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Chapter 1: Problem 42

A watt is a measure of power (the rate of energy change) equal to $1 \mathrm{~J} / \mathrm{s}$. (a) Calculate the number of joules in a kilowatt- hour. (b) An adult person radiates heat to the surroundings at about the same rate as a 100 -watt electric incandescent light bulb. What is the total amount of energy in kcal radiated to the surroundings by an adult over a 24 h period?

Short Answer

Expert verified
(a) There are \(3.6*10^6\) Joules in a kilowatt-hour. (b) An adult radiates approximately 2063 kcal of energy over a 24-hour period.

Step by step solution

01

Convert kilowatt-hour to Joules

To calculate the number of Joules in a kilowatt-hour, first, we need to convert kilowatts to watts and hours to seconds. 1 kilowatt-hour (kW-h) = 1000 watts * 3600 seconds Now we can multiply the total power by the total time to find the energy in Joules. Energy = Power × Time
02

Calculate the energy in Joules

Now we can calculate the energy in Joules by using the formula: Energy = Power × Time Energy = 1000 W × 3600 s = 3,600,000 Joules So there are \(3.6*10^6\) Joules in a kilowatt-hour.
03

Calculate the energy radiated by an adult over 24 hours

Now let's calculate the energy radiated by an adult over a 24 hour period. First, we will find the energy in Joules and then convert it into kilocalories (kcal). Since an adult radiates heat at the same rate as a 100-watt light bulb, we can use the power and multiply it with the 24-hour time period. Energy (Joules) = Power × Time
04

Calculate the energy in Joules radiated by an adult over 24 hours

Now we need to calculate the energy in Joules over a 24-hour period. First, we will convert the 24 hours into seconds. 24 hours = 86400 seconds Energy (Joules) = Power × Time = 100 W × 86400 s = 8,640,000 Joules
05

Convert energy in Joules to kilocalories (kcal)

Now we need to convert the energy from Joules to kcal using the conversion factor: 1 kcal = 4184 J Energy (kcal) = 8,640,000 Joules / 4184 Joules/kcal ≈ 2063 kcal So, an adult radiates approximately 2063 kcal of energy over a 24-hour period.

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Most popular questions from this chapter

(a) Three spheres of equal size are composed of aluminum (density $\left.=2.70 \mathrm{~g} / \mathrm{cm}^{3}\right),\( silver \)\left(\right.$ density \(\left.=10.49 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and nickel (density \(\left.=8.90 \mathrm{~g} / \mathrm{cm}^{3}\right) .\) List the spheres from lightest to heaviest. (b) Three cubes of equal mass are composed of gold (density \(=19.32 \mathrm{~g} / \mathrm{cm}^{3}\) ), platinum (density \(\left.=21.45 \mathrm{~g} / \mathrm{cm}^{3}\right),\) and lead \(\left(\right.\) density \(\left.=11.35 \mathrm{~g} / \mathrm{cm}^{3}\right) .\) List the cubes from smallest to largest. [Section 1.5\(]\)

A \(40-1 b\) container of peat moss measures \(14 \times 20 \times 30\) in. A 40-lb container of topsoil has a volume of 1.9 gal. (a) Calculate the average densities of peat moss and topsoil in units of \(\mathrm{g} / \mathrm{cm}^{3}\). Would it be correct to say that peat moss is "lighter" than topsoil? (b) How many bags of peat moss are needed to cover an area measuring $15.0 \mathrm{ft} \times 20.0 \mathrm{ft}$ to a depth of 3.0 in.?

(a) A bumblebee flies with a ground speed of \(15.2 \mathrm{~m} / \mathrm{s}\). Calculate its speed in \(\mathrm{km} / \mathrm{hr}\). (b) The lung capacity of the blue whale is \(5.0 \times 10^{3} \mathrm{~L}\). Convert this volume into gallons. (c) The Statue of Liberty is \(151 \mathrm{ft}\) tall. Calculate its height in meters. (d) Bamboo can grow up to \(60.0 \mathrm{~cm} /\) day, Convert this growth rate into inches per hour.

Indicate which of the following are exact numbers: (a) the mass of a 7.5 - by \(12.5-\mathrm{cm}\) index card, \((\mathbf{b})\) the number of grams in a kilogram, \((\mathbf{c})\) the volume of a cup of Seattle's Best coffee, (d) the number of centimeters in a kilometer, \((\mathbf{e})\) the number of microseconds in a week, \((\mathbf{f})\) the number of pages in this book.

A thief plans to steal a cylindrical platinum medal with a radius of $2.3 \mathrm{~cm}\( and a thickness of \)0.8 \mathrm{~cm}$ from a jewellery store. If the platinum has a density of \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what is the mass of the medal in \(\mathrm{kg} ?\) [The volume of a cylinder is \(\left.V=\pi r^{2} h .\right]\)
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