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The diagram shows a diagram of a heat pump. There are four components connected by pipes. They are a condenser (1), an expansion valve (2), an evaporator (3), and a compressor (4), connected in that order. The evaporator coils are outside; all of the other components are inside. Heat Q sub c is absorbed from the outside air at the evaporator, and heat Q sub h is emitted inside from the condenser.
A simple heat pump has four basic components: (1) condenser, (2) expansion valve, (3) evaporator, and (4) compressor. In the heating mode, heat transfer Q c size 12{Q rSub { size 8{c} } } {} occurs to the working fluid in the evaporator (3) from the colder outdoor air, turning it into a gas. The electrically driven compressor (4) increases the temperature and pressure of the gas and forces it into the condenser coils (1) inside the heated space. Because the temperature of the gas is higher than the temperature in the room, heat transfer from the gas to the room occurs as the gas condenses to a liquid. The working fluid is then cooled as it flows back through an expansion valve (2) to the outdoor evaporator coils.

The electrically driven compressor (work input W size 12{W} {} ) raises the temperature and pressure of the gas and forces it into the condenser coils that are inside the heated space. Because the temperature of the gas is higher than the temperature inside the room, heat transfer to the room occurs and the gas condenses to a liquid. The liquid then flows back through a pressure-reducing valve to the outdoor evaporator coils, being cooled through expansion. (In a cooling cycle, the evaporator and condenser coils exchange roles and the flow direction of the fluid is reversed.)

The quality of a heat pump is judged by how much heat transfer Q h size 12{Q rSub { size 8{h} } } {} occurs into the warm space compared with how much work input W size 12{W} {} is required. In the spirit of taking the ratio of what you get to what you spend, we define a heat pump’s coefficient of performance ( COP hp size 12{ ital "COP" rSub { size 8{"hp"} } } {} ) to be

COP hp = Q h W . size 12{ ital "COP" rSub { size 8{"hp"} } = { {Q rSub { size 8{h} } } over {W} } } {}

Since the efficiency of a heat engine is Eff = W / Q h size 12{ ital "Eff"=W/Q rSub { size 8{h} } } {} , we see that COP hp = 1 / Eff size 12{ ital "COP" rSub { size 8{"hp"} } =1/ ital "Eff"} {} , an important and interesting fact. First, since the efficiency of any heat engine is less than 1, it means that COP hp size 12{ ital "COP" rSub { size 8{"hp"} } } {} is always greater than 1—that is, a heat pump always has more heat transfer Q h size 12{Q rSub { size 8{h} } } {} than work put into it. Second, it means that heat pumps work best when temperature differences are small. The efficiency of a perfect, or Carnot, engine is Eff C = 1 T c / T h size 12{ ital "Eff" rSub { size 8{C} } =1 - left (T rSub { size 8{c} } /T rSub { size 8{h} } right )} {} ; thus, the smaller the temperature difference, the smaller the efficiency and the greater the COP hp size 12{ ital "COP" rSub { size 8{"hp"} } } {} (because COP hp = 1 / Eff size 12{ ital "COP" rSub { size 8{"hp"} } =1/ ital "Eff"} {} ). In other words, heat pumps do not work as well in very cold climates as they do in more moderate climates.

Friction and other irreversible processes reduce heat engine efficiency, but they do not benefit the operation of a heat pump—instead, they reduce the work input by converting part of it to heat transfer back into the cold reservoir before it gets into the heat pump.

A diagram of a heat pump (shown as a circle). Work W, indicated by a large, wavy orange arrow, is the total work put into the pump. Part of this work is done against friction and is lost in the form of frictional heat, Q sub f, to the cold reservoir. The portion of work that is used by the heat pump is represented by W prime. The pump transfers heat Q sub h, indicated by a large orange arrow, into the hot reservoir, a tan-colored rectangle, at temperature T sub h. Frictional heat Q sub f, indicated by a wavy orange arrow, is transferred to the cold reservoir, a blue rectangle at temperature T sub c. Heat Q sub c, indicated by a smaller wavy orange arrow, is transferred into the pump from the cold reservoir. Heat Q sub h is formed from a combination of W prime and Q sub c.
When a real heat engine is run backward, some of the intended work input W { left (W right )} {} goes into heat transfer before it gets into the heat engine, thereby reducing its coefficient of performance COP hp size 12{ ital "COP" rSub { size 8{"hp"} } } {} . In this figure, W ' {W'} {} represents the portion of W {W} {} that goes into the heat pump, while the remainder of W {W} {} is lost in the form of frictional heat Q f { left (Q rSub { {f} } right )} {} to the cold reservoir. If all of W size 12{W} {} had gone into the heat pump, then Q h size 12{Q rSub { size 8{h} } } {} would have been greater. The best heat pump uses adiabatic and isothermal processes, since, in theory, there would be no dissipative processes to reduce the heat transfer to the hot reservoir.

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Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
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