Second law of thermodynamics &
heat engines
Some processes one might imagine obey the first law of thermodynamics but still do not happen. For example, heat flows spontaneously from hot to cold but not from cold to hot even though this would conserve energy too. Other examples include ageing, dropping an egg, etc. .
The second law of thermodynamics shows why some imaginable things do not happen even though they conserve energy. In short, the second law concerns ordered and disordered forms of energy.
The mathematical statement of the second law comes in various forms. Sometimes it is stated in terms of entropy and other times in terms of heat engines.
· DSisolated > 0 (a statement of entropy non-conservation)
· It is impossible for a heat engine to have 100%
efficiency.
But what is entropy, S? The way this is defined in thermodynamics is very precise:
DS º ò dQ/T , where T must be in Kelvin.
rev
Notice the integral assumes a reversible process. A reversible process can be represented by a series of points in the PV plane, therefore, at each instant the system is near equilibrium. If a system undergoes a reversible process, at each step of the way we determine the heat injected, dQ, and divide by the absolute temperature, T. Then we sum this ratio up for the whole process. It is found that DS is a state function, so the change in entropy depends only on the initial and final states of the system, and not on the precise path connecting the two.
Free expansion is an example of an irreversible process.
Q = W = DEint = 0 but DS>0.
Later we will give several examples of exactly how to calculate entropy.
The second law can also be stated in terms of a heat engine. Indeed, thermodynamics was developed during the 1800’s when a great deal of interest in steam engines existed. (This was because the steam engine was the primary device of the Industrial Revolution; much like the PC is today in the Information Revolution.) In class we model this device by introducing low and high-temperature heat reservoirs and based on energy conservation we show,
|QH| = W + |QC| Þ W = |QH| - |QC|.
The efficiency , e, of the heat engine is the work you get out divided by the heat you had to provide, |QH|,
e º W/|QH| = 1 - |QC|/|QH|.
In terms of e, the second law of thermodynamics may be stated:
e < 1 Þ |QC| ¹ 0.
For a Carnot Heat Engine, which is reversible, e is max, and we prove in class,
emax = eC = 1 – TC/TH .