Calculate work done if 1 mole of an ideal gas compressed isothermally and reversibly from 12 dm ^3 to 6 dm ^3 at 300 K . [ R =8 314 JK ⁻¹ ~mol ⁻¹ ]

Step-by-step solution

For an ideal gas undergoing isothermal reversible compression, the work done is given by W = -nRT ( V₂ V₁ ) . Substituting n = 1 mol , R = 8.314 J K ⁻¹ mol ⁻¹ , and T = 300 K , with V₁ = 12 dm ^3 , V₂ = 6 dm ^3 , the expression becomes W = -(1)(8.314)(300) ( 6 12 ) . Evaluating the numerical coefficient yields -2494.2 J . Since (0.5) -0.6931 , the work done is W = -2494.2 (-0.6931) 1728.8 J . Converting to kilojoules, W 1.7288 kJ , which rounds to 1.729 kJ to three decimal places. The work done is positive, consist