Phase change in heat engines & heat pumps

[Redbelly98]

This question has been in the back of my mind for a while. In short, is having a phase change between liquid and vapor more desirable for a heat engine or for a heat pump?

Clearly, having a large area enclosed by the loop in a P-V diagram increased the amount of work in the cycle, so anything that enlargens that area would be desirable for a heat engine and undesirable for a heat pump or refrigerator. So, does a liquid-vapor phase change within the cycle tend to increase or decrease this area -- or is there no general answer?

 

[russ_watters]

Clearly, having a large area enclosed by the loop in a P-V diagram increased the amount of work in the cycle, so anything that enlargens that area would be desirable for a heat engine and undesirable for a heat pump or refrigerator.

No, I don't think so. I've never really thought about it in those terms, but it seems to me that for a heat engine you want to increase the area vertically and for a heat pump you want to increase it horizontally, but an overall enlarging is not necessarily desirable: efficiency is about the ratio between work and heat, not about maximizing the work or heat for a given mass flow rate.

So, does a liquid-vapor phase change within the cycle tend to increase or decrease this area -- or is there no general answer?

Well, without a liquid-vapor change, the area inside would be zero. The change in state is what enables the horizontal stretching because that's where the input and output of heat happens. The magic of a heat pump is in having the phase changes happen at two different temperatures, allowing heat absorption from an area that's already cold and heat rejection to an area that's already warm.

 

[Redbelly98]

No, I don't think so. I've never really thought about it in those terms, but it seems to me that for a heat engine you want to increase the area vertically and for a heat pump you want to increase it horizontally, but an overall enlarging is not necessarily desirable: efficiency is about the ratio between work and heat, not about maximizing the work or heat for a given mass flow rate.

Okay, that does sound like a better way of thinking about it. Thanks.

Well, without a liquid-vapor change, the area inside would be zero.

I think I'm missing something. The Carnot Cycle (for example) for an ideal gas would enclose a non-zero area, without a phase change. Or is it a matter of what is practical to actually build and operate?

The change in state is what enables the horizontal stretching because that's where the input and output of heat happens. The magic of a heat pump is in having the phase changes happen at two different temperatures, allowing heat absorption from an area that's already cold and heat rejection to an area that's already warm.

BTW, I've started doing some self study with a copy of Cengel & Boles's Thermodynamis (3rd ed.) The chapter on refrigerators and heat pumps is full of T-s diagrams, no P-v ones which would help me visualize the process better. When I can, I'll try constructing P-v diagrams for water as well as refrigerant from the tables in the book.

 

[russ_watters]

I think I'm missing something. The Carnot Cycle (for example) for an ideal gas would enclose a non-zero area, without a phase change. Or is it a matter of what is practical to actually build and operate?

Hmm... you're right, but I'm trying to envision whether an ideal-gas heat pump could actually be built...

...I suppose you could: when you compress air with an air compressor, it heats up. When you expand it through a throttling valve, it cools. Then I guess maybe the real reason we don't use them is that the heat energy of the compression is a lot smaller than the pressure energy, so the efficiency would be pretty low. There is a lot of energy involved in a phase change - I suppose that widens the diagram.

 

[minger]

BTW, I've started doing some self study with a copy of Cengel & Boles's Thermodynamis (3rd ed.) The chapter on refrigerators and heat pumps is full of T-s diagrams, no P-v ones which would help me visualize the process better. When I can, I'll try constructing P-v diagrams for water as well as refrigerant from the tables in the book.

Often times it's convenient to show both T-s and P-v diagrams for a cycle. A P-v diagram has trouble showing a isentropic process while a T-s diagram has difficulties showing an isobaric process.

For example, if you wiki the Brayton cycle (what gas turbine engines are typically modeled as), it shows both
http://upload.wikimedia.org/wikipedia/commons/3/3c/Brayton_cycle.svg

It just so happens to be more convenient in the refrigeration cycle to show it in the T-s diagram because it's easier to visualize the phase change...IMHO.