Thermodynamics-refrigerant expansion

[Losthorizons]

Hi everyone. I was wondering if anyone could steer me in the right direction. I'm trying to find the amount of work involved in an isothermal reversible expansion of a refrigerant using only an initial pressure, initial temp., and final pressure. No mass or Volumetric information given, so the traditional thermodynamic equations seem useless. So far, the only way I can see to do it is to take the area under the P-v curve. Any other ideas? Thanks

[Erik Detroit]

If you are looking for the reversible work, and have no mass flow information, then you will only be able to find the specific work (i.e. the work per unit of mass expanded).

You take the enthalpy of the starting point minus the enthalpy of the ending point.

The start point is easy since this is usually saturated or subcooled refrigerant liquid.

For the end point, you need to first find the entropy of the starting point, and then find the ending point at your final pressure that has the same entropy. In other words the expansion process is isentropic (reversible).

The real trouble here is access to the thermodynamic property data. This sounds like an engineering textbook problem. Do you have access to EES, NIST refprop, or DTU refrigeration utilities?

-Erik

[Losthorizons]

Hey, thanks for the reply. Yes, I do have all the table data available. After reading your post I felt kinda dumb and thought I was reading too much into the question. As you know things are rarely simple in thermo. Turns out it's not isentropic. Just reversible and isothermal. In other words, entropy changes, but there is no entropy produced or generated keeping the process reversible. Thanks again.

[Erik Detroit]

The more I think of it, the more that sounds like a fouled up problem statement. I took isothermal to mean adiabatic, and my answer was with that assumption.

If the process is isothermal, you will actually have to supply work to the expanding refrigerant to keep it at a constant temperature, and that is NOT a reversible process. An isentropic expansion, followed by an isentropic compression is a reversible process. Heating or supplying work to the refrigerant as it expands is not reversible since it causes a noticeable change to the surroundings of the process.

[mcgru-]

If the process is isothermal, you will actually have to supply work to the expanding refrigerant to keep it at a constant temperature, and that is NOT a reversible process. An isentropic expansion, followed by an isentropic compression is a reversible process.

Example of irreversible process - a burning match.
Heating of gas is reversible, because it could be cooled. Applying work to gas can be reversed into getting work from gas when it is expanded.

Isothermal process (while m=const) means:
P1V1=P2V2,
so P2/P1=V1/V2
but we need dV=V2-V1 to find the work A=P*dV
if V1 is unknown, the EOS can be used to find it through PV=RT for ideal gas or PV=RT*dzeta for real gases. dzeta is a compression coefficient, R - universal gas constant.

[Peter_1]

Welcome McGru.
Have you add your location to the RE members map? Can be found on the halfway the lower side of the top bar.

[mcgru-]

Have you add your location to the RE members map?

Yes, already set my location.

losthorizons, if you have p-v diagram and if there are isotherm curves, then... just don't forget to cut the box under the lower p-v-point from the result of integration.

[Erik Detroit]

Welcome to the board mcgru,

The definition of a reversible process I'm working from is "a process which can be reversed without leaving any trace on the surroundings".

I am viewing the problem from the thermodynamic point of view (it must be since only in a thermodynamics class would anyone care about such a theoretical question).

I certainly can't argue with the burning match!

Heating a gas and then cooling a gas, I think, does not fit the above definition since there are effects on the surroundings of the process.

Your example of applying work to a gas and then extracting work from the expansion will only give back the same amount of work if the process is adiabatic (it must be otherwise the heat from the compression process could leave the compressed gas), and isentropic compression and expansion (otherwise there will be losses that will change the temperature of the gas).

This is a good discussion, thank you,
Erik

[mcgru-]

Welcome to the board mcgru,

Thank you
i was here 2-3 years ago, when i was in a great interest in simulating the processes in reciprotating compressor Then my job shifted to be a less scientific. Now - i have read 2/3 of Kittel's Statistical Thermodynamics and i found it so interesting! So i feel myself empowered

The definition of a reversible process I'm working from is "a process which can be reversed without leaving any trace on the surroundings".

i'm sorry for my english (it's not my native).
But looking for the traces on the surroundings is not the the provement of reversability. As i understood from Kittel's "Statistical thermodynamics", the reversability is a process which could be led under any conditions to the same state as it were before changes.
If we take into account 2 volumes of same gas, and will heatup 1 volume, then cooldown it to the previous P-V-state, we cannot distingwish them. It will be identical. Such processes that we (as surrounding) undergo the volume - are reversible.

And another process, for example heating up the human body to the temperature over 42.C - is irreversible. At 42.C there will be denaturation of albumens. So heating up and then cooling down of human body will NOT lead to the same state. This process is irreversible.
Another irreversible process example - heating up the mixture of H2 and O2. After burning (or explosion) we cannot get H2O divided onto hydrogen and oxygen without appliance of human knowledge...


Fast compressing of thermically insulated volume of gas and then its adiabatic return to the previous state - it is just a single partial example of reversible process.

[Erik Detroit]

Yes, I can see that if you are using that definition of reversability, that your examples are correct.

I think your definition is more of a chemical definition, as with that definition you could very many things to a substance (so long as the chemical makeup does not change) and be able to return it to it's original state.

Mine (well, not mine really as I'm quite young compared with Kelvin, Planck and Lord Rankine!) comes from my college textbook: Thermodynamics by Cengel and Boles. I'm not sure it is correct for you to say there is only one definition, as clearly here we have TWO.

Regards,
Erik

[mcgru-]

I think your definition is more of a chemical definition,

I was very surprised when encountered the chemical potential definition in that Kittel's book. Being surprised, my interest in thermodynamics grew up a bit

So if we talk about thermodynamics (of a gas, liquid or a solid), i.e. such things as dependence of heat capacities on pressure or temperature, we talk about molecules and their interactions between each other. The interactions between atoms and molecules are based on interaction between their electron clouds. Condensation of substance - is an interaction between the set of molecules, its electron clouds (attraction by electric dipole forces). And in some cases, such condensation of diferent substances, through exchange of several electrons or setting up strong force of electric dipole - we call it chemical reaction.

Chemistry and thermodynamics are brother-sciences.

be able to return it to it's original state.

yes, PVT-state - look at the refrigeration cycle. It is cycle, while refrigerant is exposed to different actions - polytropic compression, state change, isobar cooling/heating, adiabatic expansion.
There are some other _cycles_ with isotherm curves on diagram.

as clearly here we have TWO.

OK,
so let it be