download the script: Caloric Properties of Mixture

Consider a gas mixture which consists of i components the following caloric properties of mixture can be obtained. Here we still assume that all gases are considered to be ideal gases and follow the ideal gas equation:

**u**: internal energy of a gas mixture per unit mass m

The total internal energy of a gas mixture is:

Then we get:

**c**: the specific heat capacity of a gas mixture at constant volume_{v}

We eliminate u and u_{i} by using u=c_{v}∙T and u_{i}= c_{vi}∙T and obtain:

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**h**: enthalpy of a gas mixture per unit mass h

The total enthalpy of a gas mixture is:

Then we get:

**c**: the specific heat capacity of a gas mixture at constant pressure_{p}

We eliminate h and h_{i} by using h=c_{p}∙T and h_{i}= c_{pi}∙T and obtain:

Furhermore we can also calculate the gas constant of mixture R=c_{p} – c_{v}:

In lots of case of chemical thermodynamics, the caloric properties will be given in J/mol and J/(mol∙K). Then we can get the following equations through the same derivation:

where: