PHYSICAL CHEMISTRY IN BRIEF

CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 102

The change in the Helmhotz energy with volume at constant temperature can be calculated
by integrating equation (3.35) with respect to the general prescription (3.31)

F(T, V 2 ) =F(T, V 1 )−

∫V 2

V 1

pdV , [T]. (3.93)

3.5.6.2 Changes at phase transitions

The changes of the Helmholtz energy at crystalline transformations, melting and boiling,
∆crystF, ∆fusFand ∆vapFduring reversible phase transitions are calculated from the relation

∆F=−p∆V , [T, p, reversible phase transition], (3.94)

where ∆V is the respective change in volume.
For irreversible phase transitions, we have the inequality
∆F <−p∆V , [T, p, irreversible phase transition]. (3.95)

In this case the change in the Helmhotz energy is calculated using the procedure described in
3.5.9.

Example

Calculate the change in the Helmholtz energy during reversible evaporation of 1.8 kg of liquid

water atT= 373.15 K andp= 101.325 kPa. Assume that in the given state the equation of

state of an ideal gas holds for water vapour, and that the volume of liquid water is negligible as

compared with that of vapour.

Solution

The assigned valuesTandpcorrespond to the normal boiling point [see7.1.5] of water, i.e. to a

reversible phase transition. Hence we use relation (3.94). The change in volume on evaporation,

based on the specification, is:

∆V=V(g)−V(l)

.

=V(g)=

nRT

p

,

where the amount of substance of water isn=^180018 = 100mol. Then

∆F=−∆V =− 100 × 8. 314 × 373 .15 =− 310 .24 kJ.