Consider 1 mol of ideal gas expanding from V to 2V at temperature T. (a) Find the work done in a reversible isothermal expansion. (b) In a free expansion into vacuum, how much work is done? (c) Which produces more work, and why? Solution: (a) W_rev = n R T ln(2V/V) = R T ln 2 = 0.693 R T. (b) Free expansion against zero external pressure: W = 0. (c) The reversible expansion produces more work (0.693 RT vs 0) because every bit of pressure pushes the piston in a controlled way; in free expansion the pressure pushes against nothing and the work opportunity is wasted as entropy.