Question

A gas has pressure P and volume V. It is now compressed adiabatically to $\frac{1}{32}$ times the original volume. Given that $(32{)}^{1.4}=128$, the final pressure is ($\gamma =1.4$)

• A. $\frac{P}{128}$
• B. $\frac{P}{32}$
• C. $32P$
• D. $128P$

Answer 1

Answer: (D)

$128P$

$P{V}^{\gamma }=P_1{\left(\frac{V}{32}\right)}^{\gamma }$
$P_1=(32{)}^{\gamma }\Rightarrow P_1=(32{)}^{1.4}\Rightarrow P_1=128P$