Page 71 - Instant notes

Entropy and change 57

‘The entropy of an isolated system increases for irreversible processes
and remains constant in the course of reversible processes. The entropy of
an isolated system never decreases’.

The second law of thermodynamics may be expressed in a large number of ways, but all
definitions are equivalent to the one given here. The statistical definition of entropy
helps visualization of the second law. As all spontaneous changes take place in such a
way as to increase the total entropy, it follows that they proceed so as to engineer the
chaotic (rather than ordered) dispersal of matter and energy:
∆S total≥0

The ‘>’ relation applies to irreversible processes, and the ‘=’ relation applies to reversible
processes (see Topic B4). It is important to appreciate that the second law of
thermodynamics as expressed above refers to an isolated system. Most experimental
systems cannot be regarded as being isolated, in which case the universe, being the next
largest container of our system, effectively becomes the isolated system. In this case, the
total entropy change is simply the sum of the entropy change in the system and in the
surroundings, and this total must be greater than or equal to zero to comply with the
second law of thermodynamics:
∆S system+∆S surroundings=∆S total≥0

For instance, the system entropy change in the reaction between hydrogen and fluorine
−1
−1
gases to generate liquid hydrogen fluoride is found to be −210 J K mol . Although this
represents a decrease in entropy, the reaction proceeds spontaneously because the total
entropy change is greater than zero. The positive entropy change arises because the
reaction is exothermic, and the heat lost to the surroundings causes ∆S surroundings to be
positive, and of greater magnitude than ∆S system.

Standard entropy change

Any non-equilibrium process leads to a change in entropy. As entropy is a state
function, the change may be calculated from the standard entropies of the initial and final
states of the system:

For a chemical reaction, for example, the standard entropy of reaction is therefore the
difference between the standard entropies of reactants and products, and may be
calculated from:

This expression resembles those used with other state functions, such as the enthalpy,
and despite the slightly simpler form, the similarity with expressions for enthalpy is even
closer than is initially evident. In the case of enthalpy for example, the corresponding
equation is