A diesel engine accomplishes ignition without a spark plug...

A diesel engine accomplishes ignition without a spark plug by an adiabatic compression of air to a temperature above the ignition temperature of the diesel fuel, which is injected into the cylinder at the peak of the compression. Suppose air is taken into the cylinder at 280 $\mathrm{K}$ and volume $V_{1}$ and is compressed adiabatically to $560^{\circ} \mathrm{C} \approx 1000^{\circ} \mathrm{F}$ ) and volume $V_{2} .$ Assuming that the air behaves as an ideal gas whose ratio of $C_{P}$ to $C_{V}$ is $1.4,$ calculate the compression ratio $V_{1} / V_{2}$ of the engine.

A diesel engine accomplishes ignition without a spark plug
by an adiabatic compression of air to a temperature above
the ignition temperature of the diesel fuel, which is injected
into the cylinder at the peak of the compression. Suppose
air is taken into the cylinder at 280 $\mathrm{K}$ and volume $V_{1}$ and is
compressed adiabatically to $560^{\circ} \mathrm{C} \approx 1000^{\circ} \mathrm{F}$ ) and volume
$V_{2} .$ Assuming that the air behaves as an ideal gas whose
ratio of $C_{P}$ to $C_{V}$ is $1.4,$ calculate the compression ratio
$V_{1} / V_{2}$ of the engine.

Key Concepts

Adiabatic Process

An adiabatic process is one in which there is no heat transfer into or out of the system. In the context of engine cycles, during adiabatic compression the work done on compressing the air directly increases its internal energy, raising the temperature according to the relation between temperature and volume changes in an adiabatic process.

Ideal Gas Behavior

Ideal gas behavior assumes that a gas follows the ideal gas law, which relates pressure, volume, and temperature without considering molecular interactions. This assumption is used to simplify calculations involving adiabatic processes, where the relationship between temperature and volume is well-defined for an ideal gas.

Specific Heat Ratio (?)

The specific heat ratio, denoted by ? (gamma), is the ratio of the specific heat at constant pressure (C?) to that at constant volume (C?). It is crucial in determining the behavior of a gas during an adiabatic process, particularly in providing the exponent in the adiabatic relation between temperature and volume.

Compression Ratio

The compression ratio is defined as the ratio of the initial volume to the final compressed volume in a piston engine. It is an important parameter in engine design since it affects the temperature rise during compression; higher compression ratios typically lead to higher temperatures, which are necessary for achieving auto-ignition in diesel engines.

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