# Thermal Efficiency

Image that you have a cup of water. Now you use a shaft to stir the water. We know from our experience that water will get hotter. We conclude that the stirring work is converted to internal energy of the water.

But now let’s think about another situation. We place this shaft in the water and heat the water up. It is obvious that the shaft will remain still – no matter how much heat energy is transferred into water. In this case, the heat absorbed by water cannot be transformed into stirring work.

From these two simple examples, we can draw the following two conclusions:

1. work → heat: the convertion is spontaneous and no device is required.
2. heat → work: some kind of device is necessary to help us fulfill this convertion

Therefore, Heat Engine (HE) is designed to achieve the convertion from heat to work.

The heat engine can be characterized by the following figure: • The heat Q1 is transferred from heat source to heat engine. Relative to heat engine, Q1 is positive → Q1>0
• Heat engine (HE) rejects heat Q0 to heat sink. This amount of heat is, to some extent, waste heat, because not all the absorbed heat can be completely converted to work. This limitation is followed by Kelvin-Planck Statement. Relative to heat engine, Q0 is negative → Q0<0
• Heat engine converts part of absorbed heat to work. And this work can be calculated by balancing the energy transport (Law of energy conservation): ∑W= Q1+ Q0

Furthermore, heat engine operates on a cycle process running clockwise in p-V-diagram (and also in T-S-diagram): Even though, according to the second law of thermodynamics, no heat engine can convert all heat to work, we still expect that we could obtain more percentage of work output by a given amount of absorbed heat.

In order to measure the performance of a heat engine, the concept “thermal efficiency”, ηth, is introduced: We see from the equation that ηth is always less than 1 (ηth<1)