(A) For process $AB$: The volume $V$ is constant $(V = V_1)$. Therefore, the work done $W_{AB} = \int P dV = 0$.For process $BC$: The temperature $T$

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$0; R T_2 \ln \left( \frac{V_2}{V_1} \right); R(T_1 - T_2)$

(A) For process $AB$: The volume $V$ is constant $(V = V_1)$. Therefore, the work done $W_{AB} = \int P dV = 0$.For process $BC$: The temperature $T$ is constant $(T = T_2)$. The work done for an isothermal process is $W_{BC} = nRT_2 \ln \left( \frac{V_f}{V_i} \right)$. Here, $n = 1$, $V_i = V_1$, and $V_f = V_2$. So, $W_{BC} = R T_2 \ln \left( \frac{V_2}{V_1} \right)$.For process $CA$: This is a process where the graph is a straight line passing through the origin in the $V-T$ diagram, which implies $V \propto T$, meaning pressure $P$ is constant (isobaric process). The work done is $W_{CA} = nR \Delta T = R(T_1 - T_2)$.

Class 11 Physics Thermodynamics Mix Examples-Thermodynamics

Difficult

$A$ cyclic process for $1 \, \text{mole}$ of an ideal gas is shown in the $V-T$ diagram. Find the work done in processes $AB$, $BC$, and $CA$ respectively.

A
$0; R T_2 \ln \left( \frac{V_2}{V_1} \right); R(T_1 - T_2)$
B
$R(T_1 - T_2); R; R T_1 \ln \left( \frac{V_1}{V_2} \right)$
C
$0; R T_2 \ln \left( \frac{V_2}{V_1} \right); R(T_2 - T_1)$
D
$0; R T_2 \ln \left( \frac{V_1}{V_2} \right); R(T_2 - T_1)$

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Class 11

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Thermodynamics

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Mix Examples-Thermodynamics

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 \,K$. The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 \,K$, what is the rise in temperature of the gas in $B$ (in $\,K$)? (Given $\gamma = 5/3$)

DifficultAP EAMCET 2007

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$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

DifficultTS EAMCET 2010

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An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $P_A/P_I$ is $(C_P/C_V = \gamma)$.

DifficultMHT CET 2026

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Match the List-$I$ with List-$II$:

List-$I$ List-$II$

$A$. Pressure varies inversely with volume of an ideal gas. $I$. Adiabatic process

$B$. Heat absorbed goes partly to increase internal energy and partly to do work. $II$. Isochoric process

$C$. Heat is neither absorbed nor released by a system. $III$. Isothermal process

$D$. No work is done on or by a gas. $IV$. Isobaric process

List-$I$	List-$II$
$A$. Pressure varies inversely with volume of an ideal gas.	$I$. Adiabatic process
$B$. Heat absorbed goes partly to increase internal energy and partly to do work.	$II$. Isochoric process
$C$. Heat is neither absorbed nor released by a system.	$III$. Isothermal process
$D$. No work is done on or by a gas.	$IV$. Isobaric process

MediumJEE MAIN 2025

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Match the "Technology" given in List-$1$ with the "Principle of Physics" given in List-$2$.
$A$. Steam engine $I$. Magnetic confinement of plasma
$B$. Electron microscope $II$. Laws of thermodynamics
$C$. Non-reflecting coatings $III$. Wave nature of electrons
$D$. Tokamak $IV$. Interference of light

MediumTS EAMCET 2025

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$A$. Steam engine	$I$. Magnetic confinement of plasma
$B$. Electron microscope	$II$. Laws of thermodynamics
$C$. Non-reflecting coatings	$III$. Wave nature of electrons
$D$. Tokamak	$IV$. Interference of light

$A$ cyclic process for $1 \, \text{mole}$ of an ideal gas is shown in the $V-T$ diagram. Find the work done in processes $AB$, $BC$, and $CA$ respectively.

Similar Questions

$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $P_A/P_I$ is $(C_P/C_V = \gamma)$.

Match the "Technology" given in List-$1$ with the "Principle of Physics" given in List-$2$.$A$. Steam engine$I$. Magnetic confinement of plasma$B$. Electron microscope$II$. Laws of thermodynamics$C$. Non-reflecting coatings$III$. Wave nature of electrons$D$. Tokamak$IV$. Interference of light

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