Two moles of an ideal gas expand isothermally from an initial pressure of 10 bar to a final pressure of 1 bar at 300 K . What is the magnitude of the difference between the work done if the process is carried out reversibly and the work done if it is carried out irreversibly against a constant external pressure of 1 bar ? (Given: R = 8.3 J K ⁻¹ mol ⁻¹ , 10 = 2.3 )

Step-by-step solution

First, calculate the work done during the reversible isothermal expansion ( w_ rev ): w_ rev = -nRT ( P₁ P₂ ) w_ rev = -2 8.3 300 ( 10 1 ) w_ rev = -4980 2.3 = -11454 J Next, calculate the work done during the irreversible isothermal expansion ( w_ irr ) against a constant external pressure P_ ext = 1 bar : w_ irr = -P_ ext (V₂ - V₁) Using the ideal gas law V = nRT P , we can substitute the volumes: w_ irr = -P_ ext ( nRT P₂ - nRT P₁ ) Since the external pressure equals the final pressure ( P_ ext = P₂ ): w_ irr =