PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 108

• Isobaric process
  p= const =⇒ Wvol=−p(V 2 −V 1 ). (4.2)


• Isochoric process
  dV = 0 =⇒ Wvol= 0. (4.3)


• Isothermal process, the equation of state of an ideal gas
  p=nRT /V =⇒ Wvol=−nRTln(V 2 /V 1 ). (4.4)


• Isothermal process, the van der Waals equation of state

p=

nRT

V −nb

−

n^2 a

V^2

=⇒ Wvol=−nRTln

V 2 −nb

V 1 −nb

+n^2 a

(

1

V 1

−

1

V 2

)

. (4.5)

• Adiabatic process for which Poisson’s equations [see4.2.1] apply

p= constV−κ =⇒ Wvol=−

const

1 −κ

(

V 21 −κ−V 11 −κ

)

=CV(T 2 −T 1 ). (4.6)

4.1.2 Irreversible volume work

In this case the external pressurepexis different from the system pressurep. During expansion
it is lower and during compression higher than the system pressure. We have

Wvol=−

∫V 2

V 1

pexdV (4.7)

To calculate work we need to knowpex = f(V). The simplest case is a constant external
pressure. Then
pex= const =⇒ Wvol=−pex(V 2 −V 1 ) (4.8)

Note:Irreversible volume work is always higher than reversible volume work. Two cases

may occur:

• During irreversible compression, we have to supply more work to the system for
  compression from the initial volumeV 1 to the final volumeV 2 than in the case of
  reversible compression,


• During irreversible expansion, the work done (Wdone = −Wvol) is smaller than
  during reversible expansion, and consequently the supplied work is greater.