1. The second law of thermodynamics states that it is impossible to convert all heat into work in a cyclic process or to transfer heat from a colder to a hotter body without a net change occurring elsewhere. 2. Entropy provides a quantitative measure of disorder or randomness in a system. The total entropy of a system and its surroundings always increases according to the second law. 3. Irreversible processes, such as friction or heat transfer across a temperature difference, result in increased entropy and disorder as the system and its surroundings evolve toward thermal equilibrium.

1. Topic 10.3
Second Law of Thermodynamics
and Entropy

2. The 2nd Law of Thermodynamics
• Heat can be completely converted into work in a single process
• but continuous conversion of heat in to work requires a cyclic
process ( a heat engine)
• All attempts to construct a heat engine that is 100% efficient
have failed
• The Kelvin- Planck statement of the 2nd Law of
thermodynamics is a qualitative statement of the impossibility
of certain types of processes

3. The Law states….
• It is impossible for an engine working in a cycle to
transform a given amount of heat from a reservoir
completely into work
or
• Not all the thermal energy in a thermal system is
available to do work

4. The Clausius Statement
• No device has been observed for which W=0
• This leads to a second way to state the second Law of
Thermodynamics
• It is impossible to make a cyclic engine whose only
effect is to transfer thermal energy from a colder
body to a hotter body

6. …and The Second Law of
Thermodynamics
• Recall that in thermodynamics, a system in an
equilibrium state is characterised by its state
variables.
• p, V, T, U, n ..
• The change in a state variable for a complete cycle
is zero.
• In contrast, the net thermal energy and net work
factors for a cycle are not equal to zero.

7. History
• In the latter half of the nineteenth century, Rudolf
Clausius proposed a general statement of the
second Law in terms of a quantity called entropy.

8. Entropy
• Is a thermodynamic function of the state of the
system
• Can be interpreted as the amount of order or disorder
of a system
• As with internal energy, it is the change in entropy is
important and not its absolute value.

9. Change in Entropy
The change in entropy ∆S of a system when an amount
of thermal energy Q is added to a system by a
reversible process at constant absolute temperature T
is given by:
∆S = Q / T
The units of the change in entropy are JK-1

10. Example
A heat engine removes 100 J each cycle from a heat
reservoir at 400 K and exhausts 85 J of thermal energy
to a reservoir at 300 K.
Compute the change in entropy for each reservoir:

11. Solution
Since the hot reservoir loses heat, we have that:
∆S = Q / T = -100 J / 400 K = -0.25 JK-1
For the cold reservoir we have:
∆S=Q/T = 85 J / 300 K = 0.283 JK-1
Therefore:
The increase in entropy of the cold reservoir is
greater than the decrease for the hot reservoir.

12. Natural Systems
• In this example and all other cases, it has been found
that the total entropy increases.
• This infers that total entropy increases in all natural
systems.
• The entropy of a given system can increase or decrease
but the change in entropy of the system ∆S, plus the
change in entropy of the environment ∆Senv must be
greater than or equal to zero.

13. That is
∆ S = ∆SS + ∆ Senv > 0

14. The Second Law of Thermodynamics
In terms of entropy, the Second Law of Thermodynamics
can be stated as:
3.The total entropy of any system plus that of its
environment increases as a result of all natural processes
4.The entropy of the Universe increases
5.Natural processes tend to move toward a state of
greater disorder.

15. Irreversible processes
 A block of ice can slide down an incline plane if the frictional
force is overcome
 But the ice cannot spontaneously move up the incline of its
own accord
 The conversion of mechanical energy to thermal energy by
friction as it slides is irreversible

16. Explanation
• If the thermal energy could be converted completely
to mechanical energy, the Kelvin-Planck statement of
the second Law would be violated.
• In terms of entropy, the system tends to greater
disorder, and the entropy increases.
• In another case, the conduction of thermal energy
from a hot body to a cold body is irreversible.

17. • Flow of thermal energy completely from a
cold body to a hot body violates the Clausius
statement of the Second Law.
• In terms of entropy, a hot body causes
greater disorder of the cold body and the
entropy increases.
• If thermal energy was given by a cold body
to a hot body there would be greater order
in the hot body

18. • And the entropy would decrease.
• This is not allowed by the Second Law.
• Irreversibility can also occur if there is
turbulence or an explosion causing a non-
equilibrium state of the gaseous system.
• The degree of disorder increases and the
entropy increases.

19. • Entropy indicates the direction in which
processes occur.
• Hence entropy is often called the arrow
of time.

20. Statistical approach
• This was first applied to the definition of entropy
by Ludwig Boltzmann (1844-1906).
• If a coin is flipped 100 times, it is not improbable
for the one hundred coins to land heads up.
• But it is highly improbable.
• The probability of rolling 100 sixes from 100 dice
is even less.

21. • A small sample of a gas contains billions of
molecules and the molecules have many
possible microstates.
• It is impossible to know the position and
velocity of each molecule at a given point in
time.

22. • The probability that these microstates suddenly
coming together into some improbable
arrangement is infinitesimal.
• In reality, the macrostate is the only measurable
part of the system.
• The Second Law in terms of probability does not
infer that a decrease in entropy is not allowed but
it suggests that the probability of this occurring is
low.

23. Heat Degradation
• A final consequence of the Second Law is the heat
degradation of the Universe.
• It can be reasoned that in any natural process,
some energy becomes unavailable to do useful
work.
• An outcome of this suggests that the Universe will
eventually reach a state of maximum disorder.

24. • An equilibrium temperature will be reached
and no work will be able to be done.
• All change of state will cease as all the energy
in the Universe becomes degraded to thermal
energy.
• This point in time is often referred to the heat
death of the Universe.