Question

The pressure and density of a diatomic gas $(γ = 7 / 5)$ change adiabatically from (P,d) to (P',d). If (d/d') = 32, the value of (P/P') should be

Moderate

Solution

$P {(\frac{1}{d})}^{7 / 5} = P^{'} {(\frac{1}{d^{'}})}^{7 / 5}$
$∴ \frac{P}{P^{'}} = {(\frac{d}{d^{'}})}^{7 / 5} = (32)^{7 / 5} = {(2^{5})}^{7 / 5} = 2^{7} = 128$

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