13.2 Math and the Environment

Rows of solar panels lined up in an open space. — **Figure 13.8** Solar panels harness the sun's energy to power homes, businesses, and various methods of transportation.Solar panels harness the sun's energy to power homes, businesses, and various methods of transportation. (credit: modification of work “Craters of the Moon solar array” by NPS Climate Change Response/Flickr, Public Domain Mark 1.0)

Learning Objectives

After completing this section, you should be able to:

Compute how conserving water can positively impact climate change.
Discuss the history of solar energy.
Compute power needs for common devices in a home.
Explore advantages of solar power as it applies to home use.

Climate change and emissions management have been debated topics in recent years. However, more and more people are recognizing the impacts that have resulted in temperature changes and are seeking timely and effective action. The World Meteorological Organization shared in a June 2021 publication that “2021 is a make-or-break year for climate action, with the window to prevent the worst impacts of climate change—which include ever more frequent more intense droughts, floods and storms—closing rapidly.” The problem no longer belongs to a few countries or regions but rather is a worldwide concern measured with increasing temperatures leading to decreased glacier coverage and resulting rise in sea levels.

The good news is, there are small steps that each of us can do that collectively can positively impact climate change.

Making a Positive Impact on Climate Change—Water Usage

Our use of water is one element that impacts climate change. Having access to clean, potable water is critical for not only our health but also for the health of our ecosystem. About 1 out of 10 people on our planet do not have easy access to clean water to drink. As each of us conserves water, we prolong the life span of fresh water from our lakes and rivers and also reduce the impact on sewer systems and drainage in our communities. Additionally, as we conserve water, we also conserve electricity that is used to bring water to and in our homes. So, what can we do to help conserve water?

Example 1 Brushing Your Teeth (One Person’s Contribution)

Brushing your teeth with the water running continually uses about 4 gal of water. Turning the faucet off when you are not rinsing uses less than one-fourth of a gallon of water. Considering the recommendation to brush your teeth twice a day, how much water would be saved in a week if the faucet was off when not rinsing?

Leaving the water running continually:

Step 1: Calculate gallons used not with water running continually:

Brushing twice a day for 7 days using 4 gal of water for each brushing

$(2 times a day) (7 days) (4 gal) = 56 gal$

Step 2: Calculate gallons used turning the faucet off when you are not rinsing:

Brushing twice a day for 7 days using 0.25 gal of water for each brushing

$(2 times a day) (7 days) (0.25 gal) = 3.5 gal$

Step 3: Calculate savings:

$\begin{matrix} Savings & = & 56 gal - 3.5 gal \\ = & 52.5 gal \end{matrix}$

During one week, 52.5 gal of water would be saved if one person turned the faucet off except when rinsing when brushing your teeth.

Example 2 Brushing Your Teeth (Multiple People’s Contribution – Town)

Using the data in Example 1, how much water would be saved in a month if one-fifth of a town’s population of 15,000 turned the faucet off when brushing their teeth except when rinsing?

Step 1: From Example 1, we found that 1 person saves 52.5 gal per week.

Step 2: Calculate the population to save water:

$One-fifth of 15,000 people equals 3,000 people$

Step 3: One-fifth of a town’s population turning off the faucet when brushing their teeth for a month:

$open parenthesis 3,000 close parenthesis open parenthesis 52.5 gal per week close parenthesis open parenthesis 4 weeks close parenthesis equals 630,000 gal$

During one month, 630,000 gallons of water would be saved if one-fifth of a town of 15,000 people turned the faucet off except when rinsing when brushing their teeth.

Example 3 Brushing Your Teeth (Multiple People’s Contribution – State)

Using the data in Example 1, how much water would be saved in a year if one-fourth of the population of the state of Minnesota, which is approximately 5.6 million people, turned the faucet off when brushing their teeth except when rinsing for a year (52 weeks)?

Step 1: From Example 1, we found that 1 person saves 52.5 gal per week.

Step 2: Calculate the population to save water:

$One-fourth of 5.6 million people equals 1.4 million people$

Step 3: One-fourth of a town’s population turning off the faucet when brushing their teeth for a month:

$open parenthesis 1.4 million close parenthesis open parenthesis 52.5 gal per week close parenthesis open parenthesis 52 weeks close parenthesis equals 3,822 million gal$

During one year, 3,822 million gal of water would be saved if one-fourth of the state of Minnesota turned the faucet off except when rinsing when brushing their teeth.

History of Solar Energy

In the mid-1800s, Willoughby Smith discovered photoconductive responsiveness in selenium. Shortly thereafter, William Grylls Adams and Richard Evans Day discovery that selenium can produce electricity if exposed to the sun was a major breakthrough. Less than 10 years later, Charles Fritts invented the first solar cells using selenium. Jumping a mere 100 years later, Bell Labs in the United States produced the first practical photovoltaic cells in the mid-1950s and developed versions used to power satellites in the same decade.

Solar panel use has exploded in recent decades and is now used by residences, organizations, businesses, and government buildings such as the White House, space to power satellites, and various methods of transportation. One reason for the expansion is a continuing drop in cost combined with an increase in performance and durability. In the mid-1950s, the cost of a solar panel was around $300 per watt capability. Twenty years later, the cost was a third of the 1950s’ cost. Currently, solar panel cost has dropped to less than $1 per watt while decreasing in size as well as increasing in longevity. The dropping price and improved performance has moved solar to a modest investment that can pay for itself in less than half the time of systems from 15 years ago.

Who Knew?

Solar Power’s Age

The sun has been harnessed by humans for centuries. The earliest recorded use of tapping the sun’s energy for power dates back to the seventh century BC when man focused the sun’s rays through a magnifying glass to create fire. Four thousand years later, we find historical record of using mirrors to focus the sun and light torches, often for ceremonial proceedings. Use of the sun to light torches continued through the centuries and has been recorded by various cultures including the Chinese civilization in 20 AD and beyond.

In more recent years, the sun was harnessed to power ovens on ships traversing to oceans in the 1700s. At the same time, the power of the sun was utilized to power steamboats through the 1800s. Mária Telkes, a Hungarian-born American scientist, invented a widely deployed solar seawater distiller used on World War II life rafts. Soon after, she partnered with architect Eleanor Raymond to design the first modern home to be completely heated by solar power. Air warmed on rooftop collectors transferred heat to salts, which stored the heat for later use.

Although solar panels as we know them today are relatively new in history, use of the sun to harness power is much older.

Compute Power Needs for Common Home Devices

A kilowatt (kW) is 1,000 watts (W). A kilowatt-hour (kWh) is a measurement of energy use, which is the amount of energy used by a 1,000-watt device to run for an hour. Using the definition of a kilowatt-hour, to calculate how long it would take to consume 1 kWh of power, we divide 1,000 by the watts use of a device.

For example, a 75 W bulb would take $1,000 \div 75 = 13.3 hours$ to use 1 kW of power.

Solar Advantages

There are multiple advantages that solar power can offer us today including reducing greenhouse gas and CO₂ emissions, powering vehicles, reducing water pollution, reducing strain on limited supply of other power options such as fossil fuels. We will look further at reducing greenhouse gas and CO₂ emissions.

Any gas that prevents infrared radiation from escaping Earth's atmosphere is a greenhouse gas. There are 24 currently identified greenhouse gases of which carbon dioxide is one. When measuring the impact of any of the greenhouse gases, the measurements are given in units of carbon dioxide emissions. For this reason, greenhouse gas and carbon dioxide have become interchangeable in discussions.

People in Mathematics

Charles Fritts and Mohammad M. Atalla

Charles Fritts, a New York inventor, is credited with creating the first solar cell, which he installed on a rooftop in New York City in 1884. While the solar cell was not very efficient, having a rate of conversion between 1 to 2%, this was a major step early in solar power energy. Today’s solar cells have an efficiency on average of 15 to 20%, which yields a notably higher impact. Nonetheless, the work that Fritts successfully completed marked the start of solar energy through the use of photovoltaic solar panels in the United States.

Mohamed M. Atalla was an Egyptian-born scientist who moved to the United States to complete his studies, and undertook research and development at Bell Laboratories in New Jersey. Many of the early efficiency gains in solar cells were due to his development of processes for using silicon within electronic devices. Atalla's work led to the invention of silicon transistors and microchips (including his own invention of the MOSFET, the most widely used transistor in the world), and quickly increased the efficiency of solar cells.

Key Terms

greenhouse gas
CO₂ emissions
watt
kilowatt (kW)

Key Concepts

Recognize how water conservation by one person, family, community, or nation can positively impact the world’s freshwater supply.
Recall components from the history of solar use by mankind.
Calculate electrical demand given watts.
Recognize advantages of residential solar power.

Formulas

$1,000 / watts equals time needed to use 1 kWh$

$watts / 1, 000 equals kilowatt hours$

Adapted from Contemporary Mathematics by OpenStax (openstax.org), licensed under CC BY-NC-SA 4.0. Changes were made. License: CC-BY-NC-SA-4.0.