14.3. Second Law of Thermodynamics http://www.ck12.org
Check Your Understanding
- In the unlikely event of the boiler room of a steamship reaching the same temperature as the steam in the steam
engine, what would the efficiency of the steam engine be?
Answer: Since there is no temperature difference between the outside environment (the room) and the environment
inside (the steam engine) the efficiency would be zero; the engine could perform no work.e=
(
1 −TTLH
)
× 100 =
(
1 −TTHH
)
× 100 = ( 1 − 1 )× 100 =0.
- What is the theoretical (ideal) efficiency of a heat engine withTL= 20 ◦C andTH= 125 ◦C?
Answer: The temperature must be expressed in Kelvin so
TL= 20 + 273 = 293 ◦K andTH= 125 + 273 = 398 ◦K
e=
(
1 −TTLH
)
× 100 =
(
1 −^293398
)
× 100 = 26. 38 → 26 .4%
- What is the ideal efficiency of a heat engine if the maximum increase in temperature achievable for the heat engine
is 75% of its low temperature?
Answer: IfTLis the low temperature of the heat engine then high temperature is
TH=TL+ 0. 75 TL= 1. 75 TL
e=(
1 −
TL
1. 75 TL
)
× 100 =
(
1 −
1
1. 75
)
× 100 = 42 .9%
Entropy and the Second Law of Thermodynamics
Building on the work of Sadi Carnot, the German physicist Rudolf Clausius (1822-1888), formulated the second law
of thermodynamics in 1865 by introducing the concept ofentropy.
Consider an isolated system composed of a box containing a hot object and a cold object separated by a layer of air.
As heat flows from the hot object to cold object, a pinwheel placed between them will turn (work is done on the
pinwheel) due to the movement of the warm air. Eventually, the hot and cold objects will reach the same temperature.
The heat will stop flowing and the pinwheel will no longer turn. Work will no longer be possible, yet the energy of
system has not changed. How can it be that the same energy is available but work can no longer be performed? It is
not the energy that matters here; it is thedifferencein energy levels.
In general, when there is a difference in energy levels there is a difference in the how “ordered” the system is. The
order of a system is a measure ofentropyof the system.The most general statement of the second law is: For all
natural processes the total entropy of a system increases. It may be that certainpartsof the system may become
more ordered, but this order will be more than offset by an increase in disorder in other parts of the system.
The sun supplies the necessary energy for flowers to grow, thus sustaining a very ordered biological system. But
the disorder the sun suffers in releasing enormous amounts of energy will eventually cause its demise (don’t worry,
we still have at least a billion of years left... as far as the sun is concerned). The result is an increase in entropy
(disorder) for the flower-sun system.
Generally, a solid is a more ordered system than a liquid, and a liquid more ordered than a gas because of the
arrangement of the atoms in these states of matter. A solid has a very rigid (orderly) arrangement of particles, a
liquid not quite as rigid (less orderly) and a gas the least orderly arrangement since there is almost no binding of the
particles to each other. Yet we can still speak of a gas with increasing disorder. For example, a hot gas dispersing
into the space around it goes from a more concentrated orderly arrangement to a more disorganized less concentrated
arrangement.
But entropy need not be restricted to the physical arrangement of real particles. The amount of entropy in a system