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.
Sisolated > 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:
S   dQ/T ,
rev
where T must be in Kelvin.
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 S 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 = Eint = 0 but S>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|

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  W/|QH| = 1 - |QC|/|QH|.
In terms of e, the second law of thermodynamics may be
stated:
e < 1  |QC|  0.
For a Carnot Heat Engine, which is reversible, e is max,
and we prove in class,
emax = eC = 1 – TC/TH .
EXAMPLES [in class]