# Two-phase Heat Capacity

1. Oct 23, 2009

### Howy

Hi,
I was woindering if anyone can help me on a problem I have been stuck on for a while now.

I have an equation to combine the heat capcity of oil and water, but I cant find an equation anywhere that combines the heat capacities for water oil and gas.

All i have is CpL = (qo(qo+qw))Cpo+(1-(qo/(qo+qw))Cpw

Does anyone know a formula for combing heat capacity of liquids and gases

Thanks, Howy

2. Oct 23, 2009

### Mapes

Hi Howy, welcome to PF. This equation should work well for liquid-gas combinations too. It's simply saying the heat capacity contributions are independent and combined according to the (atomic) fraction of each material.

3. Oct 23, 2009

### Bob S

For a two-phase solution of water and steam, say at 100 degrees C, the heat capacity should include the heat of vaporization.
Bob S

4. Oct 23, 2009

### Mapes

Ah, good catch. I was assuming no phase change (which would apply to oil, water, and air around room temperature). Including a phase change, the heat capacity could be infinite for a solution combining a liquid with its own vapor (at constant pressure), for example. Howy, can you tell us what the gas is?

5. Oct 26, 2009

### Howy

Wow,

Thanks for the hasty reply guys. Probably best to assume the following:

Water (pure)
Oil with a SG of 0.88 and a Cp of 1.7585 kj/kg.K
Gas (natural) with a Sg of 0.7 and a Cp of 5.5265 kj/kg.K

Last edited: Oct 26, 2009
6. Oct 26, 2009

### Mapes

OK, for this particular system at thermal equilibrium, I don't see a problem with calculating the mass of each component and multiplying it by the material's specific heat capacity, and summing the results to estimate the system's heat capacity.

7. Oct 26, 2009

### Howy

so do you think the following is acceptable?

Cp = (qo/qt)Cpo + (qw/qt)Cpw +(qg/qt)Cpg

8. Oct 26, 2009

### Mapes

What are the definition and units of the q's?

9. Oct 26, 2009

### Howy

qo = quantity of oil being added
qw = quantity of water being added
qg = quantity of gas being added
qt = quantity of mixture

providing units are all the same i would have thought the units aren't important as it just a ratio

10. Oct 26, 2009

### Mapes

OK, thanks for the clarification on definitions. This equation is going to give you a specific heat capacity, which isn't really meaningful, since the system isn't homogeneous. (For example, a sample random kilogram might contain all oil, all water, a mixture also containing some gas, etc.) It would be better to multiply the mass of each component by that material's specific heat capacity, then sum the results to obtain the system heat capacity (in J/K). Does this make sense?

11. Oct 27, 2009

### Howy

My understanding is, first work out each phase's mass flow rate

Wo = (densityofoil*qo)
Ww = (densityofwate*qw)
Wg = (densityofgas*qg)
WTotal = Wo + Ww + Wg

Then work out the ratio,

CpTotal = (Wo/WTotal)*Cpo + (Ww/WTotal)*Cpw + (Wg/WTotal)*Cpg