Heat Engines, Entropy, & the Second Law

Absolute Temperature

In discussing the Carnot engine or the Carnot cycle, we found that the ratio of the heat expended to the heat absorbed, Q_c/Q_h, is also equal to the ratio of the cold temperature to the hot temperature, T_c/T_h. That is,

T_c/T_h = Q_c/Q_h

We can use this to define a temperature. Let one of the temperature reservoirs be at, say, the triple point of water. That is,

T_h = T₃ = 273.16 K

Then,

T = (273.16 K) Q/Q₃

That is, if we operate a Carnot engine between an unknown temperature T and the triple point of water, T₃= 273.16 K, we find that heat Q is absorbed at the this unknown temperature T and heat Q₃ is expelled at the triple point heat reservoir. This unknown temperature T is then given by this equation.

Carnot Engine			Gasoline Engine
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(c) Doug Davis, 2002; all rights reserved