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Chapter 1: Problem 146

A 2-kW electric resistance heater in a room is turned on and kept on for 50 minutes. The amount of energy transferred to the room by the heater is (a) \(2 \mathrm{~kJ}\) (b) \(100 \mathrm{~kJ}\) (c) \(6000 \mathrm{~kJ}\) (d) \(7200 \mathrm{~kJ}\) (e) \(12,000 \mathrm{~kJ}\)

Short Answer

Expert verified
a) 1000 kJ b) 5000 kJ c) 6000 kJ d) 7000 kJ Answer: c) 6000 kJ

Step by step solution

01

Convert the time to seconds

To convert the time from minutes to seconds, we should multiply the time in minutes (50) by 60 seconds, as there are 60 seconds in 1 minute: Time (seconds) = 50 minutes x 60 seconds/minute = 3000 seconds
02

Convert the power to Watts

The power of the heater is given in kilowatts (kW), and we need to convert it to watts (W). To do this, we should multiply the power in kilowatts (2) by 1000 watts, as there are 1000 watts in 1 kilowatt: Power (Watts) = 2 kW x 1000 watts/kW = 2000 watts
03

Calculate the energy transferred to the room

Now, we can use the formula for calculating the energy transferred to the room: Energy (Joules) = Power (Watts) x Time (Seconds) Energy (Joules) = 2000 watts x 3000 seconds = 6,000,000 J As the energy is given in kJ (kilojoules) in the exercise options, we should convert the energy from Joules (6,000,000 J) to kilojoules by dividing it by 1000: Energy (kJ) = 6,000,000 J ÷ 1000 = 6000 kJ
04

Match the result with given options

The calculated energy transferred to the room is 6000 kJ. Comparing it to the given options, we find that it corresponds to the option (c) 6000 kJ. So, the correct answer is (c) 6000 kJ.

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Most popular questions from this chapter

An aluminum pan whose thermal conductivity is \(237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) has a flat bottom with diameter \(15 \mathrm{~cm}\) and thickness \(0.4 \mathrm{~cm}\). Heat is transferred steadily to boiling water in the pan through its bottom at a rate of \(1400 \mathrm{~W}\). If the inner surface of the bottom of the pan is at \(105^{\circ} \mathrm{C}\), determine the temperature of the outer surface of the bottom of the pan.

Why is the metabolic rate of women, in general, lower than that of men? What is the effect of clothing on the environmental temperature that feels comfortable?

Consider a person standing in a room maintained at \(20^{\circ} \mathrm{C}\) at all times. The inner surfaces of the walls, floors, and ceiling of the house are observed to be at an average temperature of \(12^{\circ} \mathrm{C}\) in winter and \(23^{\circ} \mathrm{C}\) in summer. Determine the rates of radiation heat transfer between this person and the surrounding surfaces in both summer and winter if the exposed surface area, emissivity, and the average outer surface temperature of the person are \(1.6 \mathrm{~m}^{2}, 0.95\), and \(32^{\circ} \mathrm{C}\), respectively.

While driving down a highway early in the evening, the air flow over an automobile establishes an overall heat transfer coefficient of \(18 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The passenger cabin of this automobile exposes \(9 \mathrm{~m}^{2}\) of surface to the moving ambient air. On a day when the ambient temperature is \(33^{\circ} \mathrm{C}\), how much cooling must the air conditioning system supply to maintain a temperature of \(20^{\circ} \mathrm{C}\) in the passenger cabin? (a) \(670 \mathrm{~W}\) (b) \(1284 \mathrm{~W}\) (c) \(2106 \mathrm{~W}\) (d) \(2565 \mathrm{~W}\) (e) \(3210 \mathrm{~W}\)

Solar radiation is incident on a \(5 \mathrm{~m}^{2}\) solar absorber plate surface at a rate of \(800 \mathrm{~W} / \mathrm{m}^{2}\). Ninety-three percent of the solar radiation is absorbed by the absorber plate, while the remaining 7 percent is reflected away. The solar absorber plate has a surface temperature of \(40^{\circ} \mathrm{C}\) with an emissivity of \(0.9\) that experiences radiation exchange with the surrounding temperature of \(-5^{\circ} \mathrm{C}\). In addition, convective heat transfer occurs between the absorber plate surface and the ambient air of \(20^{\circ} \mathrm{C}\) with a convection heat transfer coefficient of \(7 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Determine the efficiency of the solar absorber, which is defined as the ratio of the usable heat collected by the absorber to the incident solar radiation on the absorber.
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