In a piston cylinder assembly, one cubic meter of an ideal gas at $600K$ and $1000$kPa expands to five

times its initial volume. Heat capacities are given as $C_v=\frac{5}{2}R$ and $C_p=\frac{7}{2}R.$

A$.$ Determine the number of moles of the ideal gas undergoing this expansion.

B$.$ The expansion is carried out along an adiabatic irreversible path against a

restraining pressure of $100$kPa. Determine:

a$).$ Work

b$).$ Final temperature.

c$).$ Final pressure.

C$.$ Now consider the case the expansion is carried out along an adiabatic reversible

path to five times the initial volume. Determine:

a$)$ Work

b$)$ Final temperature

c$)$ Final pressure

D$.$ Compare the results for the irreversible and reversible expansion. Are the temperature, pressure,

and the work done in the reversible process smaller or larger than the irreversible case?