Question

Three moles of ideal gas is compressed isothermally and reversibly to a volume of 2 dm³ . The work done is 2.984 kJ at 22°c. Calculate V₁ for the gas.

Answer 1

Given: n = 3 moles, W_max = 2.984 kJ, V₂= 2 dm³, R = 8.314 JK^-1 mol^-1,

T = 22°C + 273 = 295 K, V₁ = ?

Since compression, W_max is positive.

∴ ${\displaystyle W_{max}=2.303 nRT{\log }_{10} \frac{V_2}{V_1}}$

∴ ${\displaystyle 2.984=2.303\times 3\times 8.314\times 295\times {\log }_{10} \frac{2}{V_1}}$

∴ 2.984 = 2.303 x 3 x 8.314 x 295 x [log₁₀ (2) - log₁₀ (V₁)]

∴ [log₁₀ (2) - log₁₀ (V₁)]  

${\displaystyle =\frac{2.984}{2.303\times 3\times 8.314\times 295}}$

∴  [log₁₀ 2 - log₁₀ V₁] = 0.1760

∴ log₁₀ V₁ = 0.1760 - log₁₀ 2

∴ log₁₀ V₁ =  0.1760 - 0.3010

∴ log₁₀ V₁ = 0.4770

∴ V₁ = Antilog (0.4770)

∴ V₁ = 3 dm³