Which of the following statements is correct?

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(A) For an isothermal process, the temperature $T$ remains constant. According to the ideal gas equation $PV = nRT$, since $n$, $R$, and $T$ are const

Vedclass · Accepted Answer

For an isothermal change, $PV = 	ext{constant}$.

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(A) For an isothermal process, the temperature $T$ remains constant. According to the ideal gas equation $PV = nRT$, since $n$, $R$, and $T$ are constant, the product $PV$ must also be constant. Therefore, $PV = 	ext{constant}$ is the correct statement.Option $B$ is incorrect because in an isothermal process, the change in internal energy $\Delta U = 0$ (as $\Delta U \propto \Delta T$).Option $C$ is correct because the adiabatic relation is $P_1 V_1^\gamma = P_2 V_2^\gamma$, which implies $\frac{P_2}{P_1} = \left( \frac{V_1}{V_2} ight)^\gamma$.Option $D$ is incorrect because in an adiabatic process, the heat exchange $Q = 0$.

List-$I$	List-$II$
$A$. Isothermal Process	$I$. Work done by the gas decreases internal energy
$B$. Adiabatic Process	$II$. No change in internal energy
$C$. Isochoric Process	$III$. The heat absorbed goes partly to increase internal energy and partly to do work
$D$. Isobaric Process	$IV$. No work is done on or by the gas

List-$I$	List-$II$
$(A)$ Isothermal	$(I)$ $\Delta W = 0$
$(B)$ Adiabatic	$(II)$ $\Delta Q = 0$
$(C)$ Isobaric	$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric	$(IV)$ $\Delta U = 0$

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Match List-$I$ with List-$II$.
List-$I$ List-$II$
$(A)$ Isothermal $(I)$ $\Delta W = 0$
$(B)$ Adiabatic $(II)$ $\Delta Q = 0$
$(C)$ Isobaric $(III)$ $\Delta U \neq 0$
$(D)$ Isochoric $(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$. The final pressure of the gas will be (given $\gamma = 3/2$): (in $,P$)

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