An ideal gas ( = 1.5 ) starting at 1 litre, 300 K , and 100 kPa is suddenly compressed to half its volume, then cooled at constant pressure back to 300 K . Finally, the gas is expanded isothermally until it achieves its original volume of 1 litre. Calculate the work done by the gas during this isothermal expansion.

Step-by-step solution

The gas undergoes an isothermal expansion at T = 300 K to reach its original volume V₄ = 1 litre . The initial volume for this process is found from the previous isobaric cooling where V₃ = V₂ T₃ T₂ = 0.5 300 300 2 = 1 2 2 litre . The work done in an isothermal process is W = nRT ! ( V₄ V₃ ) . Since nRT = P₁ V₁ = 100 J , the work equation becomes W = 100 ! ( 1 1 / (2 2 ) ) = 100 (2 2 ) . This simplifies to W = 100 (2^ 1.5 ) = 150 2 . Using 2 0.693 , the work done is 150 0.693 103.9 J .