# A litre of dry air at STP expands adiabatically to a volume of 3 litres.

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:

$\left(3^{1.4}=4.6555\right)$ [Take air to be an ideal gas]

1. (1) $60.7 \mathrm{~J}$

2. (2) $90.5 \mathrm{~J}$

3. (3) $100.8 \mathrm{~J}$

4. (4) $48 \mathrm{~J}$

Correct Option: , 2

Solution:

(2) Given, $V_{1}=1$ litre, $P_{1}=1 \mathrm{~atm}$

$V_{2}=3$ litre, $\gamma=1.40$

Using, $P V^{r}=$ constant $\Rightarrow P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma}$

$\Rightarrow P_{2}=P_{1} \times\left(\frac{1}{3}\right)^{1.4}=\frac{1}{4.6555} \mathrm{~atm}$

$\therefore$ Work done, $W=\frac{P_{1} V_{1}-P_{2} V_{2}}{\gamma-1}$

$=\frac{\left(1 \times 1-\frac{1}{4.6555} \times 3\right) 1.01325 \times 10^{5} \times 10^{-3}}{0.4}=90.1 \mathrm{~J}$

Closest value of $W=90.5 \mathrm{~J}$