An air-standard cycle is executed within a closed piston–cylinder system and consists of three processes as follows:

1-2 

V = constant heat addition from 100 kPa and 27°C to 850 kPa

2-3 

Isothermal expansion until V₃ = 7V₂

3-1 

P = constant heat rejection to the initial state

Assume air has constant properties with c_v = 0.718 kJ/kg·K,

c_p = 1.005 kJ/kg·K, R = 0.287 kJ/kg·K, and k = 1.4.

(a) Sketch the P-v and T-s diagrams for the cycle.

(b) Determine the ratio of the compression work to the expansion work (the back work ratio).

(c) Determine the cycle thermal efficiency.