Question

Oxygen gas which is at a pressure of $2^{3/5}\text{atm}$ is compressed adiabatically so that volume becomes half that of the initial volume. The final pressure of the gas is

• A. $0.25\text{atm}$
• B. $0.6\text{atm}$
• C. $4\text{atm}$
• D. $8\text{atm}$

Answer 1

The correct option is C $4\text{atm}$

Oxygen gas is diatomic, $\gamma =\frac{7}{5}$
Equation of state of an adiabatic process is $P{V}^{\gamma }=k$
$\therefore P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
Given that, $V_2=\frac{V_1}{2}$ and $P_1=2^{3/5}\text{atm}$
$\therefore P_2=P_1{\left(\frac{V_1}{V_2}\right)}^{\gamma }=2^{3/5}\times 2^{7/5}$
$\Rightarrow P_2=4\text{atm}$