PHYSICAL CHEMISTRY IN BRIEF

CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 111

4.2 Heat

That portion of internal energy which can be exchanged between a system and its surroundings
only when there is a difference in temperature (while passing from a warmer to a cooler place)
is called heat. Heat is not a state function [see3.3.2], and consequently its value does not
depend on the initial (p 1 , V 1 ) and final (p 2 , V 2 ) state only, but also on the path. It is usually
calculated from the change of internal energy and work using the first law of thermodynamics
(3.3).
Q= ∆U−W. (4.13)

In the case of reversible processes, the Second Law of thermodynamics [see equations (3.6)] may
be also used to calculate heat, provided that we know the dependence between temperature
and entropy

Q=

∫S 2

S 1

TdS=T 2 S 2 −T 1 S 1 −

∫T 2

T 1

SdT. (4.14)

Several typical examples of heat calculation are given below.

• Adiabatic process
  Q= 0. (4.15)


• Isochoric process, no work done
  Q= ∆U=U(T 2 , V)−U(T 1 , V). (4.16)


• Isobaric process, only volume work done
  Q= ∆H=H(T 2 , p)−H(T 1 , p). (4.17)


• Isothermal reversible process, ideal gas

Q=−W=nRTln

V 2

V 1

=−nRTln

p 2

p 1

. (4.18)

• Isothermal reversible process, the van der Waals equation of state

Q=nRTln

V 2 −nb

V 1 −nb

. (4.19)

• General reversible isothermal process

Q=T

∫S 2

S 1

dS=T(S 2 −S 1 ) =T∆S. (4.20)