Mean Heat Capacity
As we have said earlier, both Cp and Cv are function of both the temperature and pressure. Despite that fact, we are much more interested in temperature dependence of heat capacity because most of the heat capacities are measured at constant pressure.
Mean heat capacity is the average heat capacity between two temperature of interest. It is given by an empirical temperature dependent equation. It is generally enclosed in angular brackets to identify as a mean value and follows with a subscript H or S to denote a mean value specific to enthalpy or entropy calculation. For Ideal gas state it takes the form:
Note: Temperature is in absolute units and the heat capacity takes the unit of R.
An insulated tank is divided into two compartments by an insulated wall. One side of it contains 1kg of liquid methanol at 40°C and the other side of it contains 1kg water at 80°C. The wall is removed and the liquids are well mixed and brought to thermodynamic equilibrium. Heat of mixing is negligible. What is the final temperature of the mixture if the specific heat capacity of water and methanol are constants and have the following values:
Cpwater = 4200 J/kgºC
CpMtOH = 4970 J/kgºC