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Chapter 19: Problem 66

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some \(80 \%\) in the past four decades. In the course of a day, one kitchen refrigerator removes \(30 \mathrm{MJ}\) of energy from its contents, in the process consuming \(10 \mathrm{MJ}\) of electrical energy. The electricity comes from a \(40 \%\) efficient coal-fired power plant. The refrigerator's COP is a. \(\frac{1}{3}\). b. 2. c. 3. d. 4.

Short Answer

Expert verified
The refrigerator's Coefficient of Performance (COP) is 3, hence the correct option is c.

Step by step solution

01

Understand the definition of COP

The Coefficient of Performance (COP) for a refrigerator is defined as the ratio of the energy removed from the inside of the refrigerator to the work done on the system, or mathematically, \[ COP = \frac{{Q_c}}{{W}} \] where \(Q_c\) represents the energy removed from the system (cold reservoir), and \(W\) is the work done on the system (input energy)
02

Substitute the given values

To calculate the COP of the refrigerator, plug in the given values. Here, \(Q_c = 30 \, MJ\) is the energy removed from the refrigerator and \(W = 10 \, MJ\) is the input electrical energy. So, the COP of the refrigerator can be calculated as follows: \[ COP = \frac{{Q_c}}{{W}} = \frac{{30 \, MJ}}{{10 \, MJ}}\]
03

Calculate the Coefficient of Performance

Perform the division to get the COP: \[ COP = 3 \]

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Most popular questions from this chapter

Refrigerators remain among the greatest consumers of electrical energy in most homes, although mandated efficiency standards have decreased their energy consumption by some \(80 \%\) in the past four decades. In the course of a day, one kitchen refrigerator removes \(30 \mathrm{MJ}\) of energy from its contents, in the process consuming \(10 \mathrm{MJ}\) of electrical energy. The electricity comes from a \(40 \%\) efficient coal-fired power plant. The electrical energy a. is used to run the light bulb inside the refrigerator. b. wouldn't be necessary if the refrigerator had enough insulation. c. retains its high-quality status after the refrigerator has used it. d. ends up as waste heat rejected to the kitchen environment.

A reversible engine contains 0.20 mol of ideal monatomic gas, initially at \(600 \mathrm{K}\) and confined to \(2.0 \mathrm{L} .\) The gas undergoes the following cycle: Isothermal expansion to \(4.0 \mathrm{L}\) \(\cdot\) Isovolumic cooling to \(300 \mathrm{K}\) Isothermal compression to \(2.0 \mathrm{L}\) \(\cdot\) Isovolumic heating to \(600 \mathrm{K}\) (a) Calculate the net heat added during the cycle and the net work done. (b) Determine the engine's efficiency, defined as the ratio of the work done to the heat absorbed during the cycle.

A shallow pond contains 94 Mg of water. In winter, it's entirely frozen. By how much does the entropy of the pond increase when the ice, already at \(0^{\circ} \mathrm{C},\) melts and then heats to its summer temperature of \(15^{\circ} \mathrm{C} ?\)

Why doesn't the evolution of human civilization violate the second law of thermodynamics?

A refrigerator maintains an interior temperature of \(4^{\circ} \mathrm{C}\) while its exhaust temperature is \(30^{\circ} \mathrm{C} .\) The refrigerator's insulation is imperfect, and heat leaks in at the rate of 340 W. Assuming the refrigerator is reversible, at what rate must it consume electrical energy to maintain a constant \(4^{\circ} \mathrm{C}\) interior?
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