Question

The pressure and volume of gas(air) are $P$ and $V$ respectively. If it is compressed suddenly to $\frac{1}{32}$ of its initial volume then its final pressure will be

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

Answer 1

The correct option is C $128P$

Sudden compression is adiabatic as there is no scope for heat exchange in such short notice.
Thus $P{V}^{\gamma }$ =constant ,where $\gamma =7/5$
Hence, $P_i{V}_i^{7/5}=P_f{V}_f^{7/5}$
$\Rightarrow P{V}^{7/5}=P_f(\frac{V}{32}{)}^{7/5}\Rightarrow P_f=128P$
Hence final pressure is $128P$.