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.

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