# Specific heat capacity of gas at constant pressure

The specific heat capacity of a material on a per mass basis is $c=\delta{C}/\delta{m}$. with $C$ being the heat capacity of a body made of the material and $m$ being the mass of the body.

For gases, there is need to distinguish between different boundary conditions for the processes under consideration. Typical processes for which a heat capacity may be defined include isobaric (constant pressure, d$P$ = 0) or isochoric (constant volume, d$V$ = 0) processes.

The sources are:

• Values for 0, 15, and 25°C were calculated with $c_p$ = $C_p/M_{mol}$ with the values from encyclopedia.airliquide.com
• Values for 50, 75, and 100°C are taken from nist.gov
• Values for 50, 75, and 100°C for dry air have been calculated using the equation from Irvine & Liley, 1984.
• Equation for humid air is taken from paper by P.T. Tsilingiris: 'Thermophysical and transport properties of humid air at temperature range between 0 and 100°C', 2007
• Equation for dry air is taken from paper by T.F. Irvine and P. Liley: 'Steam and gas tables with computer equations', 1984
• Equation for air is taken from paper by A. Dumas and M. Trancossi: 'Design of Exchangers Based on Heat Pipes for Hot Exhaust Thermal Flux, with the Capability of Thermal Shocks Absorption and Low Level Energy Recovery', 2009. They are calculated from polynomial curve fits to a data set for 100 K to 1600 K in the SFPE Handbook of Fire Protection Engineering, 2nd Edition Table B-2. You may find a free air property calculator from Pierre Bouteloup
• Equations for N2 and SF6 are taken from paper by J. Vermeer: 'A simple formula for the calculation of the convective heat transfer between conductor and sheath in compressed gas insulated (CGI) cables', 1983 as published in Elektra 87
• Values for N2 for 250–375 K are taken from the engineering toolbox .
• Values for CO2 for 250–375 K are taken from the engineering toolbox .
• Values for O2 for 250–375 K are taken from the engineering toolbox .
• Equations for CO2 and O2 are a linear interpolation of the values between 250 and 375 K.

Note: 1 J = 1 W.s

Symbol
$c_{p,gas}$
Unit
J/(kg.K)
Formulae
 ${10}^3\left(1.004571427+2.05063275{\cdot}{10}^{-3} \theta_{gas}-1.631537093{\cdot}{10}^{-4} {\theta_{gas}}^2+6.2123003{\cdot}{10}^{-6} {\theta_{gas}}^3-8.830478888{\cdot}{10}^{-8} {\theta_{gas}}^4+5.071307038{\cdot}{10}^{-10} {\theta_{gas}}^5\right)$ humid air @ 1 atm (Tsilingiris2007) $1.9327{\cdot}{10}^{-10} {T_{gas}}^4-7.9999{\cdot}{10}^{-7} {T_{gas}}^3+1.1407{\cdot}{10}^{-3} {T_{gas}}^2-4.489{\cdot}{10}^{-1} T_{gas}+1.0575{\cdot}{10}^3$ air @ 1 bar (Dumas&Trancossi2009) $1030.5-0.19975T_{gas}+3.9734{\cdot}{10}^{-4} {T_{gas}}^2$ air @ 1 bar (UW/MHTL 8406, 1984) ${10}^3\left(0.103409{\cdot}{10}^1-0.284887{\cdot}{10}^{-3} T_{gas}+0.7816818{\cdot}{10}^{-6} {T_{gas}}^2-0.4970786{\cdot}{10}^{-9} {T_{gas}}^3+0.1077024{\cdot}{10}^{-12} {T_{gas}}^4\right)$ dry air @ at 1 atm (Irvine&Liley1984) $1037+0.101\theta_{gas}$ N2 (Vermeer1983) $630+1.87\theta_{gas}-4.33{\cdot}{10}^{-3} {\theta_{gas}}^2$ SF6 (Vermeer1983) $539.52+1.0149\left(\theta_{gas}+\theta_{abs}\right)$ CO2 (linear interpolation) $868.62+1.1029\left(\theta_{gas}+\theta_{abs}\right)$ O2 (linear interpolation) $\frac{3}{2} R_{gas}$ Monoatomic ideal gas $\frac{7}{2} R_{gas}$ Diatomic molecule gas $4R_{gas}$ Polyatomic molecule gas
Related
$R_{gas}$
$T_{gas}$
$\theta_{abs}$
$\theta_{gas}$
Used in
$\alpha_{gas}$
$\lambda_{gas}$
$\mathrm{Pr}_{gas}$
$T_{conv,ce}$
$W_{a,L}$
Choices
GasFormula0°C15°C25°C50°C75°C100°C
Air78%N2+21%O2+minor1005.91006.21006.51008.51010.21012.9
N2N21041.41041.41041.41041.61042.21043.3
SF6SF6627.83652.96668.99706.12739.88770.06
CO2CO2826.84841.24850.85874.53897.43919.36
COCO1042.01042.01042.11042.81044.01045.8
O2O2916.72918.22919.62923.64928.66934.55
H2H214197.614267.614306.3143791442714458
NH3NH32179.52166.22164.52176.42203.02238.6
SO2SO2669.21658.98656.2657.12663.98673.57
HeHe5193.15192.95192.95193.05193.05193.0
ArAr521.85521.65521.55521.34521.18521.05
KrKr249.5249.31249.2248.99248.83248.71
XeXe160.67160.29160.09159.7159.43159.23
NeNe1030.41030.31030.31030.31030.31030.2