A typical gas-powered generator that is used in portable power applications operates on the Otto cycle model. In this type of engine, the combustion chamber is typically a single cylinder with a piston that moves up and down to complete each of the four strokes. During the compression stroke (A→B), the piston moves up, compressing the air in the cylinder. This process is adiabatic, as there is no exchange of heat between the system and its surroundings. The temperature and pressure of the air increase, and the volume decreases as the piston moves upward. The spark plug ignites (B→C) the compressed air, causing it to rapidly combust and generate heat. The volume of the cylinder remains constant. During the power stroke (C→D), the pressure decreases and pushes the piston downward. Finally, during the exhaust stroke (D→A), the exhaust gases are expelled from the cylinder through the exhaust valve due to the high pressure, while the volume remains constant. This process is isochoric. At the end of the cycle the thermodynamic state at point A returns to its initial state. The Otto cycle in a gas-powered generator is a thermodynamic process that converts the chemical energy stored in the fuel into work. Calculate the work produced in terms of temperature at points A, B, C, and D, the number of mole n, the heat capacities ratio γ, and the gas constant R.
