PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 109

Example

Determine work during expansion into vacuum.

Solution

In this casepex= 0. According to relation (4.8),Wvol= 0.

4.1.3 Other kinds of work

• Surface work—work connected with a change of the system surface from the initial value
  A 1 to the final valueA 2. We have

Wsurf=

∫A 2

A 1

γdA , (4.9)

whereγis the surface tension.

• Electrical work—work connected with the transfer of electric chargeQacross the poten-
  tial differenceE. We have
  Wel=−

∫Q

0

EdQ. (4.10)

4.1.4 Shaft work.

Shaft workWshis defined by the relation

Wsh=

∫p 2

p 1

Vdp. (4.11)

Using the relation for the total differential of the product of two functions (3.29) we obtain

Vdp= d(pV)−pdV

and after integration we arrive at the relation between shaft work and volume work

Wsh=p 2 V 2 −p 1 V 1 −

∫V 2

V 1

pdV =p 2 V 2 −p 1 V 1 +Wvol. (4.12)