A diatomic gas $\left(\gamma=\frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_i}{32}$…
A diatomic gas $\left(\gamma=\frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_i}{32}$ where $V_i$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is '$x$ $T_{\mathrm{i}}$ '. The value of ' $x$ ' is
$5$
$4$
$3$
$2$
Solution
For adiabatic process:
$\mathrm{TV}^{\gamma-1}=$ Constant
$\therefore \quad$ Initially:
$\mathrm{T}_{\mathrm{i}} \mathrm{V}^{\frac{7}{5}-1}=$Constant
$\therefore \quad$ Final condition:
$\mathrm{xT}_{\mathrm{f}} \mathrm{V}^{\frac{7}{5}-1}=$ Constant
So,
$\mathrm{T}_{\mathrm{i}} \mathrm{V}^{\frac{7}{5}-1}=\mathrm{xT}_{\mathrm{f}} \mathrm{V}^{\frac{7}{5}-1}$
$\mathrm{TV}^{\frac{2}{5}}=\mathrm{xT}\left(\frac{\mathrm{V}}{32}\right)^{\frac{2}{5}}$
$x=4$