3.6 Enthalpy
Consider some immediate application of the first law. Equation (23) may be written
for internally reversible, quasi-static processes as
dU ¼ dQ À pdV
ð25Þ
It is useful to introduce an alternative energy function, the enthalpy function
denoted by H,
7
H U þ pV
ð26Þ
It follows that
dH T; p
ð
Þ ¼ dU þ d pV
ð Þ ¼ dQ À pdV þ pdV þ Vdp ¼ dQ þ Vdp
ð27Þ
Taking the differential of the enthalpy function
dH ¼
@H
@T
p
dT þ
@H
@p
T
dp
ð28Þ
We shall see in the next section that enthalpy is a particularly useful function for
constant pressure processes.
3.7 Heat Capacity and Molar Heat Capacity
We now consider an infinitesimal transformation of a system, that is, a quasi-static
heating
8 of the system for which the change meets internal reversibility criterion
(see Sect. 6.5). Substituting Eq. (18A) into (25),
@U
@T
V
dT þ
@U
@V
T
þ p
!
dV ¼ dQ
ð29Þ
7
For an excellent introduction to the concept of enthalpy the reader is referred to The Laws of
Thermodynamics: A Very Short Introduction by Peter Atkins [4].
8
When heat is absorbed by a system, a change of temperature may or may not take place. For
instance, the evaporation of water as a result of heating is not accompanied by temperature change
(the constant temperature is called saturation temperature); heat, in this case, is referred to as latent
heat. Heating of water without phase change is accompanied by a temperature rise; heat, in this
case, is called sensible heat. The processes considered here are heating or cooling processes that
produce temperature change in systems.
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3 The First Law: The Production of Heat …