# Solved papers for JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion JEE PYQ-Thermometry Calorimetry and Thermal Expansion

### done JEE PYQ-Thermometry Calorimetry and Thermal Expansion Total Questions - 38

• question_answer1) Heat given to a body which raises its temperature by ${{1}^{o}}C$ is                   [AIEEE 2002]

A)
water equivalent

B)
thermal capacity

C)
specific heat

D)

• question_answer2) If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should [AIEEE 2002]

A)
increase

B)
remain unchanged

C)
decrease

D)
first increase then decrease

• question_answer3) A gaseous mixture consists of 16 g of helium and 16 g of oxygen/The ratio$\frac{{{C}_{p}}}{{{C}_{v}}}$ of the mixture is            [AIEEE 2005]

A)
1.59

B)
1.62

C)
1.4

D)
1.54

• question_answer4) Three perfect gases at absolute temperatures ${{T}_{1}},{{T}_{2}}$ and ${{T}_{3}}$ are mixed. The masses of molecules are ${{m}_{1}},{{m}_{2}}$ and ${{m}_{3}}$ and the number of molecules are ${{n}_{1}},{{n}_{2}}$ and ${{n}_{3}}$ respectively. Assuming no loss of energy, the final temperature of the mixture is [AIEEE 2011]

A)
$\frac{n_{1}^{2}T_{1}^{2}+n_{2}^{2}T_{2}^{2}+n_{3}^{2}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}$

B)
$\frac{{{T}_{1}}+{{T}_{2}}+{{T}_{3}}}{3}$

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

D)
$\frac{{{n}_{1}}T_{1}^{2}+{{n}_{2}}T_{2}^{2}+{{n}_{3}}T_{3}^{2}}{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}$

• question_answer5) 100 g of water is heated from ${{30}^{o}}C$ to ${{50}^{o}}C$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4184 J/kg/K) [AIEEE 2011]

A)
2.1 kJ

B)
4.2 kJ

C)
8.4 kJ

D)
84 kJ

• question_answer6) A metal rod of Young's modulus Y and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by t°C, the linear stress developed in its is :          [AIEEE 11-05-2011]

A)
$\frac{Y}{\alpha t}$

B)
$Y\alpha t$

C)
$\frac{1}{(Y\alpha t)}$

D)
$\frac{\alpha t}{Y}$

• question_answer7) An aluminium sphere of 20 cm diameter is heated from 0°C to 100°C. Its volume changes by (given that coefficient of linear expansion for aluminium ${{\alpha}_{Al}}=23\times {{10}^{-6}}{{/}^{o}}C$) [AIEEE 11-05-2011]

A)
2.89cc

B)
9.28cc

C)
49.8 cc

D)
28.9 cc

• question_answer8) A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is Y, the force that one part of the wheel applies on the other part is:          [AIEEE 2012]

A)
$2\pi SY\alpha \Delta T$

B)
$SY\alpha \,\Delta T$

C)
$\pi SY\alpha \,\Delta T$

D)
$2SY\alpha \,\Delta T$

• question_answer9) On a linear temperature scale Y, water freezes at $-{{160}^{o}}Y$and boils at $-{{50}^{o}}Y$. On this Y scale, a temperature of 340 K would be read as : (water freezes at 273 K and boils at 373 K) [JEE ONLINE 09-04-2013]

A)
$-{{73.7}^{0}}Y$

B)
$-{{233.7}^{0}}Y$

C)
$-{{86.3}^{0}}Y$

D)
$-{{103.3}^{0}}Y$

• question_answer10) The ratio of the coefficient of volume expansion of glass container to that of a viscous liquid kept inside the container is 1 : 4. What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures?                                                   [JEE ONLINE 23-04-2013]

A)
2 : 5

B)
1 : 4

C)
1 : 64

D)
1 : 8

• question_answer11) 500 g of water and 100 g of ice at ${{0}^{0}}\operatorname{C}$are in a calorimeter whose water equivalent is $40g.$ $10\,g$ of steam at ${{100}^{0}}C$ is added to it Then water in the calorimeter is: [JEE ONLINE 23-04-2013] (Latent heat of ice = 80 cal/g, Latent heat of stem = 540 cal/g)

A)
580 g

B)
590 g

C)
600 g

D)
610 g

• question_answer12) A mass of 50g of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool form ${{30}^{0}}C$to ${{25}^{0}}C$. A mass of 100g of another liquid in identical vessel with identical surroundings takes the same time to cool from ${{30}^{0}}C$ to ${{25}^{0}}C$. The specific heat of the liquid is:                                   [JEE ONLINE 25-04-2013]

A)
$2.0\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

B)
$7.\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

C)
$3\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

D)
$0.5\operatorname{kc}\operatorname{a}\operatorname{l}/\operatorname{kg}$

• question_answer13) The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is:                                                                                                [JEE MAIN 2014] (For steel Youngs modulus is $2\times {{10}^{11}}N{{m}^{-2}}$and coefficient of thermal expansion is  $1.1\times {{10}^{-5}}{{K}^{-1}}$)

A)
$2.2\times {{10}^{7}}Pa$

B)
$2.2\times {{10}^{6}}Pa$

C)
$2.2\times {{10}^{8}}Pa$

D)
$2.2\times {{10}^{9}}Pa$

• question_answer14) Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27°C to 77°C? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).                                     [JEE ONLINE 09-04-2014]

A)
8 min 20 s

B)
6 min 2 s

C)
7 min

D)
14 min

• question_answer15) An experiment takes 10 minutes to raise the temperature of water in a container from 0°C to 100°C and another 55 minutes to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be 1 cal/g °C, the heat of vaporization according to this experiment will come out to be:                                                       [JEE MAIN 11-04-2015]

A)
530 cal/g

B)
540 cal/g

C)
550 cal/g

D)
560 cal/g

• question_answer16) A pendulum clock loses 12s a day if the temperature is 40°C and gains 4s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the coefficient of linear expansion of the metal of the pendulum shaft are respectively:-                                                                                                [JEE MAIN - I 3-4-2016]

A)
${{55}^{o}}C;\alpha =1.85\times {{10}^{-2}}{{/}^{o}}C$

B)
${{25}^{o}}C;\alpha =1.85\times {{10}^{-5}}{{/}^{o}}C$

C)
${{60}^{o}}C;\alpha =1.85\times {{10}^{-4}}{{/}^{o}}C$

D)
${{30}^{o}}C;\alpha =1.85\times {{10}^{-3}}{{/}^{o}}C$

• question_answer17) A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2s at T = 0°C. If the temperature of the wire is increased and the corresponding charge in its time period is plotted against its temperature, the resulting graph is a line of slop S. If the coefficient of linear expansion of metal is a then the value of S is:          [JEE ONLINE 09-04-2016]

A)
$\frac{1}{\alpha }$

B)
$2\alpha$

C)
$\frac{\alpha }{2}$

D)
$\alpha$

• question_answer18) 200 g water is heated from 40°C to 60°C. Ignoring the slight expansion of water, the change in its internal energy is closed to (Given specific heat of water = 4184 J/kg/K):                                                         [JEE ONLINE 09-04-2016]

A)
16.7 kJ

B)
167.4 kJ

C)
4.2 kJ

D)
8.4 kJ

• question_answer19) A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be $75{{\,}^{o}}C.$ T is given by: (Given : room temperature$=30{{\,}^{o}}C,$specific heat of copper$\text{=}\,\text{0}\text{.1}\,\text{cal/gm}{{\,}^{\text{o}}}\text{C}$              [JEE Main 2017]

A)
$\text{1250}{{\,}^{o}}\text{C}$

B)
$825{{\,}^{o}}\text{C}$

C)
$800{{\,}^{o}}\text{C}$

D)
$885{{\,}^{o}}\text{C}$

• question_answer20) A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temeprature increases by $\Delta T.$ The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young's modulus, and $\alpha$ its coefficient of linear expansion. Then, F is equal to- [JEE Online 08-04-2017]

A)
$IAY\alpha \Delta T$

B)
$AY\alpha \Delta T$

C)
$\frac{AY}{\alpha \Delta T}$

D)
${{I}^{2}}Y\alpha \Delta T$

• question_answer21) In an experiment a sphere of aluminium of mass 0.20 kg is heated upto 150°C. Immediately, it is put into water of volume 150 cc at 27°C kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40°C. The specific heat of aluminium is - (take 4.2 Joule = 1 calorie)                                                      [JEE Online 08-04-2017]

A)
$434J/k{{g}^{-o}}C$

B)
$378J/k{{g}^{-o}}C$

C)
$315J/k{{g}^{-o}}C$

D)
$476J/k{{g}^{-o}}C$

• question_answer22) A steel rail of length 5 m and area of cross section $40\,c{{m}^{2}}$ is prevented from expanding along its length while the temperature rises by ${{10}^{\text{o}}}C$. If coefficient of linear expansion and Young's modulus of steel are $1.2\,\times {{10}^{-5}}\,{{K}^{-1}}$ and $2\times {{10}^{11}}N{{m}^{-2}}$ respectively, the force developed in the rail is approximately:                           [JEE Online 09-04-2017]

• question_answer23) Linear expansion $a/{}^\circ C$. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta$ TK. Youngs modulus, Y, for this metal is: [JEE Main 09-Jan-2019 Morning]

A)
$\frac{F}{A\alpha \Delta T}$

B)
$\frac{F}{2A\alpha \Delta T}$

C)
$\frac{2\,F}{A\alpha \Delta T}$

D)
$\frac{\,F}{A\alpha (\Delta T-273)}$

• question_answer24) Consider a Youngs double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength $\lambda$ such that the first minima occurs directly in front of the slit$\left( {{S}_{1}} \right)$        [JEE Main 10-Jan-2019 Evening]

A)
$\frac{\lambda }{2(5-\sqrt{2})}$

B)
$\frac{\lambda }{2(\sqrt{5}-2)}$

C)
$\frac{\lambda }{(5-\sqrt{2})}$

D)
$\frac{\lambda }{(\sqrt{5}-2)}$

• question_answer25) An unknown metal of mass 192 g heated to a temperature of $100{}^\circ C$ was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of $8.4{}^\circ \,C$. Calculate the specific heat of the unknown metal if water temperature stabilizes at $21.5{}^\circ C$. (Specific heat of brass is $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$)                     [JEE Main 10-Jan-2019 Evening]

A)
458 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

B)
1232 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

C)
654 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

D)
916 J $394\text{ }J\text{ }k{{g}^{-1}}{{K}^{-1}}$

• question_answer26) Ice at $-20{}^\circ C$ is added to 50 g of water at $40{}^\circ C$. When the temperature of the mixture reaches $0{}^\circ C,$ it is found that 20 g of ice is still un melted. The amount of ice added to the water was close to-            [JEE Main 11-Jan-2019 Morning] (Specific heat of water $=4.2\text{ }J/g/{}^\circ C$ Specific heat of Ice $=2.1\text{ }J/g/{}^\circ C$ Heat of fusion of water at $0{}^\circ C=334\text{ }J/g$)

A)
60 g

B)
50 g

C)
40 g

D)
100 g

• question_answer27) Two rods A and B of identical dimensions are at temperature $30{}^\circ C$. If A is heated upto $180{}^\circ C$and B upto $T{}^\circ C$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is $4:3$, then the value of T is- [JEE Main 11-Jan-2019 Evening]

A)
$200{}^\circ C$

B)
$270{}^\circ C$

C)
$230{}^\circ C$

D)
$250{}^\circ C$

• question_answer28) A thermometer graduated according to a linear scale reads a value ${{x}_{0}}$ when in. contact with boiling water, and ${{x}_{0}}/3$ when in contact with ice. What is the temperature of an object in${}^\circ C$, if this thermometer in the contact with the object reads${{x}_{0}}/2$ ?                               [JEE Main 11-Jan-2019 Evening]

A)
35

B)
25

C)
66

D)
40

• question_answer29) Two identical breakers A and B contain equal volumes of two different liquids at $60{}^\circ C$ each and left to cool down. Liquid in A has density of $8\times {{10}^{2}}kg/{{m}^{3}}$and specific heat of$2000J\,k{{g}^{-1}}{{K}^{-1}}$while liquid in B has density of ${{10}^{3}}kg\,{{m}^{-3}}$and specific heat of $4000J\,k{{g}^{-1}}{{K}^{-1}}.$ Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)                                    [JEE Main 8-4-2019 Morning]

A)

B)

C)

D)

• question_answer30) A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K) [JEE Main 9-4-2019 Afternoon]

A)
${{10}^{-3}}K$

B)
${{10}^{-4}}K$

C)
${{10}^{-1}}K$

D)
${{10}^{-5}}K$

• question_answer31) The specific heats, ${{C}_{P}}$ and ${{C}_{V}}$ of a gas of diatomic molecules, A, are given (in units of$J\,mo{{l}^{-1}}{{K}^{-1}}$) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-                             [JEE Main 9-4-2019 Afternoon]

A)
A has one vibrational mode and B has two

B)
Both A and B have a vibrational mode each

C)
A is rigid but B has a vibrational mode

D)
A has a vibrational mode but B has none

• question_answer32) A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20{}^\circ C$ is : [Given that $R=8.31\text{ }J\text{ }mo{{l}^{1}}\text{ }{{K}^{1}}$]                                                [JEE Main 10-4-2019 Morning]

A)
748 J

B)
374 J

C)
350 J

D)
700 J

• question_answer33) When ${{M}_{1}}$gram of ice at $10{}^\text{o}C$ (specific heat $=0.5\text{ }cal\text{ }{{g}^{1}}{}^\text{o}{{C}^{1}})$is added to M2 gram of water at $50{}^\text{o}C,$ finally no ice is left and the water is at 0ºC. The value of latent heat of ice, in cal ${{g}^{-1}}$is: [JEE Main Held on 12-4-2019 Morning]

A)
$\frac{5{{M}_{1}}}{{{M}_{2}}}-50$

B)
$\frac{50{{M}_{2}}}{{{M}_{1}}}$

C)
$\frac{50{{M}_{2}}}{{{M}_{1}}}-5$

D)
$\frac{5{{M}_{2}}}{{{M}_{1}}}-5$

• question_answer34) Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? $\left( R=8.3\text{ }J/mol\text{ }K \right)$ [JEE Main Held on 12-4-2019 Morning]

A)
21.6 J/mol K

B)
19.7 J/mol K

C)
17.4 J/mol K

D)
15.7 J/mol K

• question_answer35) At $40{}^\text{o}C,$a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from $40{}^\text{o}C$to $20{}^\text{o}C$ it regains its original length of 0.2 m. The value of M is close to : (Coefficient of linear expansion and Young's modulus of brass are ${{10}^{5}}/{}^\text{o}C$ and ${{10}^{11}}N/{{m}^{2}},$ respectively; $g=10\,m{{s}^{-2}}$)       [JEE Main Held on 12-4-2019 Morning]

A)
$1.5\,kg$

B)
$9\text{ }kg$

C)
$0.9\text{ }kg$

D)
$0.5\text{ }kg$

• question_answer36) A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times {{10}^{5}}/{}^\circ \,C$ along the x-axis and $5\times {{10}^{6}}/{}^\circ \,C$ along the y and the z-axis. If the coefficient of volume expansion of the solid is $C\times {{10}^{6}}/{}^\circ C$then the value of C is________. [JEE MAIN Held on 07-01-2020 Morning]

• question_answer37) M grams of steam at $100{}^\circ C$ is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at $40{}^\circ C$ [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g], the value of M is _________.                         [JEE MAIN Held on 07-01-2020 Evening]

• question_answer38) Three containers ${{C}_{1}}$, ${{C}_{2}}$ and ${{C}_{3}}$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process)  ${{C}_{1}}$ ${{C}_{2}}$ ${{C}_{3}}$ T $1\ell$ $2\ell$ − $60{}^\circ C$ − $1\ell$ $2\ell$ $30{}^\circ C$ $2\ell$ − $1\ell$ $60{}^\circ C$ $1\ell$ $1\ell$ $1\ell$ $\theta$
The value of $\theta$ (in ${}^\circ C$ to the nearest integer) is _______. [JEE MAIN Held on 08-01-2020 Evening]