Skip to main content
Ch.1 - Introduction: Matter, Energy, and Measurement
Chapter 1, Problem 87

The total rate at which power is used by humans worldwide is approximately 15 TW (terawatts). The solar flux averaged over the sunlit half of Earth is 680 W>m2 (assuming no clouds). The area of Earth's disc as seen from the Sun is 1.28 * 1014 m2. The surface area of Earth is approximately 197,000,000 square miles. How much of Earth's surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can convert only 10% of the available sunlight into useful power

Verified step by step guidance
1
Calculate the total solar power received by Earth by multiplying the solar flux (680 W/m^2) by the area of Earth's disc (1.28 * 10^{14} m^2).
Determine the useful power output from the solar energy collectors by multiplying the total solar power received by the conversion efficiency (10%).
Compare the useful power output from the solar collectors to the total power used by humans worldwide (15 TW) to find the fraction of Earth's disc area needed.
Convert the fraction of Earth's disc area needed into the actual area by multiplying it by the total surface area of Earth (197,000,000 square miles).
Convert the area from square miles to a more convenient unit if necessary, such as square kilometers or square meters, for better understanding.

Verified Solution

Video duration:
3m
This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solar Flux

Solar flux refers to the amount of solar energy received per unit area, typically measured in watts per square meter (W/m²). In this context, the average solar flux over the sunlit half of Earth is 680 W/m², indicating how much solar power is available for conversion into usable energy. Understanding solar flux is crucial for calculating the potential energy that can be harnessed from sunlight.
Recommended video:
Guided course
02:46
Entropy in Thermodynamics

Energy Conversion Efficiency

Energy conversion efficiency is the ratio of useful energy output to the total energy input, expressed as a percentage. In this scenario, the solar energy collectors are assumed to convert only 10% of the available sunlight into usable power. This concept is essential for determining how much solar energy must be collected to meet the total energy demand of humanity, as it directly impacts the required surface area of solar collectors.
Recommended video:
Guided course
01:56
Conversion Factors

Surface Area Calculations

Surface area calculations involve determining the total area available for solar energy collection. The area of Earth's disc as seen from the Sun is given as 1.28 x 10^14 m², which is critical for understanding how much solar energy can be captured. Additionally, knowing the total surface area of Earth helps in assessing the proportion of land that would need to be covered by solar collectors to meet global energy needs.
Recommended video:
Guided course
03:47
Perimeter, Area, Volume
Related Practice
Textbook Question

Saline solution used in hospital contains 0.9% sodium chloride by mass. Calculate the number of grams of sodium chloride in 0.5 gal of saline solution if the solution has a density of 1.01 g/mL.

1171
views
Textbook Question
A 40-lb container of peat moss measures 14 * 20 * 30 in. A 40-lb container of topsoil has a volume of 1.9 gal. (b) How many bags of peat moss are needed to cover an area measuring 15.0 ft * 20.0 ft to a depth of 3.0 in.?
622
views
Open Question
A 10.0 g block of gold is hammered into a thin gold sheet which has an area of 150 cm2. Given the density of gold is 19.3 g/cm3, what is the approximate thickness of the gold sheet in millimeters?
Open Question
In 2005, J. Robin Warren and Barry J. Marshall shared the Nobel Prize in Medicine for discovering the bacterium Helicobacter pylori and for establishing experimental proof that it plays a major role in gastritis and peptic ulcer disease. The story began when Warren, a pathologist, noticed that bacilli were associated with the tissues taken from patients suffering from ulcers. Look up the history of this case and describe Warren’s first hypothesis. What sorts of evidence were required to establish a credible theory based on it?
Open Question
A 30.0-cm-long cylindrical plastic tube, sealed at one end, is filled with acetic acid. The mass of acetic acid needed to fill the tube is found to be 89.24 g. The density of acetic acid is 1.05 g/mL. Calculate the inner diameter of the tube in centimeters.
Textbook Question

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry. (b) The relative amount of gold in an alloy is commonly expressed in units of carats. Pure gold is 24 carat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is 50% gold is 12 carat. State the purity of the gold jewelry in carats.

1427
views