One mole of an ideal monoatomic gas initially at 300 K is expanded from an initial pressure of 10 atm to a final pressure of 1 atm. The molar heat capacity for constant volume for the gas is 32VCR=. Calculate dU, dH, q, w, and the final temperature (Tf) for each of the following paths:
(a) An expansion against a constant external pressure of 1 atm in a thermally isolated (adiabatic) system.
(b) An expansion against zero external pressure (against a vacuum) in an adiabatic system.