When a diatomic gas (rigid) undergoes adiabat | vedclass

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(B) For an adiabatic process,the relation between pressure $(P)$ and temperature $(T)$ is given by $P^{1-\gamma} T^{\gamma} = 	ext{constant}$.This ca

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$3.5$

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(B) For an adiabatic process,the relation between pressure $(P)$ and temperature $(T)$ is given by $P^{1-\gamma} T^{\gamma} = 	ext{constant}$.This can be rewritten as $P \propto T^{\frac{\gamma}{\gamma-1}}$.Comparing this with $P \propto T^{c}$,we get $c = \frac{\gamma}{\gamma-1}$.For a rigid diatomic gas,the degrees of freedom $(f)$ is $5$.The adiabatic exponent $\gamma = 1 + \frac{2}{f} = 1 + \frac{2}{5} = 1.4$.Substituting the value of $\gamma$ into the expression for $c$:$c = \frac{1.4}{1.4 - 1} = \frac{1.4}{0.4} = \frac{14}{4} = 3.5$.Therefore,the value of $c$ is $3.5$.

When a diatomic gas (rigid) undergoes adiabatic change,its pressure $(P)$ and temperature $(T)$ are related as $P \propto T^{c}$. The value of $c$ is

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