Ten liters of a monoatomic ideal gas at 25^o C and 10 atm pressure are expanded to a final pressure of 1 atm. The molar heat capacity of the gas at constant volume, Cv, is 3/2R and is independent of temperature. Calculate the work done, the heat absorbed, and the change in U and H for the gas if the process is carried out

(1) isothermally and reversibly, and

(2) adiabatically and reversibly.

Having determined the final state of the gas after the reversible adiabatic expansion, verify that the change in U for the process is independent of the path taken between the initial and final states by considering the process to be carried out as:

i. An isothermal process followed by a constant-volume process

ii. A constant-volume process followed by an isothermal process

iii. An isothermal process followed by a constant-pressure process

iv. A constant-volume process followed by a constant-pressure process

v. A constant-pressure process followed by a constant-volume process