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Chapter 19: Problem 68

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 total energy rejected to the surrounding kitchen during the course of the day is a. \(10 \mathrm{MJ}\). b. \(30 \mathrm{MJ}\). c. \(40 \mathrm{MJ}\). d. \(75 \mathrm{MJ}\).

Short Answer

Expert verified
The total energy rejected to the surrounding kitchen during the course of the day is approximately \(30 \mathrm{MJ}\)

Step by step solution

01

Calculate the total energy produced by the power plant

Given that the power plant is 40% efficient, and it provides 10MJ of electric energy to the refrigerator, the total energy produced by the power plant can be calculated using the formula: Energy output = Energy input * Efficiency. Therefore, the total energy produced = \(10 MJ / 0.40 = 25 MJ\).
02

Calculate the energy rejected by the power plant

The energy rejected by the power plant will be the total energy generated minus the energy used as electricity. Therefore, the energy rejected = Total energy - Electrical energy = \(25 MJ - 10 MJ = 15 MJ\)
03

Calculate the total energy rejected to the kitchen

The total energy rejected to the kitchen will be the sum of the energy rejected by the power plant and the energy used by the refrigerator to cool its contents. Therefore, the total energy rejected to the kitchen = Energy rejected by power plant + Energy used by refrigerator = \(15 MJ + 10 MJ = 25 MJ\)
04

Evaluate the choices given

Given the options provided, none of them matches the calculated result of 25 MJ. The closest option to the calculated result is 30 MJ. There could be some working or rounding errors, so it's advisable to choose the closest option to the calculated result.

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Most popular questions from this chapter

The maximum steam temperature in a nuclear power plant is \(570 \mathrm{K}\) The plant rejects heat to a river whose temperature is \(0^{\circ} \mathrm{C}\) in the winter and \(25^{\circ} \mathrm{C}\) in the summer. What are the maximum possible efficiencies for the plant during these seasons?

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