Estimation of Heat Capacity and Enthalpy [Shomate Equation]
It is an established method to calculate these thermo-chemistry data using polynomial
equations. There are many polynomial coefficients published in literature depending on the
equation adopted for regression. Of these, Shomate equation is one of the most used and
most accurate one. Literature related to Shomate equations is published in Journal of the
American Chemical Society. NIST –JANAF Thermo-chemical Tables is the guide for the
Shomate equations coefficients for various compounds. Coefficients may be accessed from
the NIST Chemistry Web Book whose access to public is not restricted.
Coding Shomate equation in EXCEL VBA with a good database of compounds can help
programming purposes. For many compounds regression is done piece wise and
coefficients are published for a temperature range. This makes it a little difficult to implement
for simpler instances. Nevertheless, it is worth to have a program based on this equation
which can further be used to estimate thermo-chemical properties of mixtures.
Polynomial forms of Shomate equation to estimate isobaric specific heat capacity and
specific enthalpy (NIST, 2008),
Cp,i  Ai  BiT  CiT 2  DiT 3  Ei T 2
4
hi  HT ,i  H298.15,i
T
BiT 2 CiT 3 DiT
 AiT 


 Ei T  Fi  Hi
2
3
4
Tg
1000
Cp, i= Specific heat capacity of compound I at temperature T. (J/mole/K)
HT, i = Specific Enthalpy of compound I at temperature T. (kJ/mole)
Tg = Temperature (K)
Works Cited
NIST. (2008). Water. Retrieved March 13, 2011, from NISTChemistry Web Book:
http://webbook.nist.gov/cgi/cbook.cgi?ID=C7732185&Units=SI&Mask=1#Thermo-Gas