A cylindrical pipe contains a movable piston that traps 2.00 mols of air. Originally, the air is at one atmosphere of pressure, a volume V_{0}, and at a temperature of T_{0}=298 \mathrm{~K}. First (process A) the air in the cylinder is compressed at constant temperature to a volume of \frac{1}{4} V_{0}. Then (process B) the air is allowed to expand adiabatically to a volume of V=15.0 \mathrm{~L}. After this (process C) this piston is withdrawn allowing the gas to expand to the original volume V_{0} while maintaining a constant temperature. Finally (process D) while maintaining a fixed volume, the gas is allowed to return to the original temperature T_{0}. Assume air is a diatomic ideal gas, no air flows into, or out of, the pipe at any time, and that the temperature outside the remains constant always. Possibly useful information: C_{p}=\frac{7}{2} R, C_{v}=\frac{5}{2} R, 1 \mathrm{~atm}=1.01 \times 10^{5} \mathrm{~Pa}.
a. Draw a P-V diagram of the whole process.
b. How much work is done on the trapped air during process A?
c. What is the temperature of the air at the end of process B?