A 100 g sample of an ideal gas (molar mass = 20 g mol ⁻¹ ) is enclosed in a cylinder at a constant temperature of 300 K . It undergoes an isothermal reversible expansion such that its density drops from 2.0 g L ⁻¹ to 0.2 g L ⁻¹ . The heat absorbed by the gas during this process is _________ J . (Given: R = 8.3 J K ⁻¹ mol ⁻¹ , (10) = 2.3 )

Step-by-step solution

Number of moles of the gas: n = Mass Molar mass = 100 20 = 5 moles For a fixed mass of gas, the volume is inversely proportional to its density. Therefore, the ratio of final to initial volume is: V₂ V₁ = d₁ d₂ = 2.0 0.2 = 10 For an isothermal process of an ideal gas, the change in internal energy is zero ( U = 0 ). According to the first law of thermodynamics: U = q + W q = -W The work done in an isothermal reversible expansion is: W = -nRT ( V₂ V₁ ) Thus, the heat absorbed is: q = nRT ( V₂ V₁ ) q = 5 8.3 300 (10)