In an air standard Otto cycle, 1000 kJ kg^-1 net work is done. The maximum temperature in the

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In an air standard Otto cycle, 1000 kJ kg^-1 net work is...

In an air standard Otto cycle, $1000 \mathrm{~kJ} \mathrm{~kg}^{-1}$ net work is done. The maximum temperature in the cycle is $3200 \mathrm{~K}$ and the temperature at the end of the compression stroke is $800 \mathrm{~K}$. Calculate the compression ratio of the engine.

Key Concepts

Otto Cycle

The Otto cycle is an idealized thermodynamic cycle that represents the functioning of a spark-ignition internal combustion engine. It consists of four distinct processes: adiabatic (isentropic) compression, constant-volume heat addition, adiabatic (isentropic) expansion, and constant-volume heat rejection. The cycle is used to analyze engine performance, efficiency, and work output under the air-standard assumption.

Compression Ratio

The compression ratio in an engine cycle is defined as the ratio of the maximum cylinder volume (when the piston is at the bottom dead center) to the minimum cylinder volume (when the piston is at the top dead center). It is a key parameter in determining the thermal efficiency of the cycle, influencing the temperature rise during the adiabatic compression process according to the relation T2/T1 = r^(?-1) for an ideal gas.

Adiabatic Process

An adiabatic process is a thermodynamic process where no heat is transferred to or from the working fluid. In the context of the Otto cycle, both the compression and expansion strokes are ideally adiabatic, meaning that the temperature changes are due solely to changes in volume and pressure, and can be described by the relation between temperature and volume that depends on the specific heat ratio (?).

Air-Standard Assumption

The air-standard assumption simplifies the analysis of internal combustion engine cycles by treating the working fluid as an ideal gas (usually air) with constant specific heats. This assumption allows the use of simple thermodynamic relations to predict performance characteristics such as work output and thermal efficiency, without dealing with the complexities of real fuel combustion.

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