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Section summary

  • An artifact of the second law of thermodynamics is the ability to heat an interior space using a heat pump. Heat pumps compress cold ambient air and, in so doing, heat it to room temperature without violation of conservation principles.
  • To calculate the heat pump’s coefficient of performance, use the equation COP hp = Q h W size 12{ ital "COP" rSub { size 8{"hp"} } = { {Q rSub { size 8{h} } } over {W} } } {} .
  • A refrigerator is a heat pump; it takes warm ambient air and expands it to chill it.

Conceptual questions

Explain why heat pumps do not work as well in very cold climates as they do in milder ones. Is the same true of refrigerators?

In some Northern European nations, homes are being built without heating systems of any type. They are very well insulated and are kept warm by the body heat of the residents. However, when the residents are not at home, it is still warm in these houses. What is a possible explanation?

Why do refrigerators, air conditioners, and heat pumps operate most cost-effectively for cycles with a small difference between T h size 12{T rSub { size 8{h} } } {} and T c size 12{T rSub { size 8{c} } } {} ? (Note that the temperatures of the cycle employed are crucial to its COP size 12{ ital "COP"} {} .)

Grocery store managers contend that there is less total energy consumption in the summer if the store is kept at a low temperature. Make arguments to support or refute this claim, taking into account that there are numerous refrigerators and freezers in the store.

Can you cool a kitchen by leaving the refrigerator door open?

Problem exercises

What is the coefficient of performance of an ideal heat pump that has heat transfer from a cold temperature of 25 . 0 º C size 12{-"25" "." 0°C} {} to a hot temperature of 40 . 0 º C size 12{"40" "." 0°C} {} ?


Suppose you have an ideal refrigerator that cools an environment at 20 . 0 º C size 12{-"20" "." 0°C} {} and has heat transfer to another environment at 50 . 0 º C size 12{"50" "." 0°C} {} . What is its coefficient of performance?

What is the best coefficient of performance possible for a hypothetical refrigerator that could make liquid nitrogen at 200 º C size 12{-"200"°C} {} and has heat transfer to the environment at 35 . 0 º C size 12{"35" "." 0°C} {} ?


In a very mild winter climate, a heat pump has heat transfer from an environment at 5 . 00 º C size 12{5 "." "00"°C} {} to one at 35 . 0 º C size 12{"35" "." 0°C} {} . What is the best possible coefficient of performance for these temperatures? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics .

(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of 50 . 0 º C and a cold reservoir temperature of 20 .0ºC ? (b) How much heat transfer occurs into the warm environment if 3 .60 × 10 7 J of work ( 10 . 0 kW h ) is put into it? (c) If the cost of this work input is 10.0 cents/kW h , how does its cost compare with the direct heat transfer achieved by burning natural gas at a cost of 85.0 cents per therm. (A therm is a common unit of energy for natural gas and equals 1 . 055 × 10 8 J size 12{1 "." "055"´"10" rSup { size 8{8} } " J"} {} .)

(a) 4.61

(b) 1 . 66 × 10 8 J or 3 . 97 × 10 4 kcal {1 "." "66" times "10" rSup { {8} } " J"`"or 3" "." "97" times "10" rSup { {4} } `"kcal"} {}

(c) To transfer 1 . 66 × 10 8 J {1 "." "66" times "10" rSup { {8} } " J"} {} , heat pump costs $1.00, natural gas costs $1.34.

(a) What is the best coefficient of performance for a refrigerator that cools an environment at 30 . 0 º C size 12{-"30" "." 0°C} {} and has heat transfer to another environment at 45 . C size 12{"45" "." 0°C} {} ? (b) How much work in joules must be done for a heat transfer of 4186 kJ from the cold environment? (c) What is the cost of doing this if the work costs 10.0 cents per 3 . 60 × 10 6 J size 12{3 "." "60"´"10" rSup { size 8{6} } " J"} {} (a kilowatt-hour)? (d) How many kJ of heat transfer occurs into the warm environment? (e) Discuss what type of refrigerator might operate between these temperatures.

Suppose you want to operate an ideal refrigerator with a cold temperature of 10 . C size 12{-"10" "." 0°C} {} , and you would like it to have a coefficient of performance of 7.00. What is the hot reservoir temperature for such a refrigerator?


An ideal heat pump is being considered for use in heating an environment with a temperature of 22 . 0 º C size 12{"22" "." 0°C} {} . What is the cold reservoir temperature if the pump is to have a coefficient of performance of 12.0?

A 4-ton air conditioner removes 5 . 06 × 10 7 J (48,000 British thermal units) from a cold environment in 1.00 h. (a) What energy input in joules is necessary to do this if the air conditioner has an energy efficiency rating ( EER ) of 12.0? (b) What is the cost of doing this if the work costs 10.0 cents per 3 . 60 × 10 6 J size 12{3 "." "60"´"10" rSup { size 8{6} } " J"} {} (one kilowatt-hour)? (c) Discuss whether this cost seems realistic. Note that the energy efficiency rating ( EER size 12{ ital "EER"} {} ) of an air conditioner or refrigerator is defined to be the number of British thermal units of heat transfer from a cold environment per hour divided by the watts of power input.

(a) 1 . 44 × 10 7 J {1 "." "44" times "10" rSup { {7} } "J"} {}

(b) 40 cents

(c) This cost seems quite realistic; it says that running an air conditioner all day would cost $9.59 (if it ran continuously).

Show that the coefficients of performance of refrigerators and heat pumps are related by COP ref = COP hp 1 size 12{ ital "COP" rSub { size 8{"ref"} } = ital "COP" rSub { size 8{"hp"} } -1} {} .

Start with the definitions of the COP size 12{ ital "COP"} {} s and the conservation of energy relationship between Q h size 12{Q rSub { size 8{h} } } {} , Q c size 12{Q rSub { size 8{c} } } {} , and W size 12{W} {} .

Questions & Answers

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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