Page 154 - Advanced Thermodynamics for Engineers, Second Edition

CHAPTER

GENERAL THERMODYNAMIC

RELATIONSHIPS: FOR SINGLE 7

COMPONENT SYSTEMS OR

SYSTEMS OF CONSTANT

COMPOSITION

The relationships which follow are based on single component systems or systems of constant
composition. These are a subset of the more general equations which can be derived, and which allow
for changes in composition. It will be shown in Chapter 12 that if a change in composition occurs then
another term called chemical potential, m, which defines the effect of this change is required.

7.1 THE MAXWELL RELATIONSHIPS
The concept of functional relationships between properties was introduced previously. For example,
the Second Law states that, for a reversible process, T, s, u, p and v are related in the following manner.
TdS ¼ dU þ pdV (7.1)

or, in specific (or molar) terms
Tds ¼ du þ pdv (7.1a)
Rearranging Eqn (7.1a) enables the change of internal energy, du, to be written as
du ¼ Tds pdv (7.2)

i.e.
u ¼ fðs; vÞ (7.2a)
It will be shown that in Chapter 12, in the general case where the composition can change,
Eqn (7.1) should be written as

X
TdS ¼ du þ pdV m dn i (7.1b)
i
i
where,
m i ¼ chemical potential of component i and
n i ¼ amount of component i.

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