Answer to Question #158899 in Physical Chemistry for ved

Question

Show and explain why that the final volume in adiabatic expansion of an

ideal gas is smaller than the isothermal expansion for the same change in

pressure.

Answer 1

Basic equation: dU = dQ - dW.

In isothermal expansion, temperature is held constant, therefore the change in energy is zero (dU = 0). So, all the heat absorbed (dQ) by the gas equals the work (dW) done by the ideal gas on its surroundings: dQ = pdV (greater work, greater volume change).

In adiabatic expansion, dQ = 0, thus dU = -dW. Less work is done, because it’s not possible to transfer all eternal energy into work. So, final volume is lesser.