Which of the following statements is correct | vedclass

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(C) The correct statements are $1$ and $4$.$1$. For an isothermal process, $pV = 	ext{constant}$. Differentiating with respect to $V$, we get $p + V

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$1, 4$ are correct

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(C) The correct statements are $1$ and $4$.$1$. For an isothermal process, $pV = 	ext{constant}$. Differentiating with respect to $V$, we get $p + V \frac{dp}{dV} = 0$, which gives the slope $\frac{dp}{dV} = -\frac{p}{V}$. This is correct.$2$. For an adiabatic process, $pV^{\gamma} = 	ext{constant}$. Differentiating with respect to $V$, we get $\frac{dp}{dV} V^{\gamma} + p \gamma V^{\gamma-1} = 0$, which gives the slope $\frac{dp}{dV} = -\gamma \frac{p}{V}$. Thus, statement $2$ is incorrect.$3$. In an isochoric process, volume $V$ is constant, so $dV = 0$. The graph is a vertical line, and the slope $\frac{dp}{dV}$ is undefined (or $\infty$). Thus, statement $3$ is incorrect.$4$. In an isobaric process, pressure $p$ is constant, so $dp = 0$. The graph is a horizontal line parallel to the volume axis, and the slope $\frac{dp}{dV} = 0$. This is correct.

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

Similar Questions

The slopes of the isothermal and adiabatic $p-V$ graphs of a gas are $S_I$ and $S_A$ respectively. If the heat capacity ratio of the gas is $\frac{3}{2}$,then $\frac{S_I}{S_A}=$

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 $(IV)$ $\Delta U = 0$

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Neon gas of a given mass expands isothermally to double its volume. What should be the further fractional decrease in pressure,so that the gas when adiabatically compressed from that state,reaches the original state?

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