Question

An ideal monoatomic gas at ${27}^{\circ }C$ is compressed adiabatically to $8/27$ times of its present volume. The increase in temperature of the gas is:

• A. ${375}^{\circ }C$
• B. ${402}^{\circ }C$
• C. ${175}^{\circ }C$
• D. ${475}^{\circ }C$

Answer 1

The correct option is A ${375}^{\circ }C$

Let the initial volume of the gas be $V$ i.e $V_1=V$

Thus final volume of the gas $V_2=\frac{8}{27}V$

Given : $T_1={27}^{o}C=300K$

For monoatomic gas, $\gamma =\frac{5}{3}$

Using $T{V}^{\gamma }=constant$

$⟹$ $\frac{T_2}{T_1}=(\frac{V_1}{V-2}{)}^{\gamma -1}$

$\therefore$ $\frac{T_2}{300}=(\frac{27}{8}{)}^{\frac{5}{3}-1}$

OR $\frac{T_2}{300}=(\frac{27}{8}{)}^{\frac{2}{3}}=(\frac{3}{2}{)}^2$ $⟹T_2=300\times 2.25=675K$

$⟹T_2=675-273={402}^{o}C$

Thus increase in temperature $\Delta T=T_2-T_1=402-27={375}^{o}C$