# How do you calculate temp change when compressing water?

1. Aug 16, 2016

### Bombicis

I built a pressure chamber to test small parts for leaks at 1000 psi. I can measure the pressure with an accuracy of ± 1 psi. I found that small changes in ambient temperature ± 2 °F can result in a slow but profound change in the pressure in the system, say 25 psi.

Insulating the chamber helped a little, but I really need to control for the change in temperature associated with changing pressure.

As a side note, with the ambient temperature constant, running the system from 0 to 1000 psi over 2 minutes and then monitoring the pressure always results in a slow and relatively consistent pressure drop that slowly tapers off. If the pressure is then dropped over 2 minutes to 200 psi and then monitored, the pressure slowly rises consistently over time again slowly tapering off. These results lead me to conclude that pressure induced temperature change is the cause.

2. Aug 16, 2016

### BvU

Hello Bombi,

According to the ideal gas law you have $pV = nRT$ (in decent units). So your 2 F can explain the 25 psi.
Assuming you have air in the chamber (or is it water , you don't say).
Not clear to me why you would need to control things: leaks are faults, isn't it ?
Or do you neeed leak reates at precisely 1000 psi ?

 ah, wait, there's the thread title. Could you describe the setup a little better ?

3. Aug 16, 2016

### Bombicis

Hey BvU,

Thanks for the reply!

The pressure chamber is filled with water, no air. I expect that any small bubbles left in cracks would dissolve into the water relatively in the early in the pressurization process.

The pressure vessel is 1/2" thick walled stainless steel and pressure is regulated via a piston. The total volume if the pressure vessel is about 3 liters and there is a reservoir on the side for filling and emptying the vessel.

Leaks are indeed faults, but they can occur very slowly so I need to detect the difference between a leak and temperature induced pressure fluctuations. Because this is a manufacturing environment, the quicker I can determine if a part leaks, the better. I have found that in certain cases, leaks can look similar to thermally induced pressure changes and then it can take an hour or more to tell the difference between the two.

My hope is that by monitoring both ambient and vessel temperature, I can more quickly determine the difference between a leak and thermally induced pressure change.

4. Aug 16, 2016

### BvU

I looked at the compressibility of water (2.2.1 there) and found about 0.36% difference in density going from 1 atm to 70 atm at 20 C. The work done would increase the temperature, but we need an steam tables expert to estimate the temperature rise from that. @Chestermiller or @SteamKing ?

5. Aug 16, 2016

### Staff: Mentor

The relationship between volume, pressure, and temperature for water is$$\Delta \ln V=\alpha \Delta T-\beta\Delta P$$
where $\alpha$ is the coefficient of volumetric expansion (0.000214/C) and beta is the bulk compressibility ($4.6\times 10^{-10}/Pa$). You probably also need to include the changes in volume of the container as a function of temperature and pressure.

6. Aug 16, 2016

### Bombicis

Thanks so so much both BvU and Chestermiller.

I have been wrestling with this for a while and now I think I can get my arms around the problem. I think I will need a more accurate pressure sensor as well as a very accurate thermal probe, but now I am ready to take a stab at predicting outcomes rather than finding an explanation for them.

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