Question

One mol of a gas at NTP is suddenly expanded to three times its initial volume. If $C_v=2R$, the ratio of initial to final pressure of gas will nearly be

• A. $5$
• B. $4$
• C. $3$
• D. $2$

Answer 1

Answer: (A)

$5$

$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
$P_2=P_1{\left(\frac{V_1}{V_2}\right)}^{\gamma }=1{\left(\frac{1}{3}\right)}^{3/2}$
$\frac{P_1}{P_2}=3\sqrt{3}=5.1$