Applications of Thermodynamics

Applications of Thermodynamics: Heat Pumps and Refrigerators

Photograph of various expensive refrigerators displayed in a home appliance store.

Almost every home contains a refrigerator. Most people don’t realize they are also sharing their homes with a heat pump. (credit: Id1337x, Wikimedia Commons)

Heat pumps, air conditioners, and refrigerators utilize heat transfer from cold to hot. They are heat engines run backward. We say backward, rather than reverse, because except for Carnot engines, all heat engines, though they can be run backward, cannot truly be reversed. Heat transfer occurs from a cold reservoir \({Q}_{\text{c}}\) and into a hot one. This requires work input \(W\), which is also converted to heat transfer. Thus the heat transfer to the hot reservoir is \({Q}_{\text{h}}={Q}_{\text{c}}+W\). (Note that \({Q}_{\text{h}}\), \({Q}_{\text{c}}\), and \(W\) are positive, with their directions indicated on schematics rather than by sign.) A heat pump’s mission is for heat transfer \({Q}_{\text{h}}\) to occur into a warm environment, such as a home in the winter. The mission of air conditioners and refrigerators is for heat transfer \({Q}_{\text{c}}\) to occur from a cool environment, such as chilling a room or keeping food at lower temperatures than the environment. (Actually, a heat pump can be used both to heat and cool a space. It is essentially an air conditioner and a heating unit all in one. In this section we will concentrate on its heating mode.)

Part a of the figure shows a heat pump, drawn as a circle. Work W, indicated by a bold orange arrow, is put in to to the pump to transfer heat Q sub c, indicated by a bold orange arrow, out of a cold temperature reservoir T sub c, drawn as a blue rectangle, and pumps heat Q sub h, indicated by a larger bold orange arrow, into high temperature reservoir T sub h. Part b of the figure shows a P V diagram for a Carnot cycle. The pressure P is along the Y axis and the volume V is along the X axis. The graph shows a complete cycle A D C B A. The path begins at point A, then it drops sharply down and slightly to the right until point D. This is marked as an adiabatic expansion. Then the curve drops down more gradually, still to the right, from point D to point C. This is marked as an isotherm at temperature T sub c, during which heat Q sub c enters the system. The curve then rises from point C to point B along the direction opposite to that of A D. This is an adiabatic compression. The last part of the curve rises up from point B back to A. This is marked as an isotherm at temperature T sub h, during which heat Q sub h leaves the system. The path D C is lower than path B A. Heat entering and leaving the system is indicated by bold orange arrows, with Q sub h larger than Q sub c.

Heat pumps, air conditioners, and refrigerators are heat engines operated backward. The one shown here is based on a Carnot (reversible) engine. (a) Schematic diagram showing heat transfer from a cold reservoir to a warm reservoir with a heat pump. The directions of \(W\), \({Q}_{\text{h}}\), and \({Q}_{\text{c}}\) are opposite what they would be in a heat engine. (b) \(\text{PV}\) diagram for a Carnot cycle similar to that in this figure but reversed, following path ADCBA. The area inside the loop is negative, meaning there is a net work input. There is heat transfer \({Q}_{\text{c}}\) into the system from a cold reservoir along path DC, and heat transfer \({Q}_{\text{h}}\) out of the system into a hot reservoir along path BA.

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Thermodynamics

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