The pressure P of an ideal diatomic gas varie | vedclass

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(C) From the given graph, the pressure $P$ is directly proportional to the absolute temperature $T$, i.e., $P \propto T$ or $P = kT$ (where $k$ is a c

Vedclass · Accepted Answer

$2.5$

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(C) From the given graph, the pressure $P$ is directly proportional to the absolute temperature $T$, i.e., $P \propto T$ or $P = kT$ (where $k$ is a constant).Using the ideal gas equation $PV = nRT$, we can substitute $P = kT$ to get $(kT)V = nRT$, which simplifies to $V = nR/k = 	ext{constant}$.Since the volume $V$ remains constant throughout the process, this is an isochoric process.The molar heat capacity of an ideal gas for an isochoric process is given by $C_V$.For a diatomic gas, the degrees of freedom $f = 5$.Therefore, the molar heat capacity $C_V = \frac{f}{2}R = \frac{5}{2}R = 2.5R$.Thus, the molar heat capacity is $2.5R$.

The pressure $P$ of an ideal diatomic gas varies with its absolute temperature $T$ as shown in the figure. The molar heat capacity of the gas during this process is ........... $R$ [$R$ is the gas constant].

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