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

Vedclass · Accepted Answer

$1.5$

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(A) 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 this as $P T^{-3} = 	ext{constant}$.Comparing the exponents of $P$ and $T$ in the two equations,we have the ratio $\frac{\gamma}{1-\gamma} = -3$.Solving for $\gamma$: $\gamma = -3(1-\gamma) \Rightarrow \gamma = -3 + 3\gamma \Rightarrow 2\gamma = 3 \Rightarrow \gamma = 1.5$.Since the ratio $C_P / C_V$ is defined as $\gamma$,the value is $1.5$.

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P / C_V$ for the gas is

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