The pressure and density of a diatomic gas le | vedclass

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(C) For an adiabatic process,the relationship between pressure $P$ and density $d$ is given by $P \propto d^{\gamma}$.Given $\gamma = \frac{7}{5}$ and

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$128$

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(C) For an adiabatic process,the relationship between pressure $P$ and density $d$ is given by $P \propto d^{\gamma}$.Given $\gamma = \frac{7}{5}$ and $\frac{d^{\prime}}{d} = 32$.We have the relation $\frac{P^{\prime}}{P} = \left(\frac{d^{\prime}}{d}\right)^{\gamma}$.Substituting the given values:$\frac{P^{\prime}}{P} = (32)^{7/5}$.Since $32 = 2^5$,we have:$\frac{P^{\prime}}{P} = (2^5)^{7/5} = 2^7$.Calculating the value:$2^7 = 128$.Therefore,the ratio $\frac{P^{\prime}}{P} = 128$.

The pressure and density of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is

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