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(C) For an adiabatic process,the relationship between pressure $P$ and temperature $T$ is given by $P^{1-\gamma} T^{\gamma} = 	ext{constant}$.Given t

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$\frac{3}{2}$

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(C) For an adiabatic process,the relationship between pressure $P$ and temperature $T$ is given by $P^{1-\gamma} T^{\gamma} = 	ext{constant}$.Given that $P \propto T^3$,we can write $P = k T^3$,which implies $P T^{-3} = 	ext{constant}$.Comparing this with the standard adiabatic relation $P^{1-\gamma} T^{\gamma} = 	ext{constant}$,we raise the given relation to a power $n$ such that the exponent of $T$ matches:$(P T^{-3})^n = P^n T^{-3n} = 	ext{constant}$.Equating the exponents of $T$ from $P^{1-\gamma} T^{\gamma}$ and $P^n T^{-3n}$,we have $\gamma = -3n$ and $1-\gamma = n$.Substituting $n = 1-\gamma$ into the first equation: $\gamma = -3(1-\gamma) = -3 + 3\gamma$.Rearranging gives $2\gamma = 3$,so $\gamma = \frac{3}{2}$.Thus,the ratio $\frac{C_p}{C_V} = \gamma = \frac{3}{2}$.

During an adiabatic process,if the pressure of a gas is found to be proportional to the cube of its absolute temperature,then the ratio of $\frac{C_p}{C_V}$ for the gas is:

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