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(B) For an adiabatic process,the relation between pressure $P$ and volume $V$ is $PV^{\gamma} = 	ext{constant}$.Since density $ho = \frac{m}{V}$,we

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$128$

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(B) For an adiabatic process,the relation between pressure $P$ and volume $V$ is $PV^{\gamma} = 	ext{constant}$.Since density $ho = \frac{m}{V}$,we have $V = \frac{m}{ho}$. Substituting this into the adiabatic equation:$P \left(\frac{m}{ho}ight)^{\gamma} = 	ext{constant}$$P ho^{-\gamma} = 	ext{constant}$Therefore,$\frac{P^{\prime}}{P} = \left(\frac{ho^{\prime}}{ho}ight)^{\gamma}$.Given $\frac{ho^{\prime}}{ho} = 32$ and $\gamma = \frac{7}{5}$,we substitute these values:$\frac{P^{\prime}}{P} = (32)^{\frac{7}{5}}$$\frac{P^{\prime}}{P} = (2^5)^{\frac{7}{5}} = 2^7 = 128$.

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

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