MEAN HEAT CAPACITY

The empirical form for the temperature dependence of Cp is

Cp/R = A + BT + CT2 + D/T2 ,

where the constants A, B, C and D can be found for various gases in  Table 4.1 (pg. 109) of S&VN. Depending on the temperature range of interest, this variation can be significant (see Fig. 4.1 of S&VN, pg. 108).

Graph

The mean value over a temperature range can be defined in two useful ways:
 
 
FOR ENTHALPY   FOR ENTROPY
Formula
and
Formula

Substituting for Cp and integrating, we find

Some Calculations

Enthalpy and entropy changes at constant pressure are then calculated for 1 mol by

2 Formulae