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  4. During an adiabatic process, the pressure of a gas is found to be proportional to 4 power of its absolute temperature. The γ for the gas is

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Q. During an adiabatic process, the pressure of a gas is found to be proportional to $4$ power of its absolute temperature. The $\gamma$ for the gas is

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Solution:

According to the given question
$P \propto T^{4}$
or $PT^{-4}$ = constant $\ldots\left(i\right)$
For an adiabatic process
$PT ^{\gamma / 1-\gamma}$ =constant $\ldots\left(ii\right)$
Comparing $\left(i\right)$ and $\left(ii\right)$, we get
$\therefore \frac{\gamma}{1-\gamma}=-4$
or $\gamma=-4+4\gamma$
$3\gamma=4$
$\gamma=\frac{4}{3}$