(C) For an adiabatic process, the relation between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = \text{constant}$.Since $\gamma > 1$ for

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(C) For an adiabatic process, the relation between temperature $T$ and volume $V$ is given by $TV^{\gamma-1} = \text{constant}$.Since $\gamma > 1$ for all gases, $T \propto V^{-(\gamma-1)}$.In an adiabatic expansion, the volume $V$ increases, which implies that the temperature $T$ must decrease. Thus, the Assertion is correct.However, the Reason states that volume is inversely proportional to temperature $(V \propto 1/T)$, which is incorrect. The correct relation is $T \propto V^{-(\gamma-1)}$.Therefore, the Assertion is correct but the Reason is incorrect.

Class 11 Physics Thermodynamics Adiabatic Process

Easy

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

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A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

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Slope of isotherm for a gas (having $\gamma = 5/3$) is $3 \times 10^5 \, N/m^2$. If the same gas is undergoing adiabatic change,then the adiabatic elasticity at that instant is ........... $\times 10^5 \, N/m^2$.

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An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules $3$ times (in $\times$)? $(\gamma = 1.5)$

DifficultMHT CET 2026

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$Assertion:$ In adiabatic compression,the internal energy and temperature of the system decrease.
$Reason:$ Adiabatic compression is a slow process.

EasyAIIMS 2001

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The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be (Given $\gamma =$ ratio of specific heats at constant pressure and at constant volume).

MediumJEE MAIN 2023

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An engine takes in $5$ moles of air at $20\,^{\circ}C$ and $1\,atm$,and compresses it adiabatically to $1/10^{\text{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules,the change in its internal energy during this process is $X\,kJ$. The value of $X$ to the nearest integer is

DifficultJEE MAIN 2020

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$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

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Slope of isotherm for a gas (having $\gamma = 5/3$) is $3 \times 10^5 \, N/m^2$. If the same gas is undergoing adiabatic change,then the adiabatic elasticity at that instant is ........... $\times 10^5 \, N/m^2$.

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules $3$ times (in $\times$)? $(\gamma = 1.5)$

$Assertion:$ In adiabatic compression,the internal energy and temperature of the system decrease.$Reason:$ Adiabatic compression is a slow process.

The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be (Given $\gamma =$ ratio of specific heats at constant pressure and at constant volume).

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$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

$Assertion:$ In adiabatic compression,the internal energy and temperature of the system decrease.
$Reason:$ Adiabatic compression is a slow process.