The Otto Cycle Practice Problems

A flagship gasoline engine has a compression ratio of 9.6. Determine the engine's theoretical efficiency. Take the heat capacity ratio as 1.4

What is the ideal efficiency of an internal combustion engine with a compression ratio of 12.5? Take C_p/C_v = 1.4

Otto cycle engines can be modeled as Carnot engines for simplicity. An otto cycle engine operates between T_H = 1750℃ and a surrounding temperature of 25℃ and attains 40% of the Carnot efficiency. Taking the heat of combustion of the fuel to be 44 MJ/Kg, determine the mass of fuel consumed by an engine in speeding up a 2750kg truck initially at rest to a speed of 60 mph.

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 increases and pushes the piston downward. Finally, during the exhaust stroke (D→A), the piston moves upward again,  expelling the exhaust gases from the cylinder through the exhaust valve. 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.

In a high-performance motorcycle engine, air mixed with fuel is compressed adiabatically in a cylinder before ignition. The engine operates on a process that closely follows the Otto cycle. The air-fuel mixture, which behaves as an ideal gas, enters the cylinder at a temperature of 30°C. Due to the ignition, the temperature subsequently reaches 600°C. Assuming the air-fuel mixture is diatomic, and given that the specific heat ratio γ for the gas is 1.4, calculate the maximum compression ratio of the motorcycle engine.