A refrigerator is a machine that takes heat from a cold place and moves it to a hot place. ie. Heat is taken from the inside of a box which is already cold and deposited in the kitchen which is already hot. Since the natural flow of heat is from the hot kitchen to the cold body, in the opposite direction, we can't do this trick without an input of energy, which we have to pay for.
Refrigerators work on a variety of cycles with different efficiencies. To illustrate the principles we draw a Carnot refrigerator ... which is a Carnot engine with the events changed slightly to reverse the cycle on the PV diagram.
The ideal gas is returned to its original state around a closed loop in an anti-clockwise direction, with a combination of isothermal and adiabatic changes. Each process can be reversed at any point on the cycle. The cycle is said to be reversible. Work is done and hear flows in and out, but the internal energy of the gas is returned to the same value at the end of each cycle.
The Carnot diagram shows heat Q1 taken from a cold place and heat Q2 expelled to a hot place. Q2 is larger than Q1. The difference is the work input to the system DW, which is the area inside the loop in Joules, because the internal energy of the system is unchanged at the end of each cycle. Using the engineers sign DW is negative, (done on the system): Q1 is positive, (supplied to the system): and Q2 is negative (given out by the system).
and ...
Refrigerators equire a lot of energy to do a little. Q2 is bigger than Q1, which is unfortunate, especially in Bangkok, where it would be helpful if the frig did not heat the kitchen.
Note: the heat supplied to the large kitched raises the temperature say 2°C. A smaller amount of heat is removed from the box, but the temperature of the small box is lowered by 20°C. Q1 and Q2 are heats not temperatures.
Coefficient of performance
The coefficient of performance of a particular refrigerator is defined as the heat removed from the cold box (Q1) divided by the energy input to the refrigerator (DW) [the energy we have to pay for].
Note: the definition is the same as the definition of the efficiency of a heat engine. "What you want to do, over what you have to pay for."
Note: all real refrigerators have a lower coefficient of performance than that of the equivalent Carnot refrigerator, because the processes are not perfectly reversible due to turbulence, friction etc.
Heat pumps are refrigerators with the business end on the hot side. A refrigerator and a heat pump are the same machine - physically turned around - but running in the same direction on the Carnot diagram.
A heat pump takes heat from a cold reservoir (the outside in a cold climate) and transfers it to a warm reservoir (the inside of a house). The process would violate the second law of thermodynamics without the input of energy (work).
The heat transferred to the house (the warm reservoir) is.Q2.
The owner of a heat pump is 'clever because Q2 the heat supplied to the house, is larger than DW, the work that must be paid for to get it there. The disadvantage of the refrigerator, has become the advantage of the heat pump.
Coefficient of performance
The coefficient of performance of a heat pump is defined as the heat transferred to the warm reservoir (Q2) over the work required to do the transfer, (DW).
The coefficient of performance of a Carnot heat pump is greater than 1.
Note: all real heat pumps have a lower coefficient of performance than that of the equivalent Carnot heat pump, because the processes are not perfectly reversible, due to turbulence, friction etc.
The heat pump and the refrigerator are the same thing, runing in the same direction - from a different point of view.
To make a heat pump, an air conditioner is turned around, so the hot side is inside and the cold side is outside.
The editor remembers working in Fiji at the University of the South Pacific in the late seventies. We ran an air conditioner day and night to cool the physics store-room to try to prevent equipment from rusting. That was expensive - we had no air conditioning anywhere else. The head of Physics - Dr Twidell from England - had a bright idea.
He turned the store-room air conditioner around, so the store-room was hot. Because it was hot, water evaporated and the equipment stayed dry - hot, but not wet. He figured that the equipment would be safe from rusting and the cost would be less because the heat pump was more efficient than the same thing run as a refrigerator, and the temperature differences were less. The cold room had been maintained at 18°C. The outside temperature varied from 34°C in the daytime to 26°C at night. The hot room was maintained at 40°C. The temperature differences between inside and outside, and consequently the energy requirements, were less for the hot room.
Twidell saved a little money, but he had five angry technicians.