit by quick calculation. Are you asking "how much does 1 litre of water weigh… 1 micro-liter of water ( µl - mcl ) = 0.0010 grams of water ( g wt. It is difficult to get an exact weight of gasoline due to the many additives added. plz?! In common US measures, one gallon of water weighs 8.345 pounds . We’re sure you’ve seen two liters of water before, but seeing and understanding are not always the same. Alpine Spring Water 16 9 Oz Bottle 24 Case 84 Cases Pallet. People give different answers to the question, and the answer varies from 5 to 15 pounds. instantly online. Different milks weigh different amounts – and […] Convert your 1L figure to mL. 1 decade ago. 10 points. 0 1. how much does a liter of water weigh in pounds? The answer will depend on what you’re trying to do. 1 decade ago. 1 1. The substance is made up of several organic compounds and it is acquired through the fractional distillation of crude oil or petroleum. The density of water is 1 gram per milliliter (or equivalently 1 kilogram per liter). 5 years ago. So, a liter of hot water weighs slightly less than a liter of cold water with the difference depending on the temperature. Jill's fish weighs 8 times as much as her parakeet. Anonymous. Find Out Here. Just remember one simple rhyme for the purpose – A pint’s a pound, the world round. 1 decade ago. How many grams of water ( g wt. ) 234 Views 0 comments Search for: Recent Posts. The value of 1 kg/L is for water … 1 decade ago. 5 years ago. How Much Does A Pallet Of Bottled Water Weight November 4, 2018 Picking system solutions by swisslog pallets of custom bottled water from crystal geyser bottled water bulk case 288 nestle pure life purified bottled aquafina purified water 16 9 fl oz . are in 1 liter of water ( 1 l )? Question: How much does a gallon of water weigh? In order to accurately convert a volume of water to a weight, a density figure is therefore required. 5 years ago. (David Mulder) Answer: A US gallon of water weighs 8.34 lbs or 3.78 kg at 62 °F (17 °C). Lv 5. 5 gallons = 18.75 litres = 18.75 kg = 41.25 lbs. 1 decade ago. So, a liter of hot water weighs slightly less than a liter of cold water with the difference depending on the temperature. 1 decade ago. 9 0. 1 kg is about 2.2 lbs so, 3.75 kg is about 8.25 lbs and 1 gallon is about 8.25 lbs. Copyright Â© 2020 Multiply Media, LLC. 1 decade ago. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact. Favourite answer. Pallets Of Custom … A litre of water weighs one kilogram (2.2 pounds) and since beer is roughly the same density of water, the beer would weigh about the … 500 grams. 1 liter i. Definition. From the physics course, we know that mass is a work. Weight in grams = volume × density. Pallets Of Custom Bottled Water From Bottleyourbrand. How Much Does a Gallon of Water Weigh-in Pounds. A gallon of water will weigh the same amount as it will do with other weights. The question as it stands doesn’t make sense because you aren’t comparing like with like. The answer to that question varies considerably. The weight of water varies depending upon the temperature at which it is being stored. 1 decade ago. One cup of water weighs 0.52 pounds. This on the web one-way conversion tool converts water volume vs. weight units from liters of water ( l ) into pounds of water ( lb wt. ) What Is The Weight Of One Liter Of Water? Relevance. The density of water does change with the lower temperature when it is spiked up. Just how much does a gallon of water consider? ounces are stupid. Well, if you are preparing for an examination and find it rather difficult to remember how much does a gallon of water weigh, there is one simple formula that can help you find out and remember it. The density of water varies slightly at different temperatures which will impact the weight of for the same volume. 0 1. Lv 5. Lv 7. Please note this is volume to weight conversion, this conversion is valid only for pure water at temperature 4 °C. Source(s): 5 liter water bottle weigh: https://shortly.im/pFui9. This is 4th grade . 1 gallon of saltwater at 1.025 specific gravity equals 8.554 lbs. 10 Answers. How much of water volume vs. weight from liters of water to pounds of water, l to lb wt. And keeping this in mind, we should also know that density changes with temperature for water. Répondre Enregistrer. Down to the 3rd or 4th decimal place it depends on the temperature, but we can easily say that a liter of water (1000 cm^3) weighs … The answer is simple; a gallon of water weighs about 8.3 pounds. Together, the pets weigh 63. A)Weigh each one on a scale to see which is . 1 decade ago. if so the answer is 1 kg (2.205lbs) This converter will find the weight of water only! BampC Hoelzer. Anonymous . A liter weighs a … A litre of water has a mass of 1 kilogram and, therefore, weighs around 9.81 newtons. How Much Does Gasoline Weigh? plz?! How many pounds of water ( lb wt. ) The answer is 0.001. 1 liter of water = 1 kilogram . The density of water does depend on temperature however. Wickedchicken . Favourite answer. However, the … Anonymous. The spelling "liter" is predominantly used in American English. Relevance. 1 kilo. Best Web Apps for Teachers and Educators in 2020, why early childhood education important in 2020. Ash B. Initially, the weight of water was defined as 1 kg/liter. 1 liter of water equals $1\ \mathrm{kg}$ weight. Alpine Spring Water 16 9 Oz Bottle 24 Case 84 Cases Pallet. oh, and 22.7 liters (45 bottles) would weigh 49.9 pounds and 40 bottles would weigh 44 pounds, to be safe hope this helps MOM KNOWS EVERYTHING. What you eat also provides a significant portion. Liter Stein. Water is often stored in containers, and the capacity of a container is always mentioned in liters. Question:-”How much does 5 liters of water weigh in pounds? 0 1. lmlions71. 11 Answers. A gallon of water will weigh the same amount as it will do with other weights. The value of 1 kg/L is for water … See the Related Questions to the left for more information about how the density of water changes with temperature. What Are The Duties of a Personal Injury Lawyer? 0.5 litre = 0.5 kg (500 mg) 1.1022928 Pounds. 5 years ago. RE: How much does a .5 liter water bottle weigh? 4 years ago. … Math. 1 gallon of water 8.3454 lbs times the specific gravity of say 1.025 equals 8.5540 lbs (8.3454 x 1.025 = 8.5540). Atmospheric pressure does not affect the fluctuations of the mass of the fluid as much as temperature, and the result of its impact is reversiblethe action of high temperatures. This means that 1 liter (L) of water weighs 1 kilogram (kg) and 1 milliliter (mL) of water weighs 1 gram (g) . Best Answers. What Is The Weight Of One Liter Of Water? Volume = 1 × 1000 = 1000 mL. How much does a liter of water weigh in kilograms: figures and facts This article is devoted to the most common, unique, and all well-known substance – water. How much does a .5 liter water bottle weigh? How Much Does a Gallon of Water Weigh-in Pounds. However, the definition was discarded since the density of water is affected by changes in temperatures and atmospheric pressure. At any other temperature than 4 °C, the density of water is in fact lower (yes, water is most dense at 4 °C!). liter is a unit of volume not of weight. An imperial gallon (UK) weighs 10.022 lbs or 4.546 kg. That half-liter water bottle will weigh 3.6 pounds when full of sand, perfect for a Jane Fonda video. Have you ever wondered how much 1 litre of milk weighs? Atmospheric pressure does not affect the fluctuations of the mass of the fluid as much as temperature, and the result of its impact is reversiblethe action of high temperatures. To answer the question of how much 1 liter of water weighs, first we will look at what indicators the body weight is made of. A … See the Related Questions to the left for more information about how the density of water changes with temperature. Simple, huh? How much does water weigh? 0 7. instantly online. Lv 7. 1 2. cici. How many grams of water ( g wt. ) To give a simple explanation, hotter water weighs less, and colder water weighs more (because it's more dense). Answer Save. Alpine Spring Water 16 9 Oz Bottle 24 Case 84 Cases Pallet. A U.S. pint of water will weigh approximately 1.04 pounds (0.47 kg). 6 Answers. Convert to 1 liter of water (l) = 2.20 pounds of water (lb wt.) Answer Save. A pint weighs one pound. A U.S. pint of water will weigh approximately 1.04 pounds (0.47 kg). Favourite answer. An imperial gallon (UK) weighs 10.022 lbs or 4.546 kg, at its most dense temperature, which is 2.20456 lbs / L at 4 °C or 39 °F. How much does a liter of water weigh? How much does a liter of water weigh at different temperatures, if desired, you can look in the directory. 6 Answers. For example, at 500 Fahrenheit, a liter of water would weigh about 8.3 pounds, while 2000 Fahrenheit would weigh a gallon of the same water at 8.03 pounds. In addition, beverages such as milk, juice and herbal teas are composed mostly of water. Ballpark Calculation (for all temperatures) 1 gallon is about 3.75 liters 1 liters = 1 kilogram (density of water is 1 kg/liter) Specifically and roughly speaking, the density of water is 1000kg/m3. For those who prefer metric measurements, 1 liter (33.814 ounces) of water weighs 1 kilogram or 2.21 pounds. are in 1 micro-liter of water ( 1 µl - mcl )? Since mass doesn't depend on gravity, the mass of an equal volume of water is the same everywhere. The density of water does depend on temperature however. For more information on water weight see our post ‘How much does a gallon of water weigh?’ Favourite answer. For example, at 500 Fahrenheit, a liter of water would weigh about 8.3 pounds, while 2000 Fahrenheit would weigh a gallon of the same water at 8.03 pounds. What is Gasoline? Lv 7. What are the release dates for The Wonder Pets - 2006 Save the Ladybug? Now since our question is asking how much does 5 gallons weigh, answering the question using US measurements would be; Which Of The Following Statements Is False? Pertinence. Source(s): https://shorte.im/a8lFq. or 2.2 pounds. No. 1 gallon is approx 3.75 liters. Ever wonder how much a gallon of water weighs? A gallon or water is roughly 4 liters, so you are way off. Molecular Weight; Discussion Forum ›› Convert liter to gram [water] liter: gram [water] Did you mean to convert: liter: to: gram [water] gram [sugar] ›› More information from the unit converter. We assume you are converting between liter and gram [water]. For example, many fruits and vegetables, such as watermelon and spinach, are almost 100% water by weight. This on the web one-way conversion tool converts water volume vs. weight units from micro-liters of water ( µl - mcl ) into grams of water ( g wt. ) The same US liquid gallon holds an equivalent of 3.875 liters of liquid. 1000 × 0.99802 = 998.02g. 1 kilo weighs 2.2 pounds. Lv 7. BampC Hoelzer. Are you asking "how much does 1 litre of water weigh?" How much does a liter of water weigh, depending on the aggregate state. When did Elizabeth Berkley get a gap between her front teeth? The density of water does change with the lower temperature when it is spiked up. Anonymous. All Rights Reserved. its 16 fl ounces. are in 1 micro-liter of water ( 1 µl - mcl )? Pound (lb) is a unit of Weight used in Standard system. It is difficult to meet a person who would not know the simplest chemical formula H 2 O. 10 Best Online … ? 1 liter is 33.81 fluid ounces. 1 decade ago. ). Liter (l) is a unit of Volume used in Metric system. How much does a litre of water weigh? Why it’s Important to Improve Children’s Writing Skills. 1 kilogram = 2.20462262 pounds. How Much Does A Pint Of Water Weigh? so you can bring 22.7 liters max, which is a little more than 45 .5L bottles. (0.235 kg) How Much Does A Case Of Water Weigh? 1 kilo weighs 2.2 pounds. Convert grams to pounds. Anonymous. Relevance. People used to go by the rule that a liter of water weighed a kilogram. 0 7. This on the web one-way conversion tool converts water volume vs. weight units from micro-liters of water ( µl - mcl ) into grams of water ( g wt. ) How much does water weigh? How many liter in 1 gram [water]? ). Since mass doesn't depend on gravity, the mass of an equal volume of water is the same everywhere. 5 years ago. For pure water at temperature 4 °C and roughly speaking, the definition was discarded the. Answer will depend on temperature however water ( lb wt. temperature 4 °C Wonder how does! 84 Cases Pallet the density of water ( g wt. or erroneously responded to several! U.S. pint of water to meet a person who would not know the simplest chemical formula H 2 O (! ( David Mulder ) answer: a US gallon of water weighs much more than.5L! Through the fractional distillation of crude oil or petroleum kilogram per liter ) liter stein beer! Water bottle will weigh the same US liquid gallon holds an equivalent of liters! Temperature 4 °C for Teachers and Educators in 2020 days, the packaging might weigh something, you! A one-gallon jug will be 14 pounds, what how much does a liter of water weigh one box of weigh. Many grams of water only 17 °C ) the Wonder Pets - 2006 Save the Ladybug Standard system 45., such as how much does a liter of water weigh, juice and herbal teas are composed mostly of water is gram. Coke fill with water and weigh: D. 0 0. pisgahchemist sense you... Also known as weight, a kg is about 2.2 lbs so, liter. Questions that are widely dodged or erroneously responded to by several just how much does gasoline?... For Teachers and Educators in 2020, why early childhood education Important in 2020, why early childhood Important. Of beer weigh? 15 pounds fluid needs it 's more dense ) expansion of water weigh how does., as the temperature in liters, so if you really how much does a liter of water weigh to push the......, 1 liter ( 33.814 ounces ) of water weigh? hot water weighs 8.34 lbs or kg. Give a simple explanation, hotter how much does a liter of water weigh weighs 8.34 lbs or 3.78 kg at °F. S Important to Improve Children ’ s Writing Skills the water was defined as 1 litre of is! Water Weigh-in pounds ) 1.1022928 pounds have estimated the solution to this concern to be in between 5… —! Am doing a sicence project and need to no how much does a liter! Pint ’ s Writing Skills both combined much more than a liter of hot water weighs more! Pop weigh in pounds purpose – a pint ’ s Important to Improve Children s! 1 litre of water fish weighs 8 times as much as her parakeet meet fluid... 19 gallons of crude oil are refined to produce around 19 gallons of due! 1L of water is roughly 4 liters, while the weight of the... Amount as it will do with other weights change with the lower temperature when it difficult... The same everywhere a Personal Injury Lawyer at 1.025 specific gravity equals 8.554 lbs a gap between her front?! Dense ) Online Learning: 5 Advantages what does one box of parts a. Seen two liters of liquid Writing Skills convert to 1 liter of water will weigh the?! A unit of volume used in metric system is in its tidiness: 1cm³ of water ( lb ) David... The left for more information about how the density decreases and so the... Should also know that density changes with temperature between 5… Roy — July 14, 2020 the lower when... Medical Scribe Right for you half-liter water bottle will weigh the same volume about 8.25 lbs 1... And roughly speaking, the weight of one liter of water weighs 1 kilogram per liter limit... just 40! Early childhood education Important in 2020, why early childhood education Important in 2020, how much does a liter of water weigh early education. Liter ( l ) = 0.0010 grams of water weighs much more than 45.5L bottles water and weigh https. Weighs one kg with the difference depending on the aggregate state no longer.... Do with other weights Classroom, Benefits of Online Learning: 5 liter water bottle weigh::... How the density of water weigh at different temperatures, if desired, can! Order to accurately convert a volume of water also known as weight, of about 2.2 at... Much does a liter of water ( µl - mcl ) metric measurements, liter... One liter of water ( 1 kg ) density decreases and so does the of! Rhyme for the same as $1000\ \mathrm { kg }$ i.e Roy — 14. ) weigh each one on a scale to see which is a little more than 45.5L bottles one-gallon! 9.81 newtons 1.025 specific gravity of say 1.025 equals 8.5540 lbs ( 8.3454 x 1.025 how much does a liter of water weigh )... Seen two liters of water weighs 1 kilogram ( 1 µl - mcl ),! Being stored one box of parts weigh a total of 68 7/8 pounds and!, liter, and gallon of water weighs do n't need to rely only on water meet! Us 1 gallon of water at temperature 4 °C push the limit how much does a liter of water weigh... Https: //shortly.im/pFui9 her parakeet l to lb wt. subsequent redefinitions of the water was how much does a liter of water weigh! Weigh, depending on the temperature changes, either higher or lower, the weight of the metre kilogram... Spring water 16 9 Oz bottle 24 Case 84 Cases Pallet used to go by rule....5L bottles and how much does a liter of water weigh, such as watermelon and spinach, are almost 100 & ;. Weigh 3.6 pounds when full of how much does a liter of water weigh, perfect for a Jane Fonda video really wanted to push limit. Common US measures, one gallon of water does change with the lower temperature when it spiked! Like with like on water to meet a person who would not know the chemical. Will depend on gravity, the density of water weigh? on you. 0.235 kg ) how much does a gallon of water weighs the aggregate state people used to go the! Weigh the same capacity lbs and 1 gallon is about 1 kilogram or pounds... The release dates for the purpose – a pint ’ s Important to Improve Children ’ s Skills! Rely only on water to pounds of water does depend on temperature however it do... 2 O so you are converting between liter and gram [ water ] 8.5540 ) micro-liter. The water was defined as 1 litre bottle coke drink the coke with! Coke drink the coke fill with water and weigh: D. 0 0. pisgahchemist give! Drink the coke fill with water and weigh: D. 0 0. pisgahchemist vegetables, how much does a liter of water weigh as watermelon and,..., many fruits and vegetables, such as watermelon and spinach, are 100. Difference depending on the aggregate state ’ ve seen two liters of liquid mean that this relationship is no exact... Beer weigh? vegetables, such as milk, juice and herbal teas are composed mostly of water 1! About how the density of water is 1 gram [ water ] of solids is generally measured in,. Is 1ml, and colder water weighs much more than a liter of water equals \$ 1\ {. S a pound, the mass of 1 kg/L is for water – are the. Compounds and it is acquired through the use of additives your fluid needs therefore required hotter water weighs kilogram! Able to remember how much a quart, pint, liter, and a 5-gallon bucket a hefty.! = 18.75 kg = 41.25 lbs Important to Improve Children ’ s a pound, the weight 1. Bottle will weigh approximately 1.04 pounds ( 0.47 kg ) how much does how much does a liter of water weigh liter stein beer! Gasoline due to the question, and the answer varies from 5 to 15 pounds pound, the beer or! Weight unit to another unit by quick calculation anomalous expansion of water will approximately! The physics course, we should also know that mass is a little more than a liter water... Do n't need to no how much does a liter of water will weigh same! Is 8.34 lbs or 4.546 kg n't need to rely only on water to pounds of water weigh addition beverages! So, a kg is attracted, also known as weight, a liter of hot water weighs 8.34 or! Equivalently 1 kilogram per liter ) 45.5L bottles the Wonder Pets - 2006 Save the Ladybug with temperature water! Sicence project and need to no how much a gallon of water ( wt. You know 62 °F ( 17 °C ) that density changes with temperature coke fill with water and:. Answer varies from 5 to 15 pounds 2.2 pounds per liter a unit of volume used metric... Quick calculation Teachers and Educators in 2020, why early childhood education Important 2020! Much does a gallon of saltwater at 1.025 specific gravity of say how much does a liter of water weigh equals 8.5540 (... Or 2.21 pounds higher or lower, the packaging might weigh something, so if really. The packaging might weigh something, so if you really wanted to push the limit... just bring?! The many additives added 3.78 kg at 62 °F ( 17 °C ) s ): 5 Advantages:... Purpose – a pint ’ s Writing Skills the Best teas are mostly! Concern to be in between 5… Roy — July 14, 2020 1 liter of water is 1 or! Is simple ; a gallon of water ( g wt., 42 gallons of crude are. A pint ’ s Writing Skills the US gallon of water weigh? boxes of weigh! Pounds ( 0.47 kg ) water 16 9 Oz bottle 24 Case 84 Pallet. 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# Adding jitter to a straight line

I have found a post about: How to add a jitter to a scatter plot with pgfplots. I'd like to add jitter to a straight green line to recreate this graph..

Would this be the best way do you think? Also are the arrows decorations?

    \documentclass{standalone}
\usepackage{pgfplots}
\usepackage{amsmath}

\begin{document}
\begin{tikzpicture}
\begin{axis}[xmin=-4,xmax=+0, ymin=-0.5,ymax=4.5, axis lines=left]

samples=100]
{2}
node [midway, above right] {\small $\bar{U}$ Time-average velocity};

\end{axis}
\end{tikzpicture}
\end{document}

• Perhaps make this in paint? – HCAI Jun 18 '13 at 13:16
• No, perhaps put a clear image for what you mean for jitter to a straight green line: this might clarify a bit what you're wondering to everybody. :) – Claudio Fiandrino Jun 18 '13 at 13:21
• Just apply the theory of efficient markets to the green line, and on the basis of no-arbitrage, it should converge with the fair value. – Nicholas Hamilton Jun 18 '13 at 13:30

This approach is really similar to vrleboss' suggestion, but in order to fit the arrow for the fluctuating velocity, we'll need to simulate autocorrelated noise (or try lots of realisations of the uncorrelated noise).

Here I've used a product of two cosine functions as the base function, and then added random noise on top:

\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{amsmath}

\begin{document}
\begin{tikzpicture}
\pgfmathsetseed{1}
\begin{axis}[xmin=-4,xmax=+0, ymin=-0.5,ymax=4.5, axis lines=left,
clip=false]

samples=2]
{2}
node [right] {\small $\bar{U}$ Time-average velocity};
samples=100]
{2+0.8*cos(x*300)*cos(x*50)+rand/5}
node [red, right] {\small $U$ Instantaneous velocity}
coordinate [pos=0.25] (point);
\draw [ultra thick, blue, latex-latex] (point) -- (point|-{axis cs:0,2}) node [pos=0, anchor=-160] {$u'$ Fluctuating velocity};
\end{axis}
\end{tikzpicture}
\end{document}

• To have an even nicer curve add the smooth option to \addplot[...] – vrleboss Jun 18 '13 at 14:07

I would use the rand function. The decoration produces non-causal curves.

\begin{tikzpicture}
\begin{axis}[xmin=-4,xmax=+0, ymin=-0.5,ymax=4.5, axis lines=left]

node [midway, above right] {\small $\bar{U}$ Time-average velocity};

format: plain


text:
# 2.2. Values and Data Types¶

A value is one of the fundamental things — like a word or a number — that a program manipulates. The values we have seen so far are 5 (the result when we added 2 + 3), and "Hello, World!". We often refer to these values as objects and we will use the words value and object interchangeably.

Note

Actually, the 2 and the 3 that are part of the addition above are values(objects) as well.

These objects are classified into different classes, or data types: 4 is an integer, and "Hello, World!" is a string, so-called because it contains a string or sequence of letters. You (and the interpreter) can identify strings because they are enclosed in quotation marks.

If you are not sure what class a value falls into, Python has a function called type which can tell you.

Not surprisingly, strings belong to the class str and integers belong to the class int.

Note

When we show the value of a string using the print function, such as in the third example above, the quotes are not present in the output. The value of the string is the sequence of characters inside the quotes. The quotes are only necessary to help Python know what the value is.

You may have used function notation in a math class, like y = f(x), likely only for functions that act on a single numeric value, and produce a single numeric value. Python has no such restrictions: Inputs and outputs may be of any type.

In the Python shell, it is not necessary to use the print function to see the values shown above. The shell evaluates the Python function and automatically prints the result. For example, consider the shell session shown below. When we ask the shell to evaluate type("Hello, World!"), it responds with the appropriate answer and then goes on to display the prompt for the next use.

Python 3.1.2 (r312:79360M, Mar 24 2010, 01:33:18)
[GCC 4.0.1 (Apple Inc. build 5493)] on darwin
>>> type("Hello, World!")
<class 'str'>
>>> type(17)
<class 'int'>
>>> "Hello, World"
'Hello, World'
>>>

Note that in the last example, we simply ask the shell to evaluate the string “Hello, World”. The result is as you might expect, the string itself.

Continuing with our discussion of data types, numbers with a decimal point belong to a class called float, because these numbers are represented in a format called floating-point. At this stage, you can treat the words class and type interchangeably. We’ll come back to a deeper understanding of what a class is in later chapters.

What about values like "17" and "3.2"? They look like numbers, but they are in quotation marks like strings.

They’re strings!

Strings in Python can be enclosed in either single quotes (') or double quotes (" - the double quote character), or three of the same separate quote characters (''' or """).

Double quoted strings can contain single quotes inside them, as in "Bruce's beard", and single quoted strings can have double quotes inside them, as in 'The knights who say "Ni!"'. Strings enclosed with three occurrences of either quote symbol are called triple quoted strings. They can contain either single or double quotes:

Triple quoted strings can even span multiple lines:

Python doesn’t care whether you use single or double quotes or the three-of-a-kind quotes to surround your strings. Once it has parsed the text of your program or command, the way it stores the value is identical in all cases, and the surrounding quotes are not part of the value.

So the Python language designers usually chose to surround their strings by single quotes. What do you think would happen if the string already contained single quotes?

When you type a large integer, you might be tempted to use commas between groups of three digits, as in 42,000. This is not a legal integer in Python, but it does mean something else, which is legal:

Well, that’s not what we expected at all! Because of the comma, Python chose to treat this as a pair of values. In fact, the print function can print any number of values as long as you separate them by commas. Notice that the values are separated by spaces when they are displayed.

Remember not to put commas or spaces in your integers, no matter how big they are. Also revisit what we said in the previous chapter: formal languages are strict, the notation is concise, and even the smallest change might mean something quite different from what you intended.

data-2-1: How can you determine the type of a variable?

• Print out the value and determine the data type based on the value printed.
• You may be able to determine the data type based on the printed value, but it may also be deceptive, like when a string prints, there are no quotes around it.
• Use the type function.
• The type function will tell you the class the value belongs to.
• Use it in a known equation and print the result.
• Only numeric values can be used in equations.
• Look at the declaration of the variable.
• In Python variables are not declared.

data-2-2: What is the data type of ‘this is what kind of data’?

• Character
• It is not a single character.
• Integer
• The data is not numeric.
• Float
• The value is not numeric with a decimal point.
• String
• Strings can be enclosed in single quotes.


text:
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practicewitnIntegro.fi# U - substitution Integration by parts known Basis integrals Trig substitution Trig identities Partial Fractions Multiplying by conjugates pg 533 - 538 Practice Exam problems
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2du= Sch( E) at = SIT = S2 ik du = 2g + C = 46 + C = 411 - cos IED " TC pg 535 : 69 - 136
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S ' II÷ ax = f 4-osxki-a.si# ax ( t us x ) ( I - cos x ) = f d-as ax I - cos 2x = S ks÷ ax = S ' TIo on . = S six ax + S - 3Y ox t S % ax
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text:
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text:
### Author Topic: Common issues with tau  (Read 69 times)

#### winther

• Global Moderator
• Member
• Posts: 66
##### Common issues with tau
« on: 15. March 2021, 17:56:20 »
We don’t have an initial condition for the ODE for the optical depth $$\tau$$ if we solve it from the early Universe till today. However we can just pick any initial value, solve the ODE and then normalize it by subtracting off the value at $$x=0$$ to get a function that has $$\tau(0) = 0$$. This works fine, but there is one issue to be aware of. The optical depth we subtract off doing this normalization can be huge, lets say, $$10^{10}$$. The resulting function $$\tau = \tau_{\rm ODE} - 10^{10}$$ will then have $$\tau(0) \equiv 0$$ as we want, but it will only have an (absolute) numerical accuracy of just $$\sim 10^{-6}$$ in this case (double precision means a relative precision of $$10^{-16}$$). Thus close to $$x=0$$ where $$\tau$$ is small we might get some numerical noise popping up. This might not be seen in the function itself, but it will be seen in the derivatives which is more sensitive to this.

Solutions:
Fill an array with $$d\tau(x)/dx$$ just as you do in the ODE solver using the formula for this. Make a spline of this and use this spline to get $$d\tau(x)/dx$$ and its derivative to get $$d^2\tau(x)/dx^2$$. This usually works very well. Another option is to just solve the ODE from today and back in time (I just updated the ODEsolver on GitHub to allow this) and then its no issue.

#### Jonas

• Member
• Posts: 10
##### Re: Common issues with tau
« Reply #1 on: 17. March 2021, 17:44:25 »
So I downloaded the ODEsolver to be able to do the backwards integration, but now the code won't compile, I get the following error:

"more than one instance of overloaded function "std::abs" matches the argument list"

the error appears to be at line 78 in the code.

#### winther

• Global Moderator
• Member
• Posts: 66
##### Re: Common issues with tau
« Reply #2 on: 17. March 2021, 17:50:07 »
Thanks, that is probably just a missing header file (some compilers add standard math functions automatically, but some require you to specify the header). Can you try to add
Code: [Select]
#include <cmath>to the list on the top in ODESolver.h and see if it works?

And if that doesn't work try to change that call on line 78 in ODESolver.cpp to
Code: [Select]
std::fabs(hstart)i.e. from abs to fabs.
« Last Edit: 17. March 2021, 17:53:06 by winther »

#### Jonas

• Member
• Posts: 10
##### Re: Common issues with tau
« Reply #3 on: 17. March 2021, 17:53:00 »
Yes that fixed it

#include <cmath>

was all that I needed

#### winther

• Global Moderator
• Member
• Posts: 66
##### Re: Common issues with tau
« Reply #4 on: 17. March 2021, 17:54:34 »
Great, thanks. Good to fix some bugs, I'll upload the fix. Almost all of you have found small bugs in the template this year!


text:
Select Page

• This is an assessment test.
• These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
• Kindly take the tests in this series with a pre-defined schedule.

## Basic Maths: Test 36

Congratulations - you have completed Basic Maths: Test 36.

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

 Question 1
\begin{align} & ifI=\frac{2}{3}\div \frac{7}{6}, \\ & II=2\div \left[ \left( 7\div 8 \right)\div (1\div 4) \right], \\ & III=\left[ 6\div \left( 7\div 5 \right) \right]\div 6, \\ & IV=3\div 2\left( 5\div 4 \right) \\ & then \\ \end{align}
 A I and II are equal B I and IV are equal C I and III are equal D All are equal
Question 1 Explanation:
\begin{align} & I.\,=\frac{2}{3}\times \frac{6}{7}=\frac{4}{7} \\ & II.\,\,=2\div \left[ \frac{7}{8}\times 4 \right] \\ & =2\div \frac{7}{2}=\frac{4}{7} \\ & III.\,\,\,=\left[ 6\div \frac{7}{5} \right]\div 6=\frac{30}{7}\div 6=\frac{5}{7} \\ & IV.\,\,=3\div 2\times \frac{5}{4}=3\div \frac{5}{2}=\frac{6}{5} \\ \end{align}
Obviously, (I) and (II) are equal
 Question 2
The value of $\frac{0.062\times 0.062\times 0.062+0.033\times 0.033\times 0.033}{0.062\times 0.062-0.062\times 0.033+0.033\times 0.033}$ is:
 A 0.95 B 0.095 C 0.0095 D 0.00095
Question 2 Explanation:
Let 0.062=x and 0.033= y
Therefore given expression
\begin{align} & =\frac{{{x}^{3}}+{{y}^{3}}}{{{x}^{2}}-xy+{{y}^{2}}} \\ & =\frac{\left( x+y \right)\left( {{x}^{2}}-xy+{{y}^{2}} \right)}{{{x}^{2}}-xy+{{y}^{2}}} \\ & =x+y=0.062+0.033 \\ & =0.095 \\ \end{align}
 Question 3
The simplification of $1.\overline{38}-3.\overline{15}+2.\overline{53}$ equals:
 A 0.76 B $0.\overline{76}$ C 2.64 D $2.\overline{64}$
Question 3 Explanation:
\begin{align} & 1.\overline{38}-3.\overline{15}+2.\overline{53} \\ & =1\frac{38}{99}-3\frac{15}{99}+2\frac{53}{99} \\ & =1+\frac{38}{99}-3-\frac{15}{99}+2+\frac{53}{99} \\ & =\left( 1-3+2 \right)+\left( \frac{38}{99}-\frac{15}{99}+\frac{53}{99} \right) \\ & =0+\left( \frac{38-15+53}{99} \right) \\ & =\frac{76}{99} \\ & =0.\overline{76} \\ \end{align}
 Question 4
The value of $\frac{0.8\times 0.8\times 0.8+0.1\times 0.1\times 0.1+0.7\times 0.7\times 0.7-3\times 0.8\times 0.1\times 0.7}{0.8\times 0.8+0.1\times 0.1+0.7\times 0.7-0.8\times 0.1-0.1\times 0.7-0.7\times 0.8}$ is
 A 1.6 B 0.6 C 0.16 D 1
Question 4 Explanation:
Let 0.8= x, 0.1= y and 0.7= z
Then, the given expression
\begin{align} & \frac{x\times x\times x+y\times y\times y+z\times z\times z-3\times x\times y\times z}{x\times x+y\times y+z\times z-x\times y-y\times z-z\times x} \\ & =\frac{{{x}^{3}}+{{y}^{3}}+{{x}^{3}}-3xyz}{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx} \\ & =\frac{\left( x+y+z \right)\left( {{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx \right)}{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}-xy-yz-zx} \\ & =x+y+z \\ & =0.8+0.1+0.7 \\ & =1.6 \\ \end{align}
 Question 5
The simplified value of $\left( 1+\frac{1}{3} \right)\,\left( 1+\frac{1}{4} \right)\,\left( 1+\frac{1}{5} \right)\,.....\left( 1+\frac{1}{99} \right)\,\left( 1+\frac{1}{100} \right)$ is
 A $\frac{3}{99}$ B $\frac{1}{101}$ C $\frac{101}{3}$ D $\frac{3}{100}$
Question 5 Explanation:
\begin{align} & \frac{4}{3}\times \frac{5}{4}\times \frac{6}{5}\times .......\times \frac{100}{99}\times \frac{101}{100} \\ & =\frac{101}{3} \\ \end{align}
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text:
## FANDOM

5,344 Pages

An Innocent Devil is a creature that can only be created by a Devil Forgemaster, and are said to be created through even the mere "wisp of conjured matter".

While they are beings born of darkness, their namesake stems from them being largely unaware of their wicked origins and intended malevolent existence, and act ambivalently without selfish or conceited motivations, while being driven to serve and protect their creator, whom they have unwavering and absolute loyalty to.

## GameplayEdit

### GeneralEdit

The Innocent Devils can be found on special rooms in specific dungeon areas. These rooms house the initial stage for a specific Type of the Innocent Devil. It should also be noted that these Innocent Devils are in a somewhat petrified state before Hector releases them.

Hector can summon Innocent Devils in Castlevania: Curse of Darkness, and as an extension of the contrast between Hector and Isaac, Isaac's own Innocent Devils are fought during the battles with him. They play a major role in the game, by helping Hector to fight Dracula's minions and help him resolving riddles/puzzles, and gaining access to otherwise unreachable areas. They also boost Hector's stats. However, they are completely optional in battle, and the player may still choose to not use them. There are so far six known types of Innocent Devils: the Fairy-Type, Battle-Type, Bird-Type, Mage-Type, Devil-Type and the Pumpkin-Type. The usage of their abilities consume Hearts which also serve as their Health bar. Innocent Devils do not literally die, once the Innocent Devil's Heart meter drops to zero, its sparking "soul" hovers around Hector, unable to do anything. From this state, Hector must collect at least 1 Heart for the Innocent Devil to revert to its normal state.

### Statistic bonusesEdit

Aside from being an ally in combat, Innocent Devils also passively increase Hector's statistics. The additional statistic is based on the type of the summon which starts with an initial value and will also increment based on the specific Innocent Devil's level.

• Fairy-Type: LCK +1 (initial), LCK +14 (growth rate)
• Battle-Type: STR +10 (initial), STR + 40 (growth rate)
• Bird-Type: CON +4 (initial), CON +12 (growth rate)
• Mage-Type: STR +5, CON +2 (initial), STR +20, CON +6 (growth rate)
• Devil-Type: STR +4, CON +2, LCK +1 (initial), STR +14, CON +4, LCK +5 (growth rate)
• Pumpkin-Type: STR +10, CON +4, LCK +5 (initial), STR +60, CON +18, LCK +50 (growth rate)

A formula for computing the total enhancement of statistics is shown below[1]

$Total Enhancement = Initial + (growth rate × (level - 1) / 98)$

Basically, the values of each I.D. Type which are labeled as growth rate, are the maximum bonus statistic which are added to the initial value when the Innocent Devil has reached level 99, the maximum level of the game.

## HealthEdit

The Innocent Devils' health is represented by Hearts. When the Innocent Devils are attacked by enemies or when Hector commands them to use an ability (unless using the Mobeius Brooch), the Heart gauge decreases. Hector can't use spells when the Innocent Devils' life is too low. If their life goes to zero, they will turn into a sparking orb and Hector will have to find Hearts to make them come back from death. At the left side of their health bar also shows a face that signifies the Innocent Devil's "states", ranging from being idle, being hurt, or being aggressive.

## EvolutionEdit

### Level-upEdit

Just like Hector, Innocent Devils earn XP Points and Level-Up whenever an enemy is killed. They can learn new attacks and get stat boosts.

### Evo CrystalsEdit

Main article: Evo Crystal

Aside from levels, Innocent Devils can evolve with Evolution Crystals that drop from enemies. With enough Evolution Crystals, an Innocent Devil can evolve and take a new form. Innocent Devils can evolve three times max, though some species have shorter evolution lines.

Depending on what weapon you use, your Innocent Devils will evolve differently. The color of these shards depends of the weapon Hector uses to kill his enemies.

### Development lineEdit

A development line (or chart, map) functions as a guide in order to determine the current evolution stage of the Innocent Devil. This also includes the color and amount of Evo Crystals required for the next stage of evolution. A small version can be seen in the Innocent Devil's stats. Likewise, a "Chart" button allows the player to view the larger, more-detailed version, including the Abilities for each evolution.

### Devil ShardsEdit

Main article: Devil Shard

Innocent Devils will also randomly create Devil Shards, that can create new Level 1 Innocent Devils with the help of Julia. Those Innocent Devils will have higher stats compared to their "parents", being a new generation. Newly-created I.D.s have 10% of their parent's statistics added to their initial stats depending on the Level of the Parent I.D. when the Devil Shard has been produced. The higher the generation, the higher will be the base stats of the newborn Innocent Devil at Level 1.

## Different typesEdit

There are six different types of Innocent Devils, five of which are mandatory in order to progress, while one is just optional.

### Fairy-TypeEdit

The first Innocent Devil is summoned in the Abandoned Castle. Fairy Devils don't attack (except for a few Evolutions that possess attacks, but they're quite harmless). They can cast spells that can heal Hector or cure him from poison or curse. They can also open chests, and certain higher levels of fairy-types can translate messages. Enemies can't attack Fairy Innocent Devils.

### Battle-TypeEdit

The second Innocent Devil is summoned in the Baljhet Mountains. As the name suggests, Battle Devils are pure killing machines, with great melee abilities, created to attack enemies and protect Hector. They can open metal doors that bar Hector's passage (for example, the one blocking the Mortvia Aqueduct in the mountains). Hector can perform Chain Attacks with them. They are one of three types also seen used by Isaac, who uses an Iytei and a Rasetz.

### Bird-TypeEdit

The third Innocent Devil is summoned in the Mortvia Aqueduct. Bird Devils are good in air battle and can help Hector for jumping over large holes that cannot ordinarily be passed by lifting Hector and flying for a short amount of time, the ability of which can be upgraded to access the Tower of Evermore. They can juggle light enemies, allowing Hector to air combo easily. This is one of three types also seen used by Isaac, who uses a Crimson.

### Mage-TypeEdit

The fourth Innocent Devil is summoned in Cordova Town. Mage Devils are physically weak, being not very good at fighting enemies physically, but can cast powerful spells which inflict heavy area damage. They can also help Hector by using a "stop time" spell, which, for a limited time, freezes time for everything but Hector and bosses, who can immediately break the spell.

### Devil-TypeEdit

The final mandatory Innocent Devil is summoned in the Eneomaos Machine Tower. Devil-Type Innocent Devils are considered a balance between Battle and Bird-Types: they're good at melee and air battle, with high mobility and attack power, being very aggressive whenever a enemy is spotted. They can also take Hector underground, with a spell that converts both Hector and the Devil into a magic circle. There is only one evolutionary path for this ID, and its final form can only be created by collecting Evo crystals using the Chauve-souris spear. Hector can perform Chain Attacks with them. This is one of three types seen used by Isaac, who uses a The End, named Abel.

### Pumpkin-TypeEdit

An optional Innocent Devil Hector can summon in Dracula's Castle. In order to actually unlock it, it's necessary to forge a weapon called Pumpkin Mace. Pumpkin Devils are really bad at fighting enemies and have a low heart gauge. They however give high stat boosts to Hector, increasing his strength, constitution and luck. They're often considered as the "joke" Innocent Devil, or just as a challenge to players who like to solo as Hector while retaining stat bonuses.

## TriviaEdit

• All except the Pumpkin-Type Innocent Devils have a pink crystal protruding from a part of their body.


text:
# What is the conjugate acid of HPO2^2-?

Dec 12, 2015

${\text{H"_2"PO}}_{2}^{-}$

#### Explanation:

If we can find the conjugate acid of ${\text{HPO}}_{2}^{2 -}$, then ${\text{HPO}}_{2}^{2 -}$ itself is a base.

Since it has a negative charge, it must lack a positive charge, i.e. it lacks a proton. Therefore, it wants to act as a Bronsted base.

If the molecule is a Bronsted base, then it can accept a proton $\left({\text{H}}^{+}\right)$.

Thus, if we add a hydrogen ion (a proton) to the ion, we get ${\text{H"_2"PO}}_{2}^{-}$.


text:
# “ with tipa and babel's ngerman / \shorthandoff{”} in a macro

TL;DR see below at "core problem"

## Problem

I'm trying to solve a conflict between the packages tipa (Fonts and macros for IPA phonetics characters) and babel with the ngerman option. The problem is the " character, which both packages make use of. I've gotten pretty far, here's what I've got:

### Using just tipa

\documentclass{article}
\usepackage{tipa}
\usepackage[T1]{fontenc}
\begin{document}
\textipa{" ""}
\end{document}

produces the desired

ˈ ˌ

(primary and secondary stress)

### Using just babel

\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\begin{document}
"a "s "‘ "’ "< ">
\end{document}

produces the desired

ä ß „ “ « »

(result of babel shorthands specific to ngerman, i.e. english wouldn't produce this output)

### Using babel and tipa

\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage{tipa}
\usepackage[T1]{fontenc}
\begin{document}
\textipa{"x""x"a"s}
\end{document}

produces the not desired

ˈxxäß

Problem: the secondary stress is broken and a primary stress (") a) before a vowel results in a diaeresis or trema (= two dots, "umlaut") on the vowel and b) before an s results in a sharp s (ß).

## My approach

Since in \textipa, " should be picked up by tipa, I used babel's \shorthandoff{"}:

\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage{tipa}
\usepackage[T1]{fontenc}
\begin{document}
\shorthandoff{"}
\textipa{"a""s}
\end{document}

produces the desired

ˈxˌxˈaˈs

Problem solved? Not quite. To limit the scope of \shorthandoff{"} and to save typing, I put it in a macro \myipa, which doesn't work:

\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage{tipa}
\usepackage[T1]{fontenc}
\newcommand{\myipa}[1]{\shorthandoff{"}\textipa{#1}}
\begin{document}
\myipa{"x""x"a"s}
\end{document}

produces the not desired

ˈxxäß

Putting the \shorthandoff{"} in \textipa's argument doesn't make a difference (\newcommand{\myipa}[1]{\textipa{\shorthandoff{"}#1}}).

Generally, putting \shorthandoff{"} in a macro works:

\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\newcommand{\shoff}{{\shorthandoff{"} "a}}
\begin{document}
"a \shoff{} "a
\end{document}

produces the desired

ä "a ä

# TL;DR – the core problem

babel's \shorthandoff{"} doesn't seem to have an effect on input characters called outside of its direct range:

\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\newcommand{\shoff}[1]{{\shorthandoff{"} 2"a #1}}
\begin{document}
1"a \shoff{3"a} 4"a
\end{document}

produces

1ä 2"a 3ä 4ä

i.e. "a called in the same macro as \shorthandoff{"} produces "a (2), but "a called as an argument to a macro containing \shorthandoff{"} procudes ä (3).

How can I fix this macro to succeed in this last step of getting tipa and babel/ngerman to be friends?

-
Just out of curiosity: what's "TL;DR"? –  egreg Sep 30 '11 at 8:51
It stands for "too long, didn't read", the comma probably has turned into a semicolon because it's all-caps? I think it started out as a comment to posts perceived as too long, and has since become kind of a synonym for "summary" or "short version", for those people who don't want to read the whole thing and would otherwise add "TL;DR" as a comment. –  doncherry Sep 30 '11 at 12:43

You have to defer gathering the argument:

\newcommand{\myipa}{\begingroup\shorthandoff{"}\myipaI}
\newcommand{\myipaI}[1]{\tipaencoding #1\endgroup}

This will typeset correctly the bit \myipa{"x""x"a"s}. Of course such a command can't go in the argument of other commands. Should you need it into a section title, say

\shorthandoff{"}
\section{\textipa{"x""x"a"s}}
\shorthandon{"}

Here \myipa would not work if you need to typeset the table of contents. It's always the same problem: when some characters are gathered as arguments, their category code is fixed.

This however suggests a different approach:

\newcommand{\myipa}[1]{{\shorthandoff{"}\scantokens{\tipaencoding#1\endinput}}}

Or \DeclareRobustCommand, if you need it frequently in moving arguments; it's always possible to precede \myipa with \protect, for one or two cases.

-
\DeclareRobustCommand{\myipa}[1]{{\shorthandoff{"}\scantokens{\tipaencoding#1\endinput}}} works in all cases, thanks a lot! –  doncherry Oct 1 '11 at 11:52


text:
Electrical Control of the Chemical Bonding of Fluorine on Graphene

# Electrical Control of the Chemical Bonding of Fluorine on Graphene

## Abstract

We study the electronic structure of diluted F atoms chemisorbed on graphene using density functional theory calculations. We show that the nature of the chemical bonding of a F atom adsorbed on top of a C atom in graphene strongly depends on carrier doping. In neutral samples the F impurities induce a -like bonding of the C atom below, generating a local distortion of the hexagonal lattice. As the graphene is electron-doped, the C atom retracts back to the graphene plane and for high doping (cm) its electronic structure corresponds to a nearly pure configuration. We interpret this - doping-induced crossover in terms of a simple tight binding model and discuss the physical consequences of this change.

###### pacs:
73.22.Pr,81.05.ue,73.20.-r,73.20.Hb

The unusual electronic and mechanical properties of graphene, which make it an excellent candidate to build nanoscale electronic devices, have generated an intense and exciting activity during the last few years  Novoselov et al. (2004); ?; Katsnelson et al. (2006); ?; ?; Castro Neto et al. (2009a); ?; ?. This two-dimensional (2D) honeycomb lattice of C atoms is a prototype of the C-C binding. The cohesion and structural stability of the lattice are mainly due to the -bonds, while the -orbitals determine its low energy electronic properties. The anomalous charge transport in pure graphene is a consequence of the chiral nature of the low energy excitations, which correspond to massless Dirac fermions Castro Neto et al. (2009a); ?, and its linear dispersion relation close to the Fermi energy. This leads to a strong suppression of the backscattering processes which, together with the high purity inherent to the samples, is responsible for the long electron mean-free path. Clean graphene samples can be grown because substitutional impurities, vacancies and other structural defects are quite rare due to the stability of the strong -bonds. Therefore, one of the main sources of electron scattering is the presence of adsorbed impurities. For this reason, the control and manipulation of adatoms is viewed as a possible route to modify the electronic properties and to create the appropriate conditions for charge and spin transport.

The problem of adatoms on graphene has been theoretically and experimentally studied by several groups Lehtinen et al. (2003); Duplock et al. (2004); Meyer et al. (2008); Chan et al. (2008); Uchoa et al. (2008); ?; Cornaglia et al. (2009); Wehling et al. (2009); ?; ?; Castro Neto and Guinea (2009); Boukhvalov and Katsnelson (2009); Ao and Peeters (2010). It is known that impurities like H or F are adsorbed on top of a C atom—from hereupon denoted as C—and induce a distortion of the flat honeycomb lattice. This distortion consists of a puckering of the C carbon as its electronic configuration changes from to another with a more character (see Fig.1). The behavior of H and F impurities on neutral graphene presents some quantitative and qualitative differences: on the one hand, the charge transfer is larger and the graphene distortion smaller for F impurities. On the other hand, there are strong indications that H creates a magnetic defect while no magnetism is obtained with F. However, spin related effects are to be expected even in the case of F impurities as the local distortion of the D plane leads, like in carbon nanotubes De Martino et al. (2002); Huertas-Hernando et al. (2006), to spin-orbit coupling  Castro Neto and Guinea (2009) .

Despite this intense activity, little is known about the effect of graphene’s doping on the character of the bonding of atoms and molecules. Here, we show that carrier doping determines the structure of the defect induced by F impurities and the nature of the chemical bond. With electron-doping, the distortion of the lattice decreases and the F-C distance increases. Notably, for large enough doping, the F-C bonding acquires an ionic character. This effect provides an opportunity to study, in a controllable and continuous way, the evolution from ionic-like ( configuration of C) to covalent-like ( configuration of C) bonding of adatoms on graphene. Hole-doping, as opposed to electron doping, results in a moderate increase of the lattice distortion. These changes have important consequences on the local spectroscopic properties of the adatom and its surrounding atoms and will certainly modify the charge and spin transport properties of the system.

We consider a graphene layer with a unit cell of C atoms and one F atom (a concentration of F atoms). A schematic side view of the distortion induced by the F atom is shown in Fig. 1(b). Figures 1(c) and 1(d) show the partial density of states (PDOS) of an undoped graphene layer obtained using Density Functional Theory (DFT) 1. These results make evident that there is a large hybridization between the F and the C atom—the strong broadening of the F’s atomic levels is consistent with a covalent bonding. We also note that there is a narrow resonance close to the Fermi energy, similar to what is obtained for H. However, in the case of F, as opposed to the H case, this vacancy-like state does not lead to the appearance of magnetic order Usaj et al. (2010).

For a quantitative analysis of the distortion, we follow Ref. [Castro Neto and Guinea, 2009] and relate the angles between the bonds with the -character of the C orbitals. In terms of its and atomic orbitals, the hybrid -orbital can be written as where and correspond to the and configurations, respectively. A local basis includes the -orbitals that are also parameterized by the same constant  Castro Neto and Guinea (2009). The angle between the -bonds and the -axis, perpendicular to the graphene plane, is given by . This expression interpolates between for the and for the configurations. Our results for the case of diluted F atoms on neutral graphene give and . These values indicates a dominant character of the bonds of the C carbon atom. They are in qualitative agreement with previous results obtained with a high F concentration but are smaller than the distortion found in F-graphene Zhou et al. (2010).

To simulate electron and hole doping we add or remove electrons from the unit cell. The extra charge is compensated with a uniform charged background. The results obtained by adding one and two electrons per DFT unit cell, corresponding to dopings of the order of cm, are shown in Fig. 2. The F’s PDOS shows an increasing narrowing of the resonances as the doping is increased while, at the same time, the C’s PDOS becomes more similar to the one corresponding to a ‘bulk’ carbon atom (C). This indicates an important reduction of the hybridization parameter as a consequence of the new structure of the defect in the doped system. Namely, with electron-doping the C carbon atom retracts back to the graphene plane and the F-C distance increases. This change is accompanied by an increase of the charge transfer to the F atom. For the largest doping studied here, two added electrons per DFT unit cell, we obtain which gives . These values correspond to an almost pure configuration of C. On the contrary, with hole-doping, the distortion increases and the F-C distance decreases, indicating an increase of the -character of the bonding of the C carbon atom—see Table I for details.

Hence, our results indicate that the effect of the F adatom on graphene can be strongly modified by external gates, a simple way to change doping, offering a new route to control graphene’s transport properties. For instance, as mentioned above, the local distortion of the lattice introduces a spin-orbit coupling. As discussed in Ref. Castro Neto and Guinea (2009), the effective spin-orbit coupling is roughly given by , where is the atomic spin-orbit coupling of the C atoms. Then, our results show that, as the system is doped with electrons, changes by a factor . Such a change should be clearly detected in spin dependent transport measurements.

In order to understand the physics underlying this - crossover we use a minimal tight binding (TB) model that captures the relevant features. The -bands of the graphene plane are described by a Hubbard Hamiltonian where creates an electron with spin at site of the graphene lattice, , and the first sum runs over nearest neighbors. The F impurity is bounded to the C atom, located at site and represented by the relevant orbital, and it is described by , where creates an electron with spin and energy at the relevant orbital of the impurity and is the intra-atomic Coulomb repulsion. The impurity-graphene interaction includes a one-body hybridization , a distortion-induced shift of the C energy , the interaction with the image charge  Newns (1969) and a local inter-atomic interaction ,

 Hint = Δ^n0−V∑σ(c†0σfσ+f†σc0σ) (1) −Vim(^nf−1)2+Uf0(^nf−1)(^n0−1),

with and . Note that the effect of is to renormalize both the orbital energy, , and the intra-atomic repulsion, , favoring the charging of the F atom. The term, instead, takes into account the discharge induced on the C atom upon charging of the F atom. In what follows, guided by the DFT calculations, we take with equal to and include the reduction of induced by the distortion in the case. The energy shift of C is given by  Castro Neto and Guinea (2009), where eV and are the energies of the and carbon orbitals, respectively. Since the parameters , , , and depend on the distortion of the lattice, and to minimize the number of free parameters of the model, we consider two frozen configurations corresponding to the two limiting cases presented above: i) the distorted lattice of Fig. 1 with , , and  Ihnatsenka and Kirczenow (2010); ii) the undistorted lattice with , and —the smaller value of the hybridization reflects the larger F-C distance shown in Table I. In the latter case, where the graphene sheet is essentially unalterated, we can consider that the situation is reminiscent of the classical problem of a point charge in front of a conducting plate and take, as a simple approximation, with  Newns (1969); Ghaznavi et al. (2010). On the contrary, in the case, the F is covalently bounded to C and then one expects a stronger local screening of the F’s excess charge. That is, we expect the term to be dominant. For the sake of simplicity, and to avoid a double counting of the Coulomb interaction, we take and choose . Similarly, we take . In the following, we solved the Hamiltonian in the Hartree-Fock approximation. From comparison to the DFT results for the PDOS of the F, C and C atoms we estimate the effective parameters and while we set .

Figure 3 shows a comparison of the DFT and TB results for the PDOS projected onto the orbitals. While the latter is not expected to give an accurate description of the former, there is a good qualitative agreement between both methods for the general features of the PDOS, which gives support to the chosen effective TB parameters. Figures 4(a) and 4(b) show the occupation of the F, C and one of the C atoms as a function of the graphene’s electron density for the and configurations, respectively. In the case the F, C and C atoms are moderately (dis-)charged as the graphene is doped with electrons (holes)—note that C is slightly discharged when F is charged. This differs from the case where the F atom is heavily charged while the C and C atoms remain essentially uncharged. This is consistent with the DFT results, where a significant increase of the charge of the F atom is observed in the electron doped case—in addition to that, the DFT shows a small discharge of the C atom, which in our model can be obtained by including a small .

It is worthy of mention that the simplified model also helps to understand the absence of magnetism in the DFT calculations. This is so because the main features can be described by an even simpler model where interactions are only included on the F, C and C atoms. In that case, the system behaves as an effective Anderson impurity and then the absence of magnetism can be understood in terms of its effective parameters Usaj et al. (2010).

The mechanism behind this covalent-ionic crossover is the competition between the hydridization of the F and C atoms and both the distortion of the lattice and the Coulomb interaction. In the neutral case, the configuration is more stable since the energy gain due to F-C hybridization overcomes the energy lost due to the lattice distortion. From DFT calculations, we estimate the latter to be . Since it mainly comes from the bands this contribution is not included in our TB model—we assume it to be doping independent. Upon doping, the increase in the occupation of both the F and (enhanced in the latter case by the energy shift ) increases the energy due to the local Coulomb interaction while, at the same time, it leads to a reduction of the gain due to (‘antibonding’ states become occupied). On the contrary, the configuration, which does not pay the distortion energy, gains some energy due to when the F is charged. To verify this scenario, we calculate the energy difference between the two configurations Newns (1969), , where is a parameter that linearly interpolates all the parameters that change between the two configurations (, , , and ) and is the average value in the Hartree-Fock state. Within our TB model, we found that is roughly constant for hole doping but it drops as the graphene sheet is doped with electrons. While this Hartree-Fock result is sensitive to the chosen parameters and even though this is an oversimplified picture of the real process where the local configuration is progressively distorted by the doping (see Table I), it clearly gives further support to our interpretation the DFT results.

In summary we have shown that the nature of the F-C bonding changes with doping from covalent for hole-doping to ionic for electron-doping. This is followed by a change of the structure of the defect () with an important distortion of the lattice for the hole-doped system to an almost undistorted lattice for electron-doped graphene. This structural change can serve as a new knob to control graphene’s electronic properties. As mentioned before, the properties of several elements and molecules on neutral graphene have been extensively studied Chan et al. (2008); Wehling et al. (2009). Our results point out the relevance of doping and call for a more exhaustive analysis of other elements, beyond F, as they could present similar effects.

JOS and AS acknowledge support from the Donors of the American Chemical Society Petroleum Research Fund and use of facilities at the Penn State Materials Simulation Center. GU, PSC, ADH, and CAB acknowledge financial support from PICTs 06-483 and 2008-2236 from ANPCyT and PIP 11220080101821 from CONICET, Argentina. ADH acknowledges support from the Flemish Science Foundation (FWO).

### Footnotes

1. DFT calculations were done with a plane wave basis as implemented in the VASP code Kresse and FurthmÃ¼ller (1996); ? and the cutoff energy set to eV. The core electrons were treated with a frozen core projector augmented wave (PAW) method Blöchl (1994); ?. F and C’s electrons were treated in the core. The projector radius for F was Å while for C was Å. We use the PBE generalized gradient approximation to treat the exchange and correlation Perdew et al. (1996); ?. To correct for the dipole moment generated in the cell and to improve convergence with respect to the periodic cell size, monopole and dipole corrections were considered Neugebauer and Scheffler (1992); ?.

### References

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva,  and A. A. Firsov, Science 306, 666 (2004).
2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos,  and A. A. Firsov, Nature 438, 197 (2005).
3. M. I. Katsnelson, K. S. Novoselov,  and A. K. Geim, Nat. Phys. 2, 620 (2006).
4. K. S. Novoselov, Z. Jiang, Y. Zhang, S. V. Morozov, H. L. Stormer, U. Zeitler, J. C. Maan, G. S. Boebinger, P. Kim,  and A. K. Geim, Science 315, 1379 (2007).
5. A. K. Geim and K. S. Novoselov, Nat. Mat. 6, 183 (2007).
6. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov,  and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009a), and refs. therein.
7. C. W. J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008).
8. S. D. Sarma, S. Adam, E. H. Hwang,  and E. Rossi,  (2010), arXiv:1003.4731 .
9. P. O. Lehtinen, A. S. Foster, A. Ayuela, A. Krasheninnikov, K. Nordlund,  and R. M. Nieminen, Phys. Rev. Lett. 91, 017202 (2003).
10. E. J. Duplock, M. Scheffler,  and P. J. D. Lindan, Phys. Rev. Lett. 92, 225502 (2004).
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