Question

The volume of a poly-atomic gas $\left(y=\frac{4}{3}\right)$ compressed adiabatically to $\frac{1}{8^{th}}$ of the orignal volume. if the orignal pressure of the gas is $p_0$ the new pressure will be:

• A. $8p_0$
• B. $16p_0$
• C. $6p_0$
• D. $2p_0$

Answer 1

Answer: (B)

$16p_0$

Given,

$\gamma =\frac{4}{3}$

$P_0=$ initial pressure

$V_2=\frac{V_1}{8}$

$P_0=$ final pressure

For poly adiabatically,

$P{V}^{\gamma }=constant$

$P_2{V}_2^{\gamma }=P_1{V}_1^{\gamma }$

$P_2=P_0(\frac{V_1}{V_2}{)}^{\gamma }=P_0(\frac{V_1}{V_1/8}{)}^{4/3}$

$P_2=P_0(8{)}^{4/3}=16P_0$

The correct option is B.