Question

The initial coordinates of any system are $p$ and $V$. If a gas $\left(\gamma =\frac{5}{3}\right)$ is compressed to $\frac{1}{8}$ of its original volume, then the pressure of the gas will be

• A. p
• B. 16p
• C. 4p
• D. 32p

Answer 1

Answer: (D)

$p_1{V}_1^{\gamma }=p_2{V}_2^{\gamma }$ constant
Here, $p_1=p,V_1=V$ and $V_2=\frac{V}{8}$
$\therefore$ $P{V}^{\gamma }=p_2{\left(\frac{V}{8}\right)}^{\gamma }$
$\Rightarrow$ $p_2=8^{\gamma }p=8^{5/3}p=32p$