The Second Law of Thermodynamics
The first law of thermodynamics identifies the possible processes: Those whose value of internal energy U, remains constant for an isolated system; The second law identifies spontaneous processes. The Second Law of thermodynamics, may be expressed in terms of another state function, the entropy, S. Clausius introduced the state function S in 1854 and called it the transformation content (Verwandlungsinhalt). Later, he renamed it entropy, from the Greek words εν (“inside”) and τροπή “transformation,” since S is related to the transformation of heat to work. It is defined in terms of its change dS as the ratio of the heat change to the temperature at which the heat change takes place i.e.,
dS = δqrev/T (2.1)
where qrev, represents the heat absorbed reversibly by an infenitesimal portion of the system at temperature T.
The content of the second law is
The entropy of an isolated system increases in irreversible processes and remains constant if the process is reversible.
ΔStot ≥ 0
the total entropy variation is the sum of the variation of entropies of the system and the environment.
ΔStot = ΔSsys + ΔSenv
All spontaneous processes are thermodynamically irreversible. Thermodynamic processes that occur in nature are all irreversible processes. These are processes that proceed spontaneously in one direction but not the other.
Entropy variation of the surroundings
We have focused on the entropy change of an isolated system and can properly label the ΔS, as ΔSsys . What about the entropy change of the surroundings, labeled ΔSsurr? We suggest that, parallel to equation 2.1, the entropy change of the surroundings is
dSsurr ≡ δqsurr/Tsurr
Typically, the surroundings are much larger than the system of interest, and the temperature of the relatively large surroundings can be taken as constant. Thus, this equation integrates to
ΔSsurr = δqsurr/Tsurr
For a reversible change, ΔSsurr equals ΔSsys, so the overall ΔSuniv equals zero. However, for an irreversible change, ΔSsurr always has a larger magnitude than ΔSsys, and the overall ΔSuniv will always be greater than zero.