Question

A certain mass of gas at NTP is expanded to three times its volume under adiabatic conditions. The resulting temperature of gas ,' will be ($7$ for gas is $1.40$ )

• A. $273\times {\left(\frac{1}{3}\right)}^{1.4}$
• B. $273\times (3{)}^{0.4}$
• C. $273\times {\left(\frac{1}{3}\right)}^{0.4}$
• D. $273\times (3{)}^{1.4}$

Answer 1

Answer: (C)

An adiabatic process is one in which no heat is transferred to or from working fluid.
For a gas undergoing adiabatic process $T{V}^{\gamma -1}$ = constant where $T$ is temperature, $V$ the volume and $\gamma$ the ratio of specific heat.
$\therefore \frac{T_2}{T_1}={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$
Given, $T_1=273K$
$V_2=3V_1$
$\gamma =1.4$
$\therefore T_2=273\times {\left(\frac{V_1}{3V_1}\right)}^{1.4-1}$
$=273\times {\left(\frac{1}{3}\right)}^{0.4}$