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(A) The given process is $P = aV^2$, which can be written as $PV^{-2} = a$. Comparing this with the polytropic process equation $PV^x = 	ext{constant

Vedclass · Accepted Answer

$\frac{17R}{6}$

Vedclass · Answer

(A) The given process is $P = aV^2$, which can be written as $PV^{-2} = a$. Comparing this with the polytropic process equation $PV^x = 	ext{constant}$, we get $x = -2$. The molar heat capacity $C$ for a polytropic process is given by $C = C_V + \frac{R}{1-x}$. For a diatomic gas, the molar heat capacity at constant volume is $C_V = \frac{5R}{2}$. Substituting the values, we get $C = \frac{5R}{2} + \frac{R}{1 - (-2)}$. $C = \frac{5R}{2} + \frac{R}{3} = \frac{15R + 2R}{6} = \frac{17R}{6}$.

For a certain process, the pressure of a diatomic gas varies according to the relation $P = aV^2$, where $a$ is a constant. What is the molar heat capacity of the gas for this process?

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