An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its…
An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmospheres, the value of ' $\gamma$ 'of the gas is :
$1.5$
$1.4$
$1.3$
$1.6$
Solution
Volume of the gas $\mathrm{v}=\frac{\mathrm{m}}{\mathrm{d}}$ and using $\mathrm{PV}^\gamma=$ constant
$
\begin{aligned}
& \frac{\mathrm{P}^{\prime}}{\mathrm{P}}=\frac{\mathrm{V}}{\mathrm{V}^{\prime}}=\left(\frac{\mathrm{d}^{\prime}}{\mathrm{d}}\right)^\gamma \\
& \text { or } 128=(32)^\gamma \\
& \therefore \gamma=\frac{7}{5}=1.4
\end{aligned}
$