Specific Heat Capacity & final temperature of a mixture of ideal gases

[gwalkerb]

I was looking at calculating this value for mixtures of gases (treated as ideal gases).

Some resources I've found online suggest taking the mole fraction of each constituent gas and multiplying that by the specific heat capacity, and then taking the sum.

i.e.

Cp_mix=Σ(n_i)(Cp_i)

However, since the specific heat capacity is a mass based property, shouldn't the mass fraction of each constituent be used instead of the mole fraction?

i.e.

Cp_mix=Σ(m_i)(Cp_i)

If I was using molar heat capacity, then I would use the mole fraction for mixing.

What I'm really trying to do is to determine the final pressure and temperature when a piping system containing a mixture of gases at different pressures and temperatures equalizes. I know that real gas heat capacity varies as a function of pressure and temperature, so without a process simulator I wouldn't be able to get a fully accurate result, but for now, assuming perfect ideal gases, I'm just looking to validate that my mixing rules are correct.

I know it's also not necessarily correct to specify Cp as my specific heat capacity, since the equalization process obviously varies in pressure, but Cv isn't correct either since each section is expanding into the entire volume as it equalizes.

My current simplification simply considers the mass and temperature of each section, since the gas composition is typically the same in each, and does a mass-weighted average of the temperature. But I'm looking to improve the accuracy of this calculation if possible.

i.e.

T_final=(Σ(m_i)(T_i))/(Σm_i)