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Parameter · 04 Material

Specific heat capacity cp

material.compressible.Cp Unit: J/(kg·K) Step 04 · Material

The constant specific heat capacity at constant pressure, used when the heat-capacity model is "constant" (solver thermodynamics hConst). With the temperature-dependent model the box shows cp(T)c_p(T) at the entered temperature and is locked.

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Theory

The compressible solver writes its energy equation in sensible internal energy; with a constant cpc_p, enthalpy and internal energy are linear in temperature. Together with the molar mass, cpc_p also determines:

  • the ratio of heat capacities γ\gamma, which sets the speed of sound of the acoustics;
  • the heat balance of a heat-transfer run (enthalpy flux in minus out).

Equations

hs=cp T,cv=cp−RM,γ=cpcvh_s = c_p\,T, \qquad c_v = c_p - \frac{\mathcal{R}}{M}, \qquad \gamma = \frac{c_p}{c_v}
(1)
wheremeaningunit
cpc_pSpecific heat capacity at constant pressure (this setting)J/(kg K)
cvc_vSpecific heat capacity at constant volumeJ/(kg K)
hsh_sSensible enthalpy (constant-cp convention of the heat balance)J/kg
R\mathcal{R}Universal gas constant, 8314.47J/(kmol K)
MMMolar masskg/kmol
γ\gammaRatio of heat capacities-

Default and rule

Default
1006 J/(kg K); with the temperature-dependent model, cp(T) at the entered temperature (shown, locked)
Rule

1006 J/(kg K), air near room temperature.

Source

Ideal-gas thermodynamics with a constant heat capacity. The program writes the value to the solver's constant/thermophysicalProperties with hConst thermodynamics.

Valid range > 0

Values

Positive. Used only with the constant heat-capacity model.

Hot gas

Air's cpc_p is about 1136 J/(kg K) at 700 °C, 13 % above the default; with a constant cpc_p use the value at the mean gas temperature, or the temperature-dependent model.