2.19 Energy and temperature
Speciﬁc internal energy and temperature were described in Sec. 2.17 and Sec. 2.16 , respectively. They are related through the speciﬁc heat capacity , deﬁned by Eq. (2.61 ) in Sec. 2.18 .
Analyses involving heat usually incorporate both and since:
- is the measurable quantity speciﬁed as initial and boundary data and whose data is required as part of the “results”;
- is the calculated quantity solved in energy conservation, e.g. Eq. (2.51 ), but whose data is usually of no interest.
Conversion of values between and is therefore needed, and vice versa. Incorporating Eq. (2.61 ) into a deﬁnite integral for , , gives
For applications that cover a reasonably narrow temperature range, can be assumed constant. From Eq. (2.62 ), the relation becomes
The and values become important when the composition of a ﬂuid changes due to the mixing of constituent ﬂuid species, e.g. , , or chemical reactions, e.g. with . Each ﬂuid specie possesses a diﬀerent so any change to the specie concentrations will change of the overall ﬂuid.
In those circumstances, is commonly represented by the heat of formation per unit mass, . The standard heat of formation is the change of enthalpy during the formation of 1 mole of a substance from its constituent elements at standard temperature . Measured heats of formation are available for numerous ﬂuid species.20
If an analysis involves changes to ﬂuid composition, it can then adopt and for individual ﬂuid species, to account for the change in due to changes in the concentrations of ﬂuid species.