Question

A mass of dry air at N.T.P is compressed to $\frac{1}{32}$th of its original volume suddenly . If $\gamma =1.4$ the final pressure would be:

• A. $32atm$
• B. $128atm$
• C. $\frac{1}{32}atm$
• D. $150atm$

Answer 1

Answer: (B)

$128atm$

At NTP ,pressure is $1atm$.
$\begin{array}{c}{P}_1{V_1}^{\gamma }=P_2{V_2}^{\gamma }\\ P_2=P_1\left(\frac{V_1}{V_2}\right)\gamma \\ =1\times {\left(\frac{V_1}{\frac{V_1}{32}}\right)}^{1.4}\\ ={\left(32\right)}^{\frac{7}{5}}\\ ={\left(\sqrt[5]{532}\right)}^{7}atm\\ =2^{7}atm\\ =128atm\end{array}$