Trying to understand refrigeration through statistical mechanics (i.e. what happens to each molecule), as you are trying here is going to be a bit tricky. Refrigeration is really best explained by classical thermodynamics, using properties of the fluid like enthalpy, pressure, entropy, etc. which themselves can be understood using statistical mechanics. As a matter of fact, the vapor-compression cycle was invented before Boltzmann’s theory.
Two significant mistakes in your diagram:
after the expansion valve, the droplets are not floating in “free space”. They are in an environment where the pressure is low enough that they can vaporize, but this is still in the continuum regime. There are plenty of refrigerant molecules around, the system is a vapor+liquid saturated equilibrium. (It is also best to understand that the valve enforces the low pressure by restricting the flow of refrigerant, rather than the compressor creating it, in a causal sense, but that’s mostly nitpicking)
the refrigerant droplets vaporize completely because of heat transfer from the outside in the evaporator, not vaporizing THEN absorbing heat from the outside. That’s the crux that makes the vapor-compression cycle so efficient: the heat is transferred from the outside to the refrigerant and from the refrigerant to the outside during phase changes (evaporation and condensation) at constant temperature.
My advice for understanding the vapor-compression cycle:
vaporizing a liquid requires a lot of energy (the enthalpy of vaporization). At constant pressure, this energy can be provided as heat, like boiling a pot of water (the stove provides energy).
Symmetrically, condensing a gas releases the same amount of energy, which at constant pressure is provided as heat, like water condensing on a cold mirror.
The boiling point of a substance varies as a function of pressure: at low pressure, the boiling point is low, at high pressure, the boiling point is high.
Refrigeration consists in vaporizing a liquid at low pressure, hereby sucking a lot of energy from the environment at cold temperature, and then condensing this same vapor back into a liquid at high pressure, therefore releasing the same amount of energy (plus compressor waste heat and other inefficiencies) into the environment at a higher temperature.
The compressor and the valve are there to enforce this pressure differential between the hot side and the cold side.
Thanks much for the brainpower! Agreed that this is easier to think about in terms of classical thermodynamics with its continuous fluids; I’m just on a bit of a stubbornly fundamentalist kick (ex).
If it entertains you to continue chatting, I have a couple clarifying questions:
They are in an environment where the pressure is low enough that [the droplets] can vaporize [...] the system is a vapor+liquid saturated equilibrium.
“Saturated equilibrium” sounds at odds with “pressure low enough that the droplets can vaporize.” Reconcile? (My best guess: you’re saying that the droplets evaporate enough to establish an equilibrium partial pressure very quickly after the expansion valve.)
the refrigerant droplets vaporize completely because of heat transfer from the outside in the evaporator, not vaporizing THEN absorbing heat from the outside.
IIUC: you’re saying that my diagram is incorrect in depicting the droplets vaporizing completely in the bulk of the gas; actually, the vaporization mostly (entirely?) occurs on the surface of the evaporator. Seems totally plausible. But, for heat to transfer from the exterior to the droplets, the droplets must be colder than the exterior; am I correct in identifying post-expansion-valve evaporative cooling as the reason the droplets are cold?
Trying to synthesize your response into my stubbornly-statistical-mechanical model, my update is:
immediately after the expansion valve, the droplets quickly evaporate enough to establish the equilibrium partial pressure;
that evaporation results in the liquid+vapor mixture being cold;
cold droplets (which, contra my diagram, have not mostly evaporated) settle on the surface of the evaporator;
heat conducts from outside into those droplets, which consequently finish vaporizing
Small point of terminology: “partial pressure” only makes sense in multi-species mixtures, but most refrigerants are single-species. The correct terms are 1) pressure as a descriptive term for the state of the refrigerant and 2) vapor pressure specifically for the equilibrium condition at a given temperature.
regarding your questions:
I have been a bit imprecise here. at the exit of the valve/entrance of the evaporator, the droplets are in thermodynamic equilibrium with the vapor, in the sense that there is no macroscopic vaporization (i.e. there is as much mass going from the liquid to the vapor as there is going from the vapor to the liquid). Vaporization happened inside the valve, during the Joule-Thomson process, which I am sure you have heard of at this point. The refrigerant went from all-liquid before the valve, to a partial mixture of liquid and vapor after the valve. both states are in equilibrium, or at least should be in a properly designed system.
The vaporization does happen mostly through direct conduction between the surface of the evaporator and the droplets in practice, but that’s not exactly what I meant. I wanted to say that the causal arrow is heat transfer from the outside causes the complete evaporation, not complete evaporation then heat transfer from the outside as your diagram shows. Even if no liquid droplets touch the walls of the evaporator, the heat transfer to the gaseous refrigerant would warm the gas, which would warm the droplets, which would evaporates, which would cool the gas, which would take heat from the walls, etc.
Thermodynamically, the process is the same as if you have direct wall-liquid contact: you have an amount of heat being used to transform the fluid from a partial vapor-liquid mixture to a complete vapor state.
So your update is mostly correct, except that the droplets usually vaporize “inside the valve”, not “immediately after the valve”. But that is not really relevant to the high-level physics. It depends on whether you have an orifice valve or a porous plug valve, where “the valve” begins and ends in your system, how quickly your refrigerant reaches equilibrium, which itself depends on your valve design, on turbulent mixing properties, on heat transfer properties, etc.
Trying to understand refrigeration through statistical mechanics (i.e. what happens to each molecule), as you are trying here is going to be a bit tricky. Refrigeration is really best explained by classical thermodynamics, using properties of the fluid like enthalpy, pressure, entropy, etc. which themselves can be understood using statistical mechanics. As a matter of fact, the vapor-compression cycle was invented before Boltzmann’s theory.
Two significant mistakes in your diagram:
after the expansion valve, the droplets are not floating in “free space”. They are in an environment where the pressure is low enough that they can vaporize, but this is still in the continuum regime. There are plenty of refrigerant molecules around, the system is a vapor+liquid saturated equilibrium. (It is also best to understand that the valve enforces the low pressure by restricting the flow of refrigerant, rather than the compressor creating it, in a causal sense, but that’s mostly nitpicking)
the refrigerant droplets vaporize completely because of heat transfer from the outside in the evaporator, not vaporizing THEN absorbing heat from the outside. That’s the crux that makes the vapor-compression cycle so efficient: the heat is transferred from the outside to the refrigerant and from the refrigerant to the outside during phase changes (evaporation and condensation) at constant temperature.
My advice for understanding the vapor-compression cycle:
vaporizing a liquid requires a lot of energy (the enthalpy of vaporization). At constant pressure, this energy can be provided as heat, like boiling a pot of water (the stove provides energy).
Symmetrically, condensing a gas releases the same amount of energy, which at constant pressure is provided as heat, like water condensing on a cold mirror.
The boiling point of a substance varies as a function of pressure: at low pressure, the boiling point is low, at high pressure, the boiling point is high.
Refrigeration consists in vaporizing a liquid at low pressure, hereby sucking a lot of energy from the environment at cold temperature, and then condensing this same vapor back into a liquid at high pressure, therefore releasing the same amount of energy (plus compressor waste heat and other inefficiencies) into the environment at a higher temperature.
The compressor and the valve are there to enforce this pressure differential between the hot side and the cold side.
Thanks much for the brainpower! Agreed that this is easier to think about in terms of classical thermodynamics with its continuous fluids; I’m just on a bit of a stubbornly fundamentalist kick (ex).
If it entertains you to continue chatting, I have a couple clarifying questions:
“Saturated equilibrium” sounds at odds with “pressure low enough that the droplets can vaporize.” Reconcile? (My best guess: you’re saying that the droplets evaporate enough to establish an equilibrium partial pressure very quickly after the expansion valve.)
IIUC: you’re saying that my diagram is incorrect in depicting the droplets vaporizing completely in the bulk of the gas; actually, the vaporization mostly (entirely?) occurs on the surface of the evaporator. Seems totally plausible. But, for heat to transfer from the exterior to the droplets, the droplets must be colder than the exterior; am I correct in identifying post-expansion-valve evaporative cooling as the reason the droplets are cold?
Trying to synthesize your response into my stubbornly-statistical-mechanical model, my update is:
immediately after the expansion valve, the droplets quickly evaporate enough to establish the equilibrium partial pressure;
that evaporation results in the liquid+vapor mixture being cold;
cold droplets (which, contra my diagram, have not mostly evaporated) settle on the surface of the evaporator;
heat conducts from outside into those droplets, which consequently finish vaporizing
No problem at all!
Small point of terminology: “partial pressure” only makes sense in multi-species mixtures, but most refrigerants are single-species. The correct terms are 1) pressure as a descriptive term for the state of the refrigerant and 2) vapor pressure specifically for the equilibrium condition at a given temperature.
regarding your questions:
I have been a bit imprecise here. at the exit of the valve/entrance of the evaporator, the droplets are in thermodynamic equilibrium with the vapor, in the sense that there is no macroscopic vaporization (i.e. there is as much mass going from the liquid to the vapor as there is going from the vapor to the liquid). Vaporization happened inside the valve, during the Joule-Thomson process, which I am sure you have heard of at this point. The refrigerant went from all-liquid before the valve, to a partial mixture of liquid and vapor after the valve. both states are in equilibrium, or at least should be in a properly designed system.
The vaporization does happen mostly through direct conduction between the surface of the evaporator and the droplets in practice, but that’s not exactly what I meant. I wanted to say that the causal arrow is heat transfer from the outside causes the complete evaporation, not complete evaporation then heat transfer from the outside as your diagram shows. Even if no liquid droplets touch the walls of the evaporator, the heat transfer to the gaseous refrigerant would warm the gas, which would warm the droplets, which would evaporates, which would cool the gas, which would take heat from the walls, etc.
Thermodynamically, the process is the same as if you have direct wall-liquid contact: you have an amount of heat being used to transform the fluid from a partial vapor-liquid mixture to a complete vapor state.
So your update is mostly correct, except that the droplets usually vaporize “inside the valve”, not “immediately after the valve”. But that is not really relevant to the high-level physics. It depends on whether you have an orifice valve or a porous plug valve, where “the valve” begins and ends in your system, how quickly your refrigerant reaches equilibrium, which itself depends on your valve design, on turbulent mixing properties, on heat transfer properties, etc.
Oh, that’s very interesting. I’ll have to look into that more. (And learn more about Joule-Thomson, which I know… of… but was hoping I could ignore.)
Thanks again for the brain!