A gas is expanded from an initial state to a final state along a path that consists of (a) an isothermal expansion doing 40 ~J work, (b) an adiabatic expansion doing W work, (c) an isothermal expansion doing 30 ~J work. If the total change in the internal energy of the gas is -20 ~J , the work done by the gas during the adiabatic expansion W =

Step-by-step solution

Isothermal Expansion, In this process temperature remains constant. V =0 Using 1st law of thermodynamics Q ₁= V ₁+ W ₁ Q ₁= W ₁=40 ~J ... (1) Adiabatic expansion, In this process heat remains constant, Q₂=0 U ₂=- W ... (2) Isothermal expansion, aligned & W ₃=30 ~J & U ₃=0 aligned Q ₃= W ₃=30 ~J ...(3) Change in internal energy, V =-20 ~J It can be written as aligned & U ₁+ U ₂+ U ₃=-20 ~J & 0+ U ₂+0=-20 U ₂=-20 ~J aligned Now, using equation (2), aligned & W =- V ₂=20 ~J & ~W =20 ~J aligned