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

Vedclass · Accepted Answer

$3/2$

Vedclass · Answer

(D) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by $pV^\gamma = k$,where $\gamma = C_p / C_V$ is the adiabatic index. $(i)$Given that $p \propto T^3$,we can write $p = k' T^3$,where $k'$ is a constant.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$$p = \left( \frac{k'}{n^3 R^3} ight) p^3 V^3$$1 = \left( \frac{k'}{n^3 R^3} ight) p^2 V^3$$p^2 V^3 = 	ext{constant}$$p V^{3/2} = 	ext{constant}$ (ii)Comparing equation $(i)$ and (ii),we get $\gamma = 3/2$.Therefore,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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