A polyatomic gas follows a law T^2 V^alpha = | vedclass

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(B) process in which there is no heat exchange $(Q = 0)$ is called an adiabatic process.For an adiabatic process,the relation between temperature $T$

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$\alpha = \frac{2}{3}$

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(B) process in which there is no heat exchange $(Q = 0)$ is called an adiabatic process.For an adiabatic process,the relation between temperature $T$ and volume $V$ is given by $T V^{\gamma-1} = 	ext{constant}$.Squaring both sides,we get $T^2 V^{2(\gamma-1)} = 	ext{constant}$.Comparing this with the given law $T^2 V^\alpha = 	ext{constant}$,we find $\alpha = 2(\gamma-1)$.For a polyatomic gas,the adiabatic index $\gamma$ is typically $\frac{4}{3}$.Substituting $\gamma = \frac{4}{3}$ into the expression for $\alpha$:$\alpha = 2 \left( \frac{4}{3} - 1 ight) = 2 \left( \frac{1}{3} ight) = \frac{2}{3}$.

$A$ polyatomic gas follows a law $T^2 V^\alpha = \text{constant}$. Find $\alpha$ for which the heat exchange of gas in the process becomes zero.

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