Diesel Cycle

Calculate the efficiency of the Diesel cycle, consisting of two adiabats, 1→2 and 3→4, one isobar 2→3, and one constant-volume process 4→1 (see Figure 1.1). Assume C_V and C_P are constant.

Figure 1.1

SOLUTION

We calculate the efficiency η = W/Q. The work W in

the cycle (see Figure 1.2) is

(1)

where we have again used the ideal gas law PV = nRT and nR = C_P - C_V. The heat Q absorbed by the gas during 2 → 3 is

(2)

The efficiency is

(3)

Using the equation for the adiabats gives

(4)

Figure 1.2

The ideal gas law gives

(5)

Substituting (4) and (5) into (3) gives

(6)