One mole of an ideal gas with expands from and bar by each of the following paths:

Question

(a) Constant volume;
(b) Constant temperature;
(c) Adiabatically.

Assuming mechanical reversibility, calculate W, Q, ?U, and ?H for each process. Sketch each path on a single PV diagram.

Answer 1

(a) Constant volume expansion from 8 bar and 600 K to 1 bar. Since PV/T is constant for an ideal gas, when P decreases by a factor of 8, T will also decrease by a factor of 8 to maintain constant volume, so in this case the final temperature is 600/8 = 75 K. As for any constant volume process, the work done is zero (W = 0). The heat transfer required is



The change in internal energy is ?U = Q = -10910

The change in enthalpy is





(b) For isothermal expansion, we know that ?H = ?U = 0.

The heat flow required is



The work done is





(c) For adiabatic expansion, we have





So we have





By definition, Q = 0.

Finally, W = ?U = -5591.50



On a PV diagram, the three paths look like this: