Physical Chemistry Third Edition

106 3 The Second and Third Laws of Thermodynamics: Entropy

3.1 The Second Law of Thermodynamics

and the Carnot Heat Engine

The statement of the first law of thermodynamics defines the internal energy and asserts

as a generalization of experiment fact that it is a state function. The second law of

thermodynamics establishes the entropy as a state function, but in a less direct way.

Physical Statements of the Second Law

There are two important physical statements of the second law of thermodynamics. The

Kelvin statementinvolvescyclic processes, which are processes in which the final state

of the system is the same as its initial state:It is impossible for a system to undergo a

cyclic process whose sole effects are the flow of an amount of heat from the surroundings

to the system and the performance of an equal amount of work on the surroundings.In

other words,it is impossible for a system to undergo a cyclic process that turns heat

completely into work done on the surroundings.

TheClausius statementis:It is impossible for a process to occur that has the

sole effect of removing a quantity of heat from an object at a lower temperature and

transferring this quantity of heat to an object at a higher temperature.In other words,

heat cannot flow spontaneously from a cooler to a hotter object if nothing else happens.

The Clausius statement of the second law is closely related to ordinary experience.

The Kelvin statement is less closely related, and it is remarkable that the statements are

equivalent to each other and to the mathematical statement of the second law, which

establishes that the entropy is a state function.

No violation of either physical statement of the second law of thermodynamics has

ever been observed in a properly done experiment. We regard the second law as a

summary and generalization of experimental fact. A machine that would violate the

Kelvin statement of the second law and turn heat completely into work in a cyclic

process is calleda perpetual motion machine of the second kind.

The Kelvin statement is named for
William Thomson, Lord Kelvin, already
mentioned in Chapters 1 and 2.

The Clausius statement is named for
Rudolf Julius Emmanuel Clausius,
1822–1888, a German physicist who is
generally considered to be the
discoverer of the second law of
thermodynamics.

The Clausius statement applies only to cyclic processes. Heat can be completely

turned into work done on the surroundings without violating the second law if the

system undergoes a process that is not cyclic. For example, in an isothermal reversible

expansion of an ideal gas∆U0, so that

wsurr−w∆U−qq (ideal gas, isothermal volume change) (3.1-1)

Heat transferred to the system has been completely turned into work done on the

surroundings. However, the process is not cyclic and there is no violation of the second

law of thermodynamics.

The Carnot Engine

TheCarnot heat engineis an imaginary model machine that Carnot devised in 1824 to

represent a steam engine. A simplesteamengineis depicted schematically in Figure 3.1a.

It has a cylinder with a piston connected to a crankshaft by a connecting rod. There is

an intake valve through which a boiler can inject high-pressure steam into the cylinder

and an exhaust valve through which spent steam can be exhausted into the atmosphere.

This steam engine operates with a two-stroke cycle. The cycle begins with the piston at

top dead center (the position of minimum volume in the cylinder) and with the intake