# 4.3 Refrigerators and heat pumps

 Page 1 / 4
By the end of this section, you will be able to:
• Describe a refrigerator and a heat pump and list their differences
• Calculate the performance coefficients of simple refrigerators and heat pumps

The cycles we used to describe the engine in the preceding section are all reversible, so each sequence of steps can just as easily be performed in the opposite direction. In this case, the engine is known as a refrigerator or a heat pump, depending on what is the focus: the heat removed from the cold reservoir or the heat dumped to the hot reservoir. Either a refrigerator or a heat pump is an engine running in reverse. For a refrigerator    , the focus is on removing heat from a specific area. For a heat pump    , the focus is on dumping heat to a specific area.

We first consider a refrigerator ( [link] ). The purpose of this engine is to remove heat from the cold reservoir, which is the space inside the refrigerator for an actual household refrigerator or the space inside a building for an air-conditioning unit.

A refrigerator (or heat pump) absorbs heat ${Q}_{\text{c}}$ from the cold reservoir at Kelvin temperature ${T}_{\text{c}}$ and discards heat ${Q}_{\text{h}}$ to the hot reservoir at Kelvin temperature ${T}_{\text{h}},$ while work W is done on the engine’s working substance, as shown by the arrow pointing toward the system in the figure. A household refrigerator removes heat from the food within it while exhausting heat to the surrounding air. The required work, for which we pay in our electricity bill, is performed by the motor that moves a coolant through the coils. A schematic sketch of a household refrigerator is given in [link] .

The effectiveness or coefficient of performance     ${K}_{\text{R}}$ of a refrigerator is measured by the heat removed from the cold reservoir divided by the work done by the working substance cycle by cycle:

${K}_{\text{R}}=\frac{{Q}_{\text{c}}}{W}=\frac{{Q}_{\text{c}}}{{Q}_{\text{h}}-{Q}_{\text{c}}}.$

Note that we have used the condition of energy conservation, $W={Q}_{\text{h}}-{Q}_{\text{c}},$ in the final step of this expression.

The effectiveness or coefficient of performance ${K}_{\text{P}}$ of a heat pump is measured by the heat dumped to the hot reservoir divided by the work done to the engine on the working substance cycle by cycle:

${K}_{\text{P}}=\frac{{Q}_{\text{h}}}{W}=\frac{{Q}_{\text{h}}}{{Q}_{\text{h}}-{Q}_{\text{c}}}.$

Once again, we use the energy conservation condition $W={Q}_{\text{h}}-{Q}_{\text{c}}$ to obtain the final step of this expression.

## Summary

• A refrigerator or a heat pump is a heat engine run in reverse.
• The focus of a refrigerator is on removing heat from the cold reservoir with a coefficient of performance ${K}_{\text{R}}.$
• The focus of a heat pump is on dumping heat to the hot reservoir with a coefficient of performance ${K}_{\text{P}}.$

## Conceptual questions

If the refrigerator door is left open, what happens to the temperature of the kitchen?

The temperature increases since the heat output behind the refrigerator is greater than the cooling from the inside of the refrigerator.

Is it possible for the efficiency of a reversible engine to be greater than 1.0? Is it possible for the coefficient of performance of a reversible refrigerator to be less than 1.0?

## Problems

A refrigerator has a coefficient of performance of 3.0. (a) If it requires 200 J of work per cycle, how much heat per cycle does it remove the cold reservoir? (b) How much heat per cycle is discarded to the hot reservoir?

a. 600 J; b. 800 J

During one cycle, a refrigerator removes 500 J from a cold reservoir and rejects 800 J to its hot reservoir. (a) What is its coefficient of performance? (b) How much work per cycle does it require to operate?

If a refrigerator discards 80 J of heat per cycle and its coefficient of performance is 6.0, what are (a) the quantity off heat it removes per cycle from a cold reservoir and (b) the amount of work per cycle required for its operation?

a. 69 J; b. 11 J

A refrigerator has a coefficient of performance of 3.0. (a) If it requires 200 J of work per cycle, how much heat per cycle does it remove the cold reservoir? (b) How much heat per cycle is discarded to the hot reservoir?

what is calorimeter
heat measuring device
Suvransu
What is mean electric potential
Electric density formula
Int E•dA
Vineet
what is relation betweeen potential energy of a system and work done in bringing last chaege from infinity
Einstein and his general theory of relativity, a very nice concept,which revolutionize our modern world.
what's the theory of relativity?
Piyali
it related to universe time period
jyotirmayee
it is a theory in which time is taken as relative,for diff. motion of objects.
Antares
no !!!
jyotirmayee
it is E=mc'square
jyotirmayee
what is black hole?
jyotirmayee
E=mc^2 is just a reln which sums up everything dude
Antares
what does e=mc^2 stand for?explain
Piyali
m not dude
jyotirmayee
e for speed of light
jyotirmayee
c for speed of light
jyotirmayee
m for mass of object
jyotirmayee
black hole is a super massive object in space gravitation pull of which s so strong dt evn light cannot escape. John wheeler 1st detected it, n concept of it ws given by Einstein himself from his general theory of relativity. Basically v cn si 3 types of it super massive, interstellar n intermediate
Antares
which topic now u studying?
jyotirmayee
e defined? sorry it,s wrong
jyotirmayee
how black holes r formed?
Piyali
e is not speed of light
jyotirmayee
black holes formed when the centre of very massive star collapsed itself
jyotirmayee
e is energy.
Antares
what do u mean by quantum mechanics?
jyotirmayee
in most of d cases black holes r formed by massive collapsed star or star system
Antares
sahoo u don't seem to understand relative physics, plz study that first.
Antares
Apollo is the name of a satellite !!!!!
jyotirmayee
quantum mechanics is d study of physics describing nature at d smallest level of energy of atoms n subatomic particles.
Antares
qm means explains about the microscopic particles..
KRANTHI
nope name of d sun god
Antares
why the mercury used in thermometers?
jyotirmayee
Ali brother ur exactly spelling is wrong,,,,,
jyotirmayee
why the colour of tube light white?
jyotirmayee
why the mouth became red colour ,,by the regular eating of leaf called ,,betel combining with areca?
jyotirmayee
all formula for calculate specific latent heat of any substance
hello
Nigar
real
Nigar
c'mon guys.. let's talk Physics.
Yoblaze
mass multiplied with latent heat of a substance
Yoblaze
you both?
jyotirmayee
in which class?
jyotirmayee
physics is the only subject which underestimated chemistry ,,bio
jyotirmayee
how capacitor is made in inst?
Piyali
what is dipole moment
it is the product of electric charges and distance between the two charges
Shikhar
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
brad is separation and distance ,are they different?
Ssempala
What is dielectric
its a type of medium. generally poor conductors. but their conductivity can be changed
vedanth
you just have to add impurities
vedanth
Thanks
Ssempala
grt
Ssempala
a material which behave as conductor
Shikhar
insulating material, energy level for electron transfer is very high e.g used to increase a magnetic field in a capacitor
What is the difference between specific heat capacity and heat capacity? Give the equations
presentation on power
relation between Celsius and Kelvin
0" degree Celsius=273kelvin
jyotirmayee
Newton's second laws is call with
what is mean by thermodynamics
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
show mathematically that an electron has the greater speed than the proton when they attract each other
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar