Calculate the work done if 1 mole of certain gas compressed isothermally and reversibly at 300 K from initial pressure x bar to final pressure 2 x bar [ R =8 314 ~J ~K ⁻¹ ~mol ⁻¹ ]

Step-by-step solution

Work during isothermal reversible compression of an ideal gas: The work done is given by W = - nRT ( P ₁ P ₂ ) . Substituting the given values: n = 1 mol , T = 300 K , R = 8.314 J K ⁻¹ mol ⁻¹ , and P ₁ P ₂ = x 2x = 1 2 . W = -(1) (8.314) (300) ( 1 2 ) W = -2494.2 ( 1 2 ) Since ( 1 2 ) = - (2) -0.6931 : W = -2494.2 (-0.6931) = 1728.86 J Converting to kilojoules: W = 1.72886 kJ 1.729 kJ The positive value indicates work is done on the system during compression, and this matches option A. A