# Energy requirements for heating a liquid under different pressures

1. Aug 24, 2011

### klillas

Hello,

I am interested to know how pressure affects how much energy is needed to heat up a liquid, if at all.

For example, does it require less energy to heat up water at sealevel compared to the energy needed to do the same at the bottom of the sea?

Cheers,
klillas

2. Aug 24, 2011

### edgepflow

Basic energy to heat water:

Q = mass * cp * Temperature Difference

If mass and Temperature Difference remain constant, the heat will vary with the specific heat. Some data for water:

At 60 F and 14.7 psia, cp = 0.999237 BTU/lb-R
At 60 F and and 3000 psi (about 7000 ft deep) cp = 0.983650 BTU/lb-R

So it will require about 2% less energy to heat water in the depths of the ocean.

3. Aug 24, 2011

### klillas

Thanks!
I would like to keep going until I get a correct understanding of how this works if you have the patience :)

Let's say I have a bucket upside down filled with water just below sea level and an identical bucket in the depths of the ocean. I use the same amount of energy to heat the water in the two buckets. The water expands (a little) which generates two lifting forces on the buckets.
How will the two forces compare to each other? Is one greater than the other?

Cheers,
klillas

4. Aug 25, 2011

### edgepflow

I think the difference would be small but you could estimate as follows:

The density difference will generate the buoyancy force. Assume you heat liquid from 60 F to 200 F. So compare:

* density (14.7 psia, 60 F) - density (14.7 psia, 200F)

to,

* density (3000 psia, 60 F) - density (3000 psia, 200F)

The one with the larger difference would make more force.

5. Aug 25, 2011

### klillas

Thank you,

If I read the following table correctly, it would seem that you get a larger buoyancy force at high pressures than at lower pressures if using the same amount of energy to heat the water. I simply compared the volume changes from 0C to 50C at different pressures.