A system is made up of a vertical cylinder which is sealed at the top and closed by a piston at the bottom. A valve A controls the intake of gas at the top and an exhaust valve B (also at the top) is held back by a spring that exerts a constant pressure p2 on the valve. The system goes through the following processes:• 0−→ 1: the piston is at the top of the cylinder; valve A opens up and the piston is lowered into it so that some of the gas at atmospheric pressure p0 = p1 is added to the cylinder. The gas is at room temperature T1. Valve B is closed. The maximum volume occupied by the incoming gas is V1.• 1−→ 2: Valve A is now closed and the piston moves upward, fast enough so that the process can be considered adiabatic. Valve B remains closed as long as the pressure during the rise of the piston is lower than p2. As the piston continues in its rise, the gas reaches pressure p2 = 10 p1, at a temperature T2 in a volume V2. Assume a reversible adiabatic process for which equations (5.90) and (5.83)  apply.• 2−→ 3: As the piston keeps moving up, valve B opens up, the pressure is p3 = p2 and the gas is released in the environment while valve A still remains closed until the piston reaches the top, where V3 = V0 = 0.• 3−→ 0: Valve B closes and valve A opens up. The system is ready to start over again. Analyse this cycle by using the following instructions:a) Draw the (p, V) diagram for the three processes that the system is undergoing.b) Determine the temperature T2 and the volume V2.c) Find the work W performed per cycle. Numerical Application:

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Vo = V3 = 0, Po = P₁ = 105 Pa, V₁ = 0.25 1, T₁ = 27° C and y = 1.4.