# Specific heat capacity 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$^{\circ}$C were calculated with $c_p = C_p/M_{mol}$ with the values from encyclopedia.airliquide.com
• 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$^{\circ}$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
 $5.071307038 \cdot 10^{-7} \theta_{air}^{5} - 8.830478888 \cdot 10^{-5} \theta_{air}^{4} + 0.0062123003 \theta_{air}^{3} - 0.1631537093 \theta_{air}^{2} + 2.05063275 \theta_{air} + 1004.571427$ humid air @ 1 atm (Tsilingiris2007) $1.9327 \cdot 10^{-10} T_{air}^{4} - 7.9999 \cdot 10^{-7} T_{air}^{3} + 0.0011407 T_{air}^{2} - 0.4489 T_{air} + 1057.5$ air @ 1 bar (Dumas&Trancossi2009) $0.00039734 T_{air}^{2} - 0.19975 T_{air} + 1030.5$ air @ 1 bar (UW/MHTL 8406, 1984) $1.077024 \cdot 10^{-10} T_{air}^{4} - 4.970786 \cdot 10^{-7} T_{air}^{3} + 0.0007816818 T_{air}^{2} - 0.284887 T_{air} + 1034.09$ dry air @ at 1 atm (Irvine&Liley1984) $0.101 \theta_{gas} + 1037$ N2 (Vermeer1983) $- 0.00433 \theta_{gas}^{2} + 1.87 \theta_{gas} + 630$ SF6 (Vermeer1983) $1.0149 T_{gas} + 539.52$ CO2 (linear interpolation) $1.1029 T_{gas} + 868.62$ O2 (linear interpolation) $1.5 R_{gas}$ Monoatomic ideal gas $3.5 R_{gas}$ Diatomic molecule gas $4 R_{gas}$ Polyatomic molecule gas
Related
$R_{gas}$
$T_{air}$
$T_{gas}$
$\theta_{air}$
$\theta_{gas}$
Gas temperature [$^{\circ}$C]
Used in
$\alpha_{gas}$
$\mathrm{Pr}_{gas}$
$T_{conv_{ce}}$
Choices
GasFormula0$^{\circ}$C15$^{\circ}$C25$^{\circ}$C250 K275 K300 K325 K350 K375 K
Air-1005.91006.21006.5
N2N21041.41041.41041.4103910391040104010411042
SF6SF6627.83652.96668.99
CO2CO2826.84841.24850.85791819846871895918
COCO1042.01042.01042.1
O2O2916.72918.22919.62913915918923928934
H2H214197.614267.614306.3
NH3NH32179.52166.22164.5
SO2SO2669.21658.98656.2
HeHe5193.15192.95192.9
ArAr521.85521.65521.55
KrKr249.5249.31249.2
XeXe160.67160.29160.09