# A Heat transaction of a non-ideal gas

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1. Jul 6, 2016

### Uthpala Kaushalya

Here I want to know how to find the heat interactions of non-ideal gases in the following processes.
1. Isobaric process
2. Isochoric process

I know that internal energy U depends on temperature and volume. And the enthalpy depends on temperature and pressure.
How calculation of heat transaction can be calculated? and what's the connection between following taylor series expansion with calculating the heat interaction.

U(T,V)
U(T+T, V+V) = U(T,V) + ∂u/∂ t |v * T + ∂u/∂v |T * V + Higher Terms

2. Jul 6, 2016

### nasu

Why don't use the heat capacities of the gases, as functions of T and P?
Are talking about actual gases or just about a model of non-ideal gas (like Van der Waals)?
If it's a specific gas (like nitrogen) you may need to find some actual values of parameters for that gas rather than using a general formula.
Here is a paper that may help.
http://journals.aps.org/pr/pdf/10.1103/PhysRev.34.1615 [Broken]

Last edited by a moderator: May 8, 2017
3. Jul 6, 2016

### Staff: Mentor

You would like to have an equation for calculating the changes internal energy with changes in temperature and volume for a non-ideal gas. Is that correct? In this equation, you would like everything expressed in terms of known functions like heat capacity and p-v-T behavior?

4. Jul 6, 2016

Yes :)

5. Jul 6, 2016

### Uthpala Kaushalya

Last edited by a moderator: May 8, 2017
6. Jul 6, 2016

### nasu

No, you should be able to find other articles that have free access. I don't think this is a very rare topic.

7. Jul 6, 2016

### Staff: Mentor

The following equation is in every thermo book:
$$dU=C_vdT-\left[P-T\left(\frac{\partial P}{\partial T}\right)_V\right]dV$$