<< Chapter < Page Chapter >> Page >

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} {} ?

4.82

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} {} ?

0.311

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?

27.6ºC

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

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply
Practice Key Terms 2

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, College physics ii. OpenStax CNX. Nov 29, 2012 Download for free at http://legacy.cnx.org/content/col11458/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics ii' conversation and receive update notifications?

Ask