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P-T Relationship

The ratio of ...

Question

The ratio of $[C_{p} / C_{v}]$ of the specific heats at a constant pressure and at a constant volume of any perfect gas.

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Solution

$C_{p} = C_{v} + R$
And $C_{v} = \frac{3}{2} R$
$\frac{C_{p}}{C_{v}} = \frac{C_{v} + R}{\frac{3}{2} R} = \frac{\frac{3}{2} R + R}{\frac{3}{2} R} = \frac{\frac{5 R}{2}}{\frac{3 R}{2}} = \frac{5 R}{2} \times \frac{2}{3 R} = \frac{5}{3}$

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