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(D) For an adiabatic process, the relation between pressure $p$ and volume $V$ is given by $pV^\gamma = 	ext{constant}$, where $\gamma = C_p / C_V$.

Vedclass · Accepted Answer

$3/2$

Vedclass · Answer

(D) For an adiabatic process, the relation between pressure $p$ and volume $V$ is given by $pV^\gamma = 	ext{constant}$, where $\gamma = C_p / C_V$. Given that $p \propto T^3$, we can write $p = k T^3$. Using the ideal gas equation $pV = nRT$, we have $T = \frac{pV}{nR}$. Substituting this into the given relation: $p = k \left( \frac{pV}{nR} ight)^3$ $p = k \frac{p^3 V^3}{(nR)^3}$ $1 = \left( \frac{k}{(nR)^3} ight) p^2 V^3$ $p^2 V^3 = 	ext{constant}'$ $p V^{3/2} = 	ext{constant}''$ Comparing this with the standard adiabatic equation $pV^\gamma = 	ext{constant}$, we get $\gamma = 3/2$. Thus, the value of $C_p / C_V$ is $3/2$.

During an adiabatic process, the pressure of a gas is proportional to the cube of its temperature. The value of $C_p / C_V$ for that gas is

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