# Are smaller heat-pumps more efficient?

I was a doing a placement at a company, and they were designing a new heat pump. I was told the more compact you can make a heat-pump, the better it is for efficiency, and they mentioned something about this was because the power density was increased.

I get there are benefits from using less material and making something lighter which would improve efficiency in that regard, but I don't get the benefit of a higher power density in a heat pump. I understand that in a heat engine like a combustion engine you want a high compression ratio so you'd want to make the thing as compact as possible, but why is a better power density also good for a heat-pump? Is it this just the thing with all types of machinery which have some sort of volume which is compressed? If so Why?

Edit: I didn't really want to say COP but rather efficiency to keep the question more general. These guys seemed pretty certain that having a small high rpm heat pump gave improved performance, whilst I assume they meant COP could be something else they are looking at. Maybe a better way to ask this is: Are there any theoretical benefits to the COP of a heat pump by making it smaller?

• The term "efficiency" is used inconsistently a lot, are you sure they meant it in terms of, say, coefficient of performance? – Carlton Nov 18 '15 at 14:20
• To add on to what @Carlton said, "efficiency" is terribly generic. All that really means is what you get out for what you put in. But those measures of input and output could be anything - cost, power, size, etc. And all too often, "more efficient" means "better" but that depends on what your definition of good is. You can only optimize for one variable at a time. This is getting ranty, but the tl;dr is that we need to know how you're measuring efficiency to give a good answer. – Trevor Archibald Nov 18 '15 at 17:51
• Theoretically the pumping losses at least increase for smaller units, due to the square-cube rule: with a linear increase in size the volume of e.g. a tube increases by the cube, while the surface area (which causes the friction losses) increases by the square. And assuming a fixed power output, larger pipes mean lower flow speeds, decreasing the friction losses in a larger unit even more. Though usually a larger unit will also have more power output. – JanKanis Apr 6 '18 at 19:16