Question

One mole of an ideal gas is initially at $ 0^{\circ}C $ and $ 1$ atm pressure. If it absorbs $1000$ cal heat during a reversible isothermal expansion, what will be its final volume?

• A. 102.5 litre
• B. 242.5 litre
• C. 22.4 litre
• D. 121.25 litre

Answer 1

Answer: (D)

Since the gas is under S.T.P conditions,
Hence $V_{1}=22.4$ litre, $V_{2}=?$
For isothermal and reversible expansion, $\Delta E=0 $
$\therefore q=-W$
$=-\left[-n R T \times 2.303 \log V_{2} / V_{1}\right]$
or $100 \times 4.184 \,J$
$=1 \times 8.314 \times 273 \times 2.303 \times \log \frac{V_{2}}{22.4}$
or $4184=5227.17 \log \frac{V_{2}}{22.4}$
or $\frac{V_{2}}{22.4}=$ antilog $0.8004$
$V_{2}=121.25\, ml$