# Solved papers for JEE Main & Advanced Physics Transmission of Heat JEE PYQ-Transmission Of Heat

### done JEE PYQ-Transmission Of Heat Total Questions - 32

• question_answer1) Wavelength of light used in an optical instrument are ${{\lambda }_{1}}=4000\,\overset{0}{\mathop{A}}\,$ and ${{\lambda }_{2}}=5000\,\overset{0}{\mathop{A}}\,$, then ratio of their respective resolving powers (corresponding to${{\lambda }_{1}}$and${{\lambda }_{2}}$) is                                            [AIEEE 2002]

A)
$16:25$

B)
$9:1$

C)
$4:5$

D)
$5:4$

• question_answer2) Which of the following is more close to a black body?                                             [AIEEE 2002]

A)
Black board paint

B)
Green leaves

C)
Black holes

D)
Red roses

• question_answer3) Which statement is incorrect?                                                                    [AIEEE 2002]

A)
All reversible cycles have same efficiency

B)
Reversible cycle has more efficiency than an irreversible one

C)
Carnot cycle is a reversible one

D)
Carnot cycle has the maximum efficiency in all cycles

• question_answer4)                                                            Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The ratio of the energy radiated per second by the first sphere to that by the second is                        [AIEEE 2002]

A)
$1:1$

B)
$16:1$

C)
$4:1$

D)
$1:9$

• question_answer5) The earth radiates in the infrared region of the spectrum. The spectrum is correctly given by                  [AIEEE 2003]

A)
Rayleigh Jeans law

B)

C)

D)
Wien's law

• question_answer6) According to Newton's law of cooling, the rate of cooling of a body is proportional to ${{(\Delta \theta )}^{n}}$, where $\Delta \theta$ is the difference of the temperature of the body and the surroundings and n is equal to [AIEEE 2003]

A)
2

B)
3

C)
4

D)
1

• question_answer7) If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on the earth to what it was previously, will be                                             [AIEEE 2004]

A)
4

B)
16

C)
32

D)
64

• question_answer8)  The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and$2K$and thickness$x$and$4x,$respectively are${{T}_{2}},$and${{T}_{1}}({{T}_{2}}>{{T}_{1}})$. The rate of heat transfer through the slab, in a steady state is$\left( \frac{A({{T}_{2}}-{{T}_{1}})K}{x} \right)f,$with f equals                                                [AIEEE 2004]

A)
1

B)
1/2

C)
2/3

D)
1/3

• question_answer9)  The figure shows a system of two concentric spheres of radii${{r}_{1}},{{r}_{2}}$and kept at temperatures ${{T}_{1}},{{T}_{2}},$respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to           [AIEEE 2005]

A)
$\frac{({{r}_{2}}-{{r}_{1}})}{({{r}_{1}}{{r}_{2}})}$

B)
in $\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)$

C)
$\frac{{{r}_{1}}{{r}_{2}}}{({{r}_{2}}-{{r}_{1}})}$

D)
$({{r}_{2}}-{{r}_{1}})$

• question_answer10) Assuming the sun to be a spherical body of radius R at a temperature of T K, evaluate the total radiant power, incident on earth, at a distance r from the sun.                                                                                    [AIEEE 2006]

A)
$4\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}$

B)
$\pi r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}$

C)
$r_{0}^{2}{{R}^{2}}\sigma {{T}^{4}}/4\pi {{r}^{2}}$

D)
${{R}^{2}}\sigma {{T}^{4}}/{{r}^{2}}$

• question_answer11)  One end of a thermally insulated rod is kept at a temperature$m{{y}^{2}}+(1-{{m}^{2}})xy-m{{x}^{2}}=0$and the other at$xy=0,$. The rod is composed of two sections of lengths$-\frac{1}{2}$and$-2$and thermal conductivities$\pm 1$and$F(x)=f(x)+f\left( \frac{1}{x} \right),$ respectively. The temperature at the interface of the two sections is                                                                                                                                       [AIEEE 2007]

A)
$f(x)=\int_{1}^{x}{\frac{\log \,t}{1+t}}dt$

B)
$\frac{1}{2}$

C)
$f:R\to R$

D)
$f(x)=$

• question_answer12) A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length$x$of the bar from its hot end is best described by which of the following figures?   [AIEEE 2009]

A)

B)

C)

D)

• question_answer13) A liquid in a beaker has temperature $\theta (t)$ at time t and ${{\theta }_{0}}$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between ${{\log }_{e}}(\theta -{{\theta }_{0}})$ and t is:                                   [AIEEE 2012]

A)

B)

C)

D)

• question_answer14) The heat radiated per unit area in 1 hour by a furnace whose temperature is 3000 K is $(\sigma =5.7\times {{10}^{-8}}W\,{{m}^{-2}}{{K}^{-4}})$                                             [JEE ONLINE 07-05-2012]

A)
$1.7\times {{10}^{10}}J$

B)
$1.1\times {{10}^{12}}J$

C)
$2.8\times {{10}^{8}}J$

D)
$4.6\times {{10}^{6}}J$

• question_answer15) A large cylindrical rod of length L is made by joining two identical rods of copper and steel of length $\left( \frac{L}{2} \right)$each. The rods are completely insulated from the surroundings. If the free end If copper rod is maintained at 100°C and that of steel at 0°C then the temperature of junction is Thermal conductivity of copper is 9 times that if steel)                                                                                                                 [JEE ONLINE 19-05-2012]

A)
90°C

B)
50°C

C)
10°C

D)
67°C

• question_answer16) If a piece of metal is heated to temperature$\theta$ and then allowed to cool in a room which is at temperature ${{\theta }_{0}},$  the graph between the temperature T of the metal and time t will be closed to:                            [JEE MAIN 2013]

A)

B)

C)

D)

• question_answer17) Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross section of each rod End of copper rod is maintained at 100 °C where as ends of brass and steel are kept at 0 °C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is:                                                                                                           [JEE MAIN 2014]

A)
4.8 cal/s

B)
6.0 cal/s

C)
1.2 cal/s

D)
2.4 cal/s

• question_answer18)  A hot body, obeying Newtons law of cooling is cooling down from its peak value 80°C to an ambient temperature of 30°C. It takes 5 minutes in cooling down from 80°C to 40°C.                                  [JEE ONLINE 11-04-2014] How much time will it take to cool down from 62°C to 32°C? (Given In 2 = 0.693, In 5 = 1.609)

A)
3.75 minutes

B)
8.6 minutes

C)
9.6 minutes

D)
6.5 minutes

• question_answer19) Hot water cools from 60°C to 50°C in the first 10 minutes and to 42°C in the next 10 minutes. The temperature of the surroundings is:                                                                                                         [JEE ONLINE 12-04-2014]

A)
25°C

B)
10°C

C)
15°C

D)
20°C

• question_answer20) A black colored solid sphere of radius R and mass M is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature ${{T}_{0}}.$ The initial temperature of the sphere is $3{{T}_{0}}.$If the specific heat of the material of the sphere varies as $\alpha {{T}^{3}}$per unit mass with the temperature T of the sphere, where $\alpha$ is a constant, then the time taken for the sphere to cool down to temperature $2{{T}_{0}}$  will be ($\sigma$is Stefan Boltzmann constant)                  [JEE ONLINE 19-04-2014]

A)
$\frac{M\alpha }{4\pi {{R}^{2}}\sigma }\ln \left( \frac{3}{2} \right)$

B)
$\frac{M\alpha }{4\pi {{R}^{2}}\sigma }\ln \left( \frac{16}{3} \right)$

C)
$\frac{M\alpha }{16\pi {{R}^{2}}\sigma }\ln \left( \frac{16}{3} \right)$

D)
$\frac{M\alpha }{16\pi {{R}^{2}}\sigma }\ln \left( \frac{3}{2} \right)$

• question_answer21) Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume$u=\frac{U}{V}\propto {{T}^{4}}$and pressure$p=\frac{1}{3}\left( \frac{U}{V} \right).$If the shell now undergoes an adiabatic expansion the relation between T and R is:                                                            [JEE MAIN 2015]

A)
$T\propto \frac{1}{R}$

B)
$T\propto \frac{1}{{{R}^{3}}}$

C)
$T\propto {{e}^{-R}}$

D)
$T\propto {{e}^{-3R}}$

• question_answer22) A body takes 10 minutes to cool from $60{}^\circ C$ to$50{}^\circ C$. The temperature of surroundings is constant at$25{}^\circ C$. Then, the temperature of the body after next 10 minutes will be approximately     [JEE Online 15-04-2018 (II)]

A)
$43{}^\circ C$

B)
$47{}^\circ C$

C)
$41{}^\circ C$

D)
$45{}^\circ C$

• question_answer23)  Temperature difference of $120{}^\circ \,C$ is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length $\frac{3L}{2}$, is connected across AB (See figure). In steady  state,  temperature  difference between P and Q will be close to:                 [JEE Main 09-Jan-2019 Morning]

A)
$45{}^\circ \,C$

B)
$75{}^\circ \,C$

C)
$35{}^\circ \,C$

D)
$60{}^\circ \,C$

• question_answer24)  A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature$27{}^\circ C$. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about:                                              [JEE Main 09-Jan-2019 Evening] [Take$\,R=8.3$ J/K mole]

A)
10 J

B)
0.9 kJ

C)
14 kJ

D)
6 kJ

• question_answer25) A heat source at $T={{10}^{3}}$ K is connected to another heat reservoir at $T={{10}^{2}}$ K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 $W{{K}^{-}}^{1}{{m}^{-}}^{1}$, the energy flux through it in the steady state is  [JEE Main 10-Jan-2019 Morning]

A)
200 $W{{m}^{-}}^{2}$

B)
65 $W{{m}^{-}}^{2}$

C)
120 $W{{m}^{-}}^{2}$

D)
90 $W{{m}^{-}}^{2}$

• question_answer26) Two kg of a monoatomic gas is at a pressure of $4\times {{10}^{4}}N/{{m}^{2}}$. The density of the gas is $8\text{ }kg/{{m}^{3}}$. What is the order of energy of the gas due to its thermal motion?   [JEE Main 10-Jan-2019 Evening]

A)
${{10}^{4}}$ J

B)
${{10}^{3}}J$

C)
${{10}^{5}}\text{ }J$

D)
${{10}^{6}}J$

• question_answer27) When 100 g of a liquid A at $100{}^\circ C$is added to 50 g of a liquid B at temperature$75{}^\circ C$, the temperature of the mixture becomes$90{}^\circ C$. The temperature of the mixture, if 100 g of liquid A at $100{}^\circ C$ is added to 50 g of liquid B at $50{}^\circ C$will be-                                                                                                     [JEE Main 11-Jan-2019 Evening]

A)
$70{}^\circ C$

B)
$85{}^\circ C$

C)
$60{}^\circ C$

D)
$80{}^\circ C$

• question_answer28)  A metal ball of mass 0.1 kg is heated upto $500{}^\circ C$ and dropped into a vessel of heat capacity$800\,\,J{{K}^{-1}}$ and containing 0.5 kg water. The initial temperature of water and vessel is $30{}^\circ C$. What is the approximate percentage increment in the temperature of the water?                      [JEE Main 11-Jan-2019 Evening] [Specific heat capacities of water and metal are, respectively, 4200 $Jk{{g}^{-1}}\,{{K}^{-1}}$and 400    $J\,k{{g}^{-1}}\,{{K}^{-1}}$]

A)
15%

B)
30%

C)
25%

D)
20%

• question_answer29) A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is ${{K}_{1}}$and that of the outer cylinder is${{K}_{2}}$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is- [JEE Main 12-Jan-2019 Morning]

A)
$\frac{2{{K}_{1}}+3{{K}_{2}}}{5}$

B)
$\frac{{{K}_{1}}+{{K}_{2}}}{2}$

C)
${{K}_{1}}+{{K}_{2}}$

D)
$\frac{{{K}_{1}}+3{{K}_{2}}}{4}$

• question_answer30) Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on $H{{e}^{+}}$ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is:    [JEE Main 8-4-2019 Morning]

A)
$n=1\to n=4$

B)
$n=2\to n=4$

C)
$n=2\to n=5$

D)
$n=2\to n=3$

• question_answer31) Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $'{{\theta }_{2}}'$and $'{{\theta }_{1}}'$ respectively, $({{\theta }_{2}}>{{\theta }_{1}}).$The temperature at the interface is:-[JEE Main 9-4-2019 Afternoon]

A)
$\frac{{{\theta }_{2}}+{{\theta }_{1}}}{2}$

B)
$\frac{{{\theta }_{1}}}{10}+\frac{9{{\theta }_{2}}}{10}$

C)
$\frac{{{\theta }_{1}}}{3}+\frac{2{{\theta }_{2}}}{3}$

D)
$\frac{{{\theta }_{1}}}{6}+\frac{5{{\theta }_{2}}}{6}$

• question_answer32)  One kg of water, at $20{}^\text{o}C,$is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20\Omega$. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to: [Specific heat of water $=4200\text{ }J/kg\text{ }{}^\text{o}C$), Latent heat of water = 2260 kJ/kg]                                                                       [JEE Main 12-4-2019 Afternoon]

A)
3 minutes

B)
22 minutes

C)
10 minutes

D)
16 minutes