The pressure and density of a diatomic gas γ$$=75$$ change adiabatically from (P$$,$$d) to P′,d′. If d′$$d=32$$, then the value of P′$$/P$$ is $$________________$$.

PVγ$$=P$$′V′γPmγdγ$$=P$$′m′γd′γ⇒P′$$P=d$$′dγ$$=(32)7/5=128$$

Thermodynamic processes

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Question

The pressure and density of a diatomic gas $(γ = \frac{7}{5})$ change adiabatically from $(P, d) to (P^{'}, d^{'})$ . If $\frac{d^{'}}{d} = 32,$ then the value of $P^{'} / P$ is ________________.

Moderate

Solution

${PV}^{γ} = P^{'} {V^{'}}^{γ}$
$P \frac{m^{γ}}{d^{γ}} = P^{'} \frac{m^{' γ}}{{d^{'}}^{γ}} \Rightarrow \frac{P^{'}}{P} = {(\frac{d^{'}}{d})}^{γ} = (32)^{7 / 5} = 128$

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