Thermodynamics – JEE Main Previous Year Questions with Solutions

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Previous Years AIEEE/JEE Main Questions

Q. Assuming the gas to be ideal the work done on the gas in taking it from A to B is :-

(1) 400 R            (2) 500 R            (3) 200 R            (4) 300

[AIEEE-2009]

Sol. (1)

Q. The work done on the gas in taking it from D to A is :-

(1) –690 R            (2) +690 R            (3) –414 R               (4) +414 R

[AIEEE-2009]

Sol. (4)

Q. The net work done on the gas in the cycle ABCDA is :-

(1) 1076 R            (2) 1904 R           (3) Zero             (4) 276 R

[AIEEE-2009]

Sol. (4)

Q. A diatomic ideal gas is used in a carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from V to 32 V, the efficiency of the engine is :-

(1) 0.25            (2) 0.5           (3) 0.75             (4) 0.99

[AIEEE-2010]

Sol. (3)

Q. A Carnot engine operating between temperatures $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ has efficientcy $\frac{1}{6} .$ When $\mathrm{T}_{2}$ is lowered

by $62 \mathrm{K},$ its efficiency increases to $\frac{1}{3} .$ Then $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are, respectively:-

(1) 330 K and 268 K             (2) 310 K and 248 K              (3) 372 K and 310 K                 (4) 372 K and 330 K

[AIEEE-2011]

Sol. (3)

Q. The specific heat capacity of a metal at low temperautre (T) is given as $\mathrm{C}_{\mathrm{p}}\left(\mathrm{kJk}^{-1} \mathrm{kg}^{-1}\right)=32\left(\frac{\mathrm{T}}{400}\right)^{3}$ A 100 gram vessel of this metal is to be cooled from 20°K to 4°K by a special refrigerator operating at room temperature (27°C). The amount of work required to cool the vessel is:-

(1) equal to 0.002 kJ

(2) greater than 0.148 kJ

(3) between 0.148 kJ and 0.028 kJ

(4) less than 0.028 kJ

[AIEEE-2011]

Sol. (3)

Q. A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure P and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be :-

(1) $\frac{\mathrm{P}}{2}, \mathrm{T}$

(2) $\frac{\mathrm{P}}{2}, \frac{\mathrm{T}}{2}$

(3) P, T

(4) $\mathrm{P}, \frac{\mathrm{T}}{2}$

[AIEEE-2011]

Sol. (1)

Q. Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly (Assume the gas to be close to ideal gas) :-

[AIEEE-2012]

Sol. (2)

Q. A Carnot engine, whose efficiency is 40% takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be :-

(1) 600 K

(2) efficiency of Carnot engine cannot be made larger than 50%

(3) 1200 K

(4) 750 K

[AIEEE-2012]

Sol. (4)

Q. The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat, extracted from the source in a single cycle is :

(1) $\mathrm{p}_{0} \mathrm{v}_{0}$

( 2)$\left(\frac{13}{2}\right) \mathrm{p}_{0} \mathrm{v}_{0}$

( 3)$\left(\frac{11}{2}\right) \mathrm{p}_{0} \mathrm{v}_{0}$

(4) $4 \mathrm{p}_{0} \mathrm{v}_{0}$

[jEE-Mains-2013]

Sol. (2)

Q. One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

[jEE-Mains-2014]

Sol. (2)

Q. 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 $\mathrm{u}=\frac{\mathrm{U}}{\mathrm{V}} \propto \mathrm{T}^{4}$ and pressure $\mathrm{p}=\frac{1}{3}\left(\frac{\mathrm{U}}{\mathrm{v}}\right)$. If the shell now undergoes an adiabatic expansion the relation between T and R is –

(1) $\mathrm{T} \propto \frac{1}{\mathrm{R}}$

(2) $\mathrm{T} \propto \frac{1}{\mathrm{R}^{3}}$

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

(4) $\mathrm{T} \propto \mathrm{e}^{-3 \mathrm{R}}$

[jEE-Mains-2015]

Sol. (1)

Q. ‘n’ moles of an ideal gas undergoes a process $\mathrm{A} \rightarrow \mathrm{B}$ as shown in the figure. The maximum temperature of the gas during the process will be :

(1) $\frac{9 \mathrm{P}_{0} \mathrm{V}_{0}}{\mathrm{nR}}$ (1) $\frac{9 \mathrm{P}_{0} \mathrm{V}_{0}}{\mathrm{nR}}$ (3) $\frac{3 \mathrm{P}_{0} \mathrm{V}_{0}}{2 \mathrm{nR}}$ (4) $\frac{9 \mathrm{P}_{0} \mathrm{V}_{0}}{2 \mathrm{nR}}$

[jEE-Mains-2016]

Sol. (2)

Q. An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by $\mathrm{P} \mathrm{V}^{\mathrm{n}}$ = constant, then n is given by (Here $\mathrm{C}_{\mathrm{P}}$ and $\mathrm{C}_{\mathrm{v}}$ are molar specific heat at constant pressure and constant volume, respectively) :-

(1) $\mathrm{n}=\frac{\mathrm{C}-\mathrm{C}_{\mathrm{V}}}{\mathrm{C}-\mathrm{C}_{\mathrm{P}}}$

(2) $\mathrm{n}=\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}$

(3) $\quad \mathrm{n}=\frac{\mathrm{C}-\mathrm{C}_{\mathrm{P}}}{\mathrm{C}-\mathrm{C}_{\mathrm{V}}}$

(4) $\mathrm{n}=\frac{\mathrm{C}_{\mathrm{P}}-\mathrm{C}}{\mathrm{C}-\mathrm{C}_{\mathrm{V}}}$

[jEE-Mains-2016]

Sol. (3)

Q. $\mathrm{C}_{\mathrm{p}}$ and $\mathrm{C}_{\mathrm{v}}$ are specific heats at constant pressure and constant volume respectively. It is observed that

$\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=$ = a for hydrogen gas $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=$ = b for nitrogen gas The correct relation between a and b is :

(1) a = 14 b

(2) a = 28 b

(3) $a=\frac{1}{14} b$

(4) a = b

[jEE-Mains-2017]

Sol. (1)

Q. Two moles of an ideal monoatomic gas occupies a volume V at $27^{\circ}$ C. The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

(1) (a) 195 K (b) –2.7 kJ

(2) (a) 189 K (b) –2.7 kJ

(3) (a) 195 K (b) 2.7 kJ

(4) (a) 189 K (b) 2.7 kJ

[jEE-Mains-2018]

Sol. (2)