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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
.
- A refrigerator is a heat pump; it takes warm ambient air and expands it to chill it.
Conceptual questions
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?
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Why do refrigerators, air conditioners, and heat pumps operate most cost-effectively for cycles with a small difference between
and
? (Note that the temperatures of the cycle employed are crucial to its
.)
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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.
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Problem exercises
What is the coefficient of performance of an ideal heat pump that has heat transfer from a cold temperature of
to a hot temperature of
?
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Suppose you have an ideal refrigerator that cools an environment at
and has heat transfer to another environment at
. What is its coefficient of performance?
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What is the best coefficient of performance possible for a hypothetical refrigerator that could make liquid nitrogen at
and has heat transfer to the environment at
?
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(a) What is the best coefficient of performance for a heat pump that has a hot reservoir temperature of
and a cold reservoir temperature of
? (b) How much heat transfer occurs into the warm environment if
of work (
) is put into it? (c) If the cost of this work input is
, 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
.)
(a) 4.61
(b)
(c) To transfer
, heat pump costs $1.00, natural gas costs $1.34.
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(a) What is the best coefficient of performance for a refrigerator that cools an environment at
and has heat transfer to another environment at
? (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
(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.
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Suppose you want to operate an ideal refrigerator with a cold temperature of
, and you would like it to have a coefficient of performance of 7.00. What is the hot reservoir temperature for such a refrigerator?
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An ideal heat pump is being considered for use in heating an environment with a temperature of
. What is the cold reservoir temperature if the pump is to have a coefficient of performance of 12.0?
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A 4-ton air conditioner removes
(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 (
) of 12.0? (b) What is the cost of doing this if the work costs 10.0 cents per
(one kilowatt-hour)? (c) Discuss whether this cost seems realistic. Note that the energy efficiency rating (
) 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)
(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).
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Show that the coefficients of performance of refrigerators and heat pumps are related by
.
Start with the definitions of the
s and the conservation of energy relationship between
,
, and
.
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Questions & Answers
What are the factors that affect demand for a commodity
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
Lambiv
how is the graph works?I don't fully understand
hi guys good evening to all
Lambiv
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
Can I ask you other question?
Shukri
What is different between quantity demand and demand?
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
how do you save a country economic situation when it's falling apart
what is the difference between economic growth and development
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
any question about economics?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
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Source:
OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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