I am using the Redlich Kwong equation of state and I see that there is an option for
Redlick Kwong polynomial for Heat Capacity. What is this and how is the
Redlich Kwong Heat Capacity calculated?
The Redlich-Kwong heat capacity is calculated from the zero pressure polynomial valid for ideal gases
using analytical derivatives of the RK equation of state and the fundamental thermodynamic
relationships between state variables.
The ideal gas heat capacity is a function only of T. The RK heat capacity depends upon pressure
and temperature. A table of values is calculated over the default range of the Redlich Kwong library, or
by the range that the user has set in the GUI.
Since the RK equation of state is not explicit in V, the The procedure followed is this:
Cp is computed using this general relationship:
Cp = Cv + v*T*beta^2 / kappa
Beta and Kappa are estimated from analytic derivatives
of the EOS,
(dp/dT)_v and (dp/dv)_T.
beta = -1/v * (dp/dT)_v / (dp/dv)_T
Kappa = -1/v * 1 / (dp/dv)_T
Cv is given by:
Cv = (du/dT)_v
and u (internal energy) is given by:
u(T) = integral[T=T_ref:T=T] Cvo(T) dT
+ integral[v=v_ref:v=v] [T*(dp/dT)_v-p] dp
(du/dT)_v is taken analytically and Cvo(T) is calculated
Cvo(T) = Cpo(T) - R
Cpo(T)/R = a1 + a2*T + a3*T^2 + a4*T^3 + a5*T^4
is the ideal gas Cp polynomial for which the user provides the 5 "a" coefficients.