Q.14 A gas of 0.5 mole at 300 K expands isothermally from an initial volume of 2.0 litre to a final volume of 6.0 litre. What is the work done by gas?
Best answer
Answer: \(W \approx 1371\) J (\(1.371 \times 10^3\) J)
For an isothermal expansion of an ideal gas,
\[W = nRT\ln\frac{V_f}{V_i} = 2.303\,nRT\log_{10}\frac{V_f}{V_i}\]\[W = 2.303 \times 0.5 \times 8.319 \times 300 \times \log_{10}\frac{6.0}{2.0}\]\[W = 2.303 \times 1247.85 \times \log_{10}3 = 2.303 \times 1247.85 \times 0.4771 \approx 1371 \text{ J}\]The work is positive, as the gas does work on the surroundings while expanding.
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