The second law of thermodynamics

The first law of thermodynamics relates the input of heat energy to the mechanical work that may be obtained from it. It says nothing about the way that this conversion may take place, however, nor does it put any restrictions on it.

The second law of thermodynamics states the way in which these changes of energy may take place. It is considered by many eminent scientists to be one of the most fundamental laws of Physics and yet in one of its forms it may be stated in the following very simple manner:

Two alternative ways of stating the second law are:

Entropy

To study the second law further we have to define a new quantity known as the entropy of a body.

In all heat engines energy is taken in as 'high grade energy' and only some of it is converted into useful work, the remainder being emitted as 'low grade energy' at a lower temperature.

The fundamental idea of an increase of the entropy of a system can give us a way of checking the passage of time. Physicists call this the 'arrow of time' that tells us that time is passing and in 'which direction'. For example if you watch a film of a pile of bricks falling over it is easy to tell if the film is being run backwards since in only one case is the entropy or disorder increasing. Mixing hot and cold water to give a bucket of lukewarm water shows an entropy increase - you would not expect the lukewarm water to 'unmix' itself!

It is important to refer back to the original definition of the second law and notice the word 'isolated'. Human intervention is 'not allowed' to rebuild the pile of bricks. However even with human help it is not easy to see how we could 'unmix' the water!

We can put this idea on a cosmic scale. If we look into the universe we see discrete sources of energy - the stars. As time passes their energy is being spread out throughout space and if we could return many aeons in the future we would find this energy smeared out through the universe. Hot spots and cold spots have degenerated into a warm sea of energy. The entropy and hence the disorder of the universe would have increased. The second law of thermodynamics therefore relates to what physicists call the 'heat death' of the universe.

The entropy is best considered as a measure of the disorder of the body and you will see later that the total entropy of the universe can never decrease, only remain constant (for a reversible process) or increase (for an irreversible change).

The entropy change (ΔS) of a system is defined as follows:

DS= integral [dQ/T]
where dQ is the heat taken in by the system at temperature T and the integral is taken from state 1 to state 2.

If the change occurs at a fixed temperature - that is, an isothermal change - then:

For example, the entropy change of 1 kg of ice when it turns to water at 273 K is the latent heat of fusion Q divided by the temperature and is 1223 J K^-1.

It is easy to show that the change of entropy is consistent with the second law of thermodynamics Let a hot body give out heat Q at temperature T₁ and let this heat be absorbed by a cold body at T₂ (where T₁ is obviously greater than T₂).

Now the entropy change of the universe is given by:


and since T₁ > T₂ there is a net increase in entropy of the universe. This entropy increase is consistent with heat being able to pass from a hot body to a cold one.

The first law of thermodynamics is thus a law of energy while the second law of thermodynamics is a law of entropy.