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(C) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by Poisson's equation: $p V^{\gamma} = 	ext{constant}$.Using t

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$\frac{5}{2}$

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(C) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by Poisson's equation: $p V^{\gamma} = 	ext{constant}$.Using the ideal gas law $pV = RT$,we can write $V = \frac{RT}{p}$.Substituting this into the adiabatic equation:$p \left( \frac{RT}{p} ight)^{\gamma} = 	ext{constant}$$p^{1-\gamma} T^{\gamma} = 	ext{constant}$$p \propto T^{\frac{\gamma}{\gamma-1}}$.Comparing this with the given relation $p \propto T^{C}$,we get $C = \frac{\gamma}{\gamma-1}$.For a monoatomic gas,the adiabatic index $\gamma = \frac{5}{3}$.Substituting the value of $\gamma$:$C = \frac{5/3}{5/3 - 1} = \frac{5/3}{2/3} = \frac{5}{2}$.

In an adiabatic change,the pressure and temperature of a monoatomic gas are related by the relation $p \propto T^{C}$,where $C$ is equal to

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