Determine thermal efficiency of an ideal diesel cycle

Question

Response to the following problem:

Show that the thermal efficiency of an ideal Diesel cycle is given by

η = (1 - 1/γ) [(1/r_E)^γ  - (1/r_c)^γ / (1/r_E) - (1/r_c)]

Where the ratio r_c = V_I/V₂ is called the compression ratio and the ratio r_E = V₃/V₂ is called the expansion atio for a diesel engine. The compression ratio of a diesel engine is much larger than that of a gasoline engine, because there is no preignition as only air is being compressed. Take r_c = 20, r_s = 5, and, ϒ = 1.4 and calculate the thermal efficiency.