Question

One litre gas at 400 K and 300 atm pressure is compressed to a pressure of 600 atm and 200 K. The compressibility factor changes from 1.2 to 1.6 respectively. The final volume $V_2\left(L\right)$ of the gas is ______.

Report your answer as $\alpha$, where $\alpha =\frac{1}{V_2}$.

Answer 1

$Z_1=\frac{P_1{V}_1}{R{T}_1}$ and $Z_2=\frac{P_2{V}_2}{R{T}_2}$
$\frac{Z_1}{Z_2}=\frac{P_1}{P_2}\times \frac{T_2}{T_1}\times \frac{V_1}{V_2}$
$V_2=\frac{P_1}{P_2}\times \frac{T_2}{T_1}\times V_1\times \frac{Z_2}{Z_1}=\frac{300\times 200\times 1\times 1.6}{600\times 400\times 1.2}$

$\Rightarrow V_2=\frac{1}{3};\Rightarrow \alpha =3$