3 The Second and Third Laws
of Thermodynamics: Entropy
PRINCIPAL FACTS AND IDEAS
1. There are two principal physical statements of the second law of
thermodynamics: (1) If a system undergoes a cyclic process it cannot turn
heat put into the system completely into work done on the surroundings.
(2) Heat cannot flow spontaneously from a cooler to a hotter object if
nothing else happens.
2. The second law implies that no heat engine can have an efficiency as
great as unity.
3. The mathematical statement of the second law establishes a new state
function, the entropy, denoted by S and defined through its differential by
dS
dq rev
T
4. The mathematical statement of the second law provides a means of
calculating the entropy change of any process that begins and ends at
equilibrium states.
5. The second law implies that no macroscopic process can decrease the
entropy of the universe.
6. Entropy is connected with lack of information through the Boltzmann
definition of the statistical entropy:
S st k B ln(Ω)
where k B is Boltzmann’s constant and Ω is the number of mechanical
states that corresponds to the thermodynamic state of the system,
corresponding to a fixed energy.
7. The third law of thermodynamics allows the entropy of any pure perfect
crystalline substance consistently to be set equal to zero at absolute zero
of temperature.
8. The second and third laws of thermodynamics imply that zero
temperature on the Kelvin scale is unattainable.
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