Topic 10.3

Second Law of Thermodynamics and Entropy

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

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

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

…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.

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.

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.

Change in EntropyThe 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

ExampleA 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:

SolutionSince 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.

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.

That is

S = SS + Senv > 0

The Second Law of Thermodynamics

In terms of entropy, the Second Law of Thermodynamics can be stated as:

1.The total entropy of any system plus that of its environment increases as a result of all natural processes2.The entropy of the Universe increases3.Natural processes tend to move toward a state of greater disorder.

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

• 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.

Explanation

• 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

•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.

•Entropy indicates the direction in which processes occur.

•Hence entropy is often called the arrow of time.

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.

• 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.

• 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.

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.

• 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.