Conceptual Physics

Third: The gas expands adiabatically, moving the piston to do work.

Fourth: Finally, there is an “exhaust” step involving both an up and a down stroke of the

piston where the combusted mixture in the cylinder is replaced through some valves by

a fresh mixture of air and gasoline at lower pressure and temperature. The piston

moves in and out, but it returns to its original position so this is considered a constant-

volume process, as shown on the pressure-volume graph. The cycle then begins again.

The theoretical efficiency of the engine can be computed as shown in Equation 1 on the

right. Vmax is the volume of the cylinder when the piston is “out”. That is the maximum

volume, and Vmin is the minimum volume. The ratio of the molar specific heats for the

air-fuel mixture CP/CV is indicated by Ȗ (the Greek letter gamma). The ratio Vmax/Vminis

called the compression ratio of the engine. The higher the compression ratio, the more

efficient the engine.

In Example 1 on the right, you see an example problem that computes the theoretical

efficiency of a typical car engine. The actual efficiency of real car engines ranges from

20-26%, less than the equation predicts, due to the heat expelled from the engine and

other factors.

You may be familiar with octane ratings for gasoline. Typical octane ratings, as seen on

the pumps at gas stations, are in the range of 85 to 95. The octane rating of a gasoline

indicates the tendency of the gasoline-air mixture to self ignite when it is compressed.

The higher the octane rating, the more compression the mixture can withstand before

combusting spontaneously. High compression gasoline engines require high octane fuel

to prevent “knocking” that occurs when the fuel mixture in the cylinder ignites before the

compression cycle is complete, creating a shockwave that collides with the piston.

A diesel engine operates in a similar fashion to a gasoline engine, but does not require

a spark plug. Instead, air alone is compressed in the cylinder, causing it to reach very a

high temperature. Then, fuel is injected into the cylinder, where it is ignited due to the

high temperature. To create the high temperature needed to ignite the fuel, diesel

engines have higher compression ratios than typical gasoline engines. This means they

are more efficient than gasoline engines.

·Mixture expands, doing work

·“Exhaust” expelled, new air/gasoline

injected

Otto cycle efficiency

eice = efficiency of internal combustion

engine

Vmax = max volume of cylinder

Vmin = min volume of cylinder

Vmax/ Vmin is "compression ratio"

Ȗ = CP/CV, ratio of molar specific heats

(^392) Copyright 2007 Kinetic Books Co. Chapter 21