Question

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma =1.40$, the work done by air is $(\text{Assume}{3}^{1.4}=4.6555)$ [Take air to be an ideal gas]

• A. $110.8J$
• B. $60.7J$
• C. $48J$
• D. $89.5J$

Answer 1

The correct option is D $89.5J$

We know that for adiabatic change at constant temperature
$P{V}^{\gamma }$ = constant
$P_1=1\text{atm},T_2=273K$
$P_1{V}_1^{\gamma }=P_2{V}_2^{\gamma }$
$P_2=P_1{\left[\frac{V_1}{V_2}\right]}^{\gamma }=1\text{atm}{\left(\frac{1}{3}\right)}^{1.4}$
Now, work done $\left(W\right)=\frac{P_1{V}_1-P_2{V}_2}{\gamma -1}$
$W=\left(\frac{1\times 1-\frac{1}{4.65}\times 3}{0.4}\right)\times 1.01\times {10}^2=89.5J$