First slide

Work done by gas

Question

One mole of O₂ gas having a volume equal to 22.4 litres at 0°C and 1 atmospheric pressure in compressed isothermally so that its volume reduces to 11.2 litres. The work done in this process is

Easy

A

1672.5J
B

1728J
C

–1728J
D

–1572.5J

Solution

V₁ = 22.4 litres; V₂ = 11.2 litres
R = 8.314 J/mol - K
T = 273 + 0 = 273 K; n = 1 mole
$w = 2.303nRT\log \left( {\frac{{{V_2}}}{{{V_1}}}} \right)$
$= 1 \times 8.314 \times 273 \times 2.3026{\log _{10}}\left( {\frac{{11.2}}{{22.4}}} \right)$
$= 273 \times 2.3026 \times 8.314 \times ( - 0.3010)$
$= 8.314 \times 2.3026 \times 273 \times ( - 0.3010)$
$= - 1573.10 \approx - 1572.5J$
$W = nRT\,\,\,\ln \left( {\frac{{{v_f}}}{{{v_i}}}} \right)$
$= 1 \times 8.314 \times 273 \times \ln \left( {\frac{{11.2}}{{22.4}}} \right)$
= - 8.314 × 273 × 0.693 J
= - 1572.5 J

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