Question

An ideal gas at pressure $1\text{bar}$ and temperature $300\text{K}$ is compressed till the final volume is ${\frac{1}{16}}^{th}$ of the original volume following a polytropic process $P{V}^{1.25}=$ constant. If the final pressure of the gas is $x\times {10}^3\text{kPa}$, then $x$ is

Answer 1

A polytropic process is given by the equation $P{V}^{\eta }=\text{constant}$
$\therefore P_1{V}_1^{\eta }=P_2{V}^{\eta }2..........\left(1\right)$
Given,
$P_1=1\text{bar}={10}^5\text{Pa}$
$V_2=\frac{1}{16}{V}_1$
$\eta =1.25$
Substituting the given values in $\left(1\right)$ we get,
${10}^5\times V_1^{1.25}=P_2\times {\left(\frac{1}{16}\right)}^{1.25}{V}_1^{1.25}$
$\Rightarrow P_2=32\times {10}^5\text{Pa}=3200\text{kPa}$