First slide

Thermodynamic processes

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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