In the companion Part 1 of this two-part series paper several improvements to the mathematical model of the energy conversion processes, taking place in a diesel engine cylinder, have been proposed. Analytical mathematical dependencies between thermal parameters (pressure, temperature, volume) and caloric parameters (internal energy, enthalpy, specific heat capacities) have been obtained. These equations have been used to provide an improved mathematical model of diesel engine indicator process. The model is based on the first law of thermodynamics, by taking into account imperfections in the working media which appear when working under high pressures and temperatures. The numerical solution of the simultaneous differential equations is obtained by Runge-Kutta type method. The results show that there are significant differences between the values calculated by equations for ideal gas and real gas under conditions of high pressures and temperatures. These equations are then used to solve the desired practical problem in two different two-stroke turbo-charged engines (8DKRN 74/160 and Sulzer-RLB66). The numerical experiments show that if the pressure is above 8 to 9 MPa, the working medium imperfections must be taken into consideration. The mathematical model presented here can also be used to model combustion process of other thermal engines, such as advanced gas turbine engines and rockets.