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.