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The coefficient of performance of a refrigerator is6.0 . The refrigerator's compressor uses 115Wof electric power and is 95%efficient at converting electric power into work. What are (a) the rate at which heat energy is removed from inside the refrigerator and (b) the rate at which heat energy is exhausted into the room?

Short Answer

Expert verified

aThe rate at which heat energy is removed inside refridger,Pc=660W,

bThe rate at which heat energy is exhausted into the room,Ph=780W.

Step by step solution

01

Step: 1 Equating the Equation:

The definition of a refrigerator's coefficient of performance can be written as

K=QcWin=Qc/tWin/t=PcPin

Here Pcis power of cooling and Pinis electrical power used. As a result, we can calculate the pace at which the refrigerator takes out energy as

Pc=PinK

The motor's power input, on the other hand, is given as

Pin=Pe.

Pe is electrical power consumed.

02

Step: 2  Finding the value of Pc: (part a)

where Peis the electric power of the motor and is its efficiency. So, we put that in our previous result and find

Pc=PinK=KPe

Numerically, we will have

Pc=0.956115Pc660W.

03

Step: 3 Finding the value of Ph: (part b)

The best explanation is that the total heating power discharged into the environment equals the sum of the cooling and motor power. Because the loss in an electric motor is likewise transformed to heat, we shall analyse its electric power for the motor.. That is,

Ph=Pc+PePh660+115Ph780W.

The differences are due to the fact that we are rounding to only have one meaningful figure after the decimal point.

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Most popular questions from this chapter

shows the thermodynamic cycles of two heat engines. Which heat engine has the larger thermal efficiency? Or

are they the same? Explain.

A heat engine using 1.0molof a monatomic gas follows the cycle shown in FIGURE P21.55. 3750Jof heat energy is transferred to the gas during process 12.

a. Determine Ws,Q, and Ethfor each of the four processes in this cycle. Display your results in a table.

b. What is the thermal efficiency of this heat engine?

A heat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. The same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. Heat pumps are widely used for home heating. You can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat QH, warming the indoors. Perhaps this seems a little silly, but consider the following. Electricity can be directly used to heat a home by passing an electric current through a heating coil. This is a direct, 100%conversion of work to heat. That is, 15kWof electric power (generated by doing work at the rate of 15kJ/sat the power plant) produces heat energy inside the home at a rate of 15kJ/s. Suppose that the neighbor鈥檚 home has a heat pump with a coefficient of performance of 5.0, a realistic value. Note that 鈥渨hat you get鈥 with a heat pump is heat delivered, QH, so a heat pump鈥檚 coefficient of performance is defined asK=QH/Win.

a. How much electric power inkWdoes the heat pump use to deliver 15kJ/sof heat energy to the house?

b. An average price for electricity is about 40MJper dollar. A furnace or heat pump will run typically 250 hours per month during the winter. What does one month鈥檚 heating cost in the home with a 15kW electric heater and in the home of the neighbor who uses a heat pump?

What are (a) the heat extracted from the cold reservoir and (b) the coefficient of performance for the refrigerator shown in Figure Ex-21.20?

The cycle of FIGURE EX 21.10consists of four processes. Make a table with rows labeled Ato Dand columns labeled Eth, Ws, and Q. Fill each box in the table with +,-, or 0to indicate whether the quantity increases, decreases, or stays the same during that process.

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