Heat Engines, Entropy, & the Second Law

Gasoline Engine


The Otto cycle is a reasonable approximation to a common, four-stroke, internal combustion gasoline engine.

Intake (O -> A) Air-fuel mixture is drawn into the cylinder at ambient, atmospheric pressure. The volume of the cylinder increases from V2 to V1.

Compression (A -> B) The air-fuel mixtures is compressed adiabatically from volume V1 to volume V2. This is an adiabatic compression primarily because of its speed. Work is done on the gas ("gas" meaning air-fuel mixture, not "gasoline"); that work is the area under the curve from A to B. The temperature rises from TA to TB.

Combustion (B -> C) Heat Qh is added to the system by combusion of the fuel and oxygen. This causes the temperature and pressure to rise rapidly. At this point there is essentially no change in the volume so no work is done (yet!) as the system goes from state B to state C.

For a common automobile engine this combustion occurs because of a spark from the spark plug. For a diesel engine, this combustion occurs because the gas is compressed enough that the temperature becomes great enough to cause the combustion.

Power (C -> D) The gas expands adiabatically (again, primarily due to speed) from volume V2 to volume V1. Temperature and pressure decrease. Work is done as the gas expands. This work is the area under the curve between states C and D.

Exhaust (D -> A) An exhaust valve is opened, letting the pressure decrease. The expelled gas also carries with it exhaust heat Qc given to the ambient temperature reservoir.

Final Exhaust (A -> O) The rest of the gas is expelled and the volume decreases from V1 to V2.

The efficiency of an ideal Otto cycle engine is given by

Notice that increasing the compression ratio (V1/V2) increases the efficiency. The compression ratio of a typical, common automobile engine is about 8; for a high-performance engine, perhaps 10. The compression ratio for a diesel engine is about 20.

A compression ratio of 8 and a value of gamma of 1.4 gives a theoretical efficiency of 56%. That is, the efficiency of an Otto cycle engine would be 56%. Measured efficiencies of real internal combustion engines are usually below 20% and, perhaps, 40% for diesel engines.


Heat Pumps

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(c) Doug Davis, 2002; all rights reserved