Consider the adiabatic expansion of 0.500 mol of an ideal monatomic gas with C_{V ,m} = 3/2R. The initial state is described by P = 6.25 bar and T = 300.K. 

a. Calculate the final temperature if the gas undergoes a reversible adiabatic expansion to a final pressure of P = 1.25 bar. 

b. Calculate the final temperature if the same gas undergoes an adiabatic expansion against an external pressure of P = 1.25 bar to a final pressure P = 1.25 bar.

Explain the difference in your results for parts (a) and (b).