A monoatomic ideal gas follows the process, $T V^{3 / 2} = c o n s t a n t$ . The molar specific heat for this process is $(\frac{5 R}{y})$ , where $R$ is gas constant. Find the value of $^{'} y^{'}$ .

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Solution

Compairing $T V^{3 / 2}$ = Constant with $T V^{γ - 1}$ =Constant.
We get,
$γ = \frac{5}{2}$
Given, $C_{p} = \frac{5 R}{y}$
We know,
$\frac{C_{p}}{C_{v}}$ $= γ = \frac{5}{2}$
$C_{p} - C_{v} = R ∴ C_{p} - \frac{2}{5} C_{p} = R ∴ \frac{3}{5} C_{p} = R ∴ C_{p} = \frac{5 R}{3} ∴ y = 3$

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A monoatomic ideal gas follows the process:

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