(D) For a polytropic process $PV^x = \text{constant}$, the work done $W$ is given by $W = \frac{nR(T_1 - T_2)}{x - 1}$.Given $n = 1$ and $x = 3$.The t

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(D) For a polytropic process $PV^x = \text{constant}$, the work done $W$ is given by $W = \frac{nR(T_1 - T_2)}{x - 1}$.Given $n = 1$ and $x = 3$.The temperature change is $\Delta T = T_2 - T_1$, so $T_1 - T_2 = -\Delta T$.Substituting these values into the formula:$W = \frac{1 \cdot R \cdot (-\Delta T)}{3 - 1}$$W = \frac{-R \Delta T}{2}$The magnitude of the work done is $|W| = \left| \frac{-R \Delta T}{2} \right| = \frac{R \Delta T}{2}$.

Class 11 Physics Thermodynamics Polytropic Process

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One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).

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A
$R \Delta T$
B
$\frac{1}{4} R \Delta T$
C
$R^3 \Delta T$
D
$\frac{R}{2} \Delta T$

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One mole of an ideal gas undergoes a process $PV^3 = \text{constant}$, where $P$ and $V$ are pressure and volume respectively. Let $W$ be the work done by the gas as its temperature is increased by $\Delta T$. The value of $|W|$ is ($R$ is the universal gas constant).

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