Calculation of temperature drop after a pressure release

In summary, the speaker is encountering a problem with calculating the temperature drop after a pressure release in a water sample using an adiabatic temperature change equation. They have equations to calculate all the necessary parameters, but when numerically integrating the equation, they are obtaining surprising results of a slight temperature increase instead of a drop. The speaker is unsure if the equation is valid for negative thermal expansion coefficients and is seeking an explanation for this behavior. They have provided various experimental conditions and observations, and are asking for suggestions and help in resolving the issue.
  • #1
lari
2
0
I have a problem when calculating the temperature drop after a pressure release in a water sample. I use the following expression for the adiabatic temperature change:
(delta T/delta P)= alpha*T*V/Cp
where alpha is the thermal expansion coefficient, T is the temperature in Kelvin, V is the specific volume and Cp is the specific heat. I have appropriate equations to calculate all these parameters (all dependent on both pressure and temperature).
I calculate the temperature drop numerically integrating this equation with 0.1 MPa pressure increments. Nevertheless, for expansions from 100 MPa and -10ºC, I obtain surprising results: a little temperature increase (sample temperature after expansion is about -9.8ºC). That is due to the negative sign of the thermal expansion coefficient at low pressures and temperatures. However, in practice, I record a temperature drop in the sample (about -10.3ºC). Is the equation employed valid for negative thermal expansion coefficients? How can I explain this behaviour? Thanks in advance.
 
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  • #2
Are you sure the equation is valid for what one is considering and the conditions.

"for expansions from 100 MPa and -10ºC," to what pressure is one reducing? This is basically ice at high pressure ~1000 atm (1 atm = 0.101325 MPa). That's very high pressure.

By reducing the pressure, one is unloading the ice. I'm not sure the temperature should change just by reducing the pressure (basically decompressing ice), although one would release the stored mechanical energy, and the amplitude of atomic vibrations would increase by very little.

Also consider when it is appropriate to use CV and CP.
 
  • #3
Sorry! Pressure release is to atmospheric conditions, that is, 0.1 MPa. I forgot to say it in my previous message. Sample initially is at liquid state. I proved several conditions: 100 MPa/-10ºC, 200 MPa/-10ºC, 200 MPa/-20ºC and 450 MPa/-10ºC. All these conditions correspond to liquid state according to the phase diagram of pure water, except 100 MPa/-10ºC. But, these conditions remain close to the melting curve of water and, taking into account that a considerable supercooling is needed under pressure to initiate nucleation, I have experimentally observed that water remained in liquid state at these conditions. Also I have experimentally observed a temperature drop in the samples after the pressure release. My problem is that the above mentioned equation yields a positive temperature increment after the pressure release. That is due to the fact that the thermal expansion coefficient has negative values at relatively "low pressures", that is 50 MPa and lower, and low temperatures. Nevertheless, experimentally, I always recorded a temperature drop in the sample after expansion. Thanks again.
 
  • #4
'All these conditions correspond to liquid state according to the phase diagram of pure water, except 100 MPa/-10ºC.'
I agree with lari on this point. Let's try a simpler thought to prove this. Since the density of ice is lower then that of water, the volume of ice is always larger than that of water in same mass.So ice will melt under great presure.
There, I have some suggestions for lari.I hope those may help you.
First,what I think the most possible one, is that maybe your conditions of experiment are not so ideal. I mean perhaps your didn't consider some effective factors such as the outside environment may had heat exchange with your water sample, etc.
Then,maybe your equations are not correct or have bigger errors in some conditions such as high presure.
I hope these may help you.
 
Last edited:

1. How does pressure affect temperature?

According to the ideal gas law, pressure and temperature have a direct relationship. This means that as pressure increases, so does temperature, and vice versa. Therefore, a pressure release will result in a temperature drop.

2. What factors affect the temperature drop after a pressure release?

The temperature drop after a pressure release is affected by several factors, including the volume of the gas, the initial pressure, and the type of gas. Additionally, the rate of pressure release and the surrounding environment can also impact the temperature drop.

3. How can I calculate the temperature drop after a pressure release?

The temperature drop can be calculated using the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas. By rearranging the equation, the temperature drop can be determined by dividing the initial pressure by the final pressure and multiplying by the initial temperature.

4. Is there a standard temperature drop after a pressure release?

No, the temperature drop after a pressure release can vary depending on the factors mentioned above. In general, a larger pressure release or a larger volume of gas will result in a greater temperature drop. However, the specific temperature drop can only be accurately calculated using the ideal gas law.

5. How can the temperature drop after a pressure release be useful in practical applications?

The temperature drop after a pressure release is a crucial factor in many industrial processes, including refrigeration and air conditioning. It is also important in safety measures, as it can help predict the effects of pressure releases in pressurized systems. Additionally, understanding the temperature drop can aid in the design and maintenance of equipment to ensure efficient and safe operation.

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