PHYSICAL CHEMISTRY IN BRIEF

CHAP. 13: PHYSICAL CHEMISTRY OF SURFACES [CONTENTS] 438

The value −T(∂γff/∂T) corresponds to the heat exchanged with the surroundings and
related to unit area. On changing the area by ∆Awe obtain

Q=−T

(

∂γff

∂T

)

∆A. (13.9)

Note:The total interfacial energy is far less dependent on temperature than the interfacial

tension itself.

Example

Determine the work, heat and internal energy change of water if its liquid-vapour interface area

increases by 2 m^2 at a temperature of 291 K. For water at 291 K we have:

γ= 73mN m−^1 ,(∂γ`g/∂T) =− 0. 145 mN m−^1 K−^1.

Solution

Work is given by relation (13.1), i.e.w=γ`g∆A, and thus

w= 73× 10 −^3 ·2 = 0. 146 N m= 0. 146 J.

Heat may be calculated from

Q=− 2 ·291 (− 0. 145 × 10 −^3 ) = 84. 4 × 10 −^3 J.

From the first law of thermodynamics(∆U=Q+W)we obtain

∆U= 0.146 + 0.0844 = 0. 2304 J.

It is obvious from the result that under normal circumstances, when the change of the surface

area is relatively small, we do not have to consider surface changes in relation to energy.