8.2 Temperature Scales - CPO Science

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<strong>8.2</strong> <strong>Temperature</strong> <strong>Scales</strong><br />

<strong>8.2</strong><br />

The Fahrenheit and Celsius temperature scales are commonly used scales for reporting temperature values.<br />

Scientists use the Celsius scale almost exclusively, as do many countries of the world. The United States relies on<br />

the Fahrenheit scale for reporting temperature information. You can convert information reported in degrees<br />

Celsius to degrees Fahrenheit or vice versa using conversion formulas.<br />

Fahrenheit (°F) to Celsius (°C) conversion formula:<br />

⎛ ⎞<br />

C = ⎜ ⎟ ° F − 32<br />

⎝9<br />

⎠<br />

o 5<br />

( )<br />

Celsius (°C) to Fahrenheit (°F) conversion formula:<br />

⎛9<br />

⎞<br />

° F = ⎜ ×° C⎟+<br />

32<br />

⎝5<br />

⎠<br />

• What is the Celsius value for 65° Fahrenheit<br />

Solution:<br />

⎛5⎞<br />

° C = ⎜ ⎟( 65° F−32)<br />

⎝9<br />

⎠<br />

⎛5⎞<br />

° C = ⎜ ⎟( 33 ) = ( 5 × 33 ) ÷ 9<br />

⎝9<br />

⎠<br />

° C = 165 ÷9<br />

° C = 18.3<br />

• 200 °C is the same temperature as what value on the Fahrenheit scale<br />

Solution:<br />

⎛9<br />

⎞<br />

° F = ⎜ ⎟( 200 ° C) + 32<br />

⎝5<br />

⎠<br />

° F = [ 9 × 200 °C ÷ 5] + 32<br />

( )<br />

° F = [1800 ÷ 5] + 32<br />

° F = 360 + 32<br />

° F = 392

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Page 2 of 4<br />

1. For each of the problems below, show your calculations. Follow<br />

the steps from the examples on the previous page.<br />

a. What is the Celsius value for 212 °F<br />

b. What is the Celsius value for 98.6 °F<br />

c. What is the Celsius value for 40 °F<br />

d. What is the Celsius value for 10 °F<br />

e. What is the Fahrenheit value for 0 °C<br />

f. What is the Fahrenheit value for 25 °C<br />

g. What is the Fahrenheit value for 75 °C<br />

<strong>8.2</strong><br />

2. The weatherman reports that today will reach a high of 45 °F. Your friend from Sweden asks what the<br />

temperature will be in degrees Celsius. What value would you report to your friend<br />

3. Your parents order an oven from England. The temperature dial on the new oven is calibrated in degrees<br />

Celsius. If you need to bake a cake at 350 °F in the new oven, at what temperature should you set the dial<br />

4. A German automobile’s engine temperature gauge reads in Celsius, not Fahrenheit. The engine temperature<br />

should not rise above about 225 °F. What is the corresponding Celsius temperature on this car’s gauge<br />

5. Your grandmother in Ireland sends you her favorite cookie recipe. Her instructions say to bake the cookies at<br />

190 °C. To what Fahrenheit temperature would you set the oven to bake the cookies<br />

6. A scientist wishes to generate a chemical reaction in his laboratory. The temperature values in his laboratory<br />

manual are given in degrees Celsius. However, his lab thermometers are calibrated in degrees Fahrenheit. If<br />

he needs to heat his reactants to 232 °C, what temperature will he need to monitor on his lab thermometers<br />

7. You call a friend in Europe during the winter holidays and say that the temperature in Boston is 15 degrees.<br />

He replies that you must enjoy the warm weather. Explain his comment using your knowledge of the<br />

Fahrenheit and Celsius scales. To help you get started, fill in this table. What is 15 °F on the Celsius scale<br />

What is 15°C on the Fahrenheit scale<br />

°F f °C<br />

15 °F =<br />

= 15°C<br />

8. Challenge questions:<br />

a. A gas has a boiling point of –175 °C. At what Fahrenheit temperature would this gas boil<br />

b. A chemist notices some silvery liquid on the floor in her lab. She wonders if someone accidentally<br />

broke a mercury thermometer, but did not thoroughly clean up the mess. She decides to find out if the<br />

silver stuff is really mercury. From her tests with the substance, she finds out that the melting point for<br />

the liquid is 35°F. A reference book says that the melting point for mercury is –38.87 °C. Is this<br />

substance mercury Explain your answer and show all relevant calculations.

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Page 3 of 4<br />

Extension: the Kelvin temperature scale<br />

<strong>8.2</strong><br />

For some scientific applications, a third temperature scale is used: the Kelvin scale. The Kelvin scale is<br />

calibrated so that raising the temperature one degree Kelvin raises it by the same amount as one degree Celsius.<br />

The difference between the scales is that 0 °C is the freezing point of water, while 0 K is much, much colder. On<br />

the Kelvin scale, 0K (degree symbols are not used for Kelvin values) represents absolute zero. Absolute zero is<br />

the temperature when the average kinetic energy of a perfect gas is zero—the molecules display no energy of<br />

motion. Absolute zero is equal to –273 °C, or –459 °F. When scientists are conducting research, they often obtain<br />

or report their temperature values in Celsius, and other scientists must convert these values into Kelvin for their<br />

own use, or vice versa. To convert Celsius values to their Kelvin equivalents, use the formula:<br />

K = °C + 273<br />

Water boils at a temperature of 100 °C. What would be the corresponding temperature for the Kelvin scale<br />

K = °C + 273<br />

K = 100 °C + 273<br />

K = 373<br />

To convert Kelvin values to Celsius, you perform the opposite operation; subtract 273 from the Kelvin value to<br />

find the Celsius equivalent.<br />

A substance has a melting point of 625 K. At what Celsius temperature would this substance melt<br />

°C = K + 273<br />

°C = 625 K −273<br />

°C = 352<br />

Although we rarely need to convert between Kelvin and Fahrenheit, use the following formulas to do so:<br />

⎛9<br />

⎞<br />

°F = ⎜ × K ⎟−460<br />

⎝5<br />

⎠<br />

5<br />

K = (°F + 460)<br />

9

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Page 4 of 4<br />

1. Surface temperatures on the planet Mars range from –89 °C to –31 °C. Express this temperature<br />

range in Kelvin.<br />

2. The average surface temperature on Jupiter is about 165K. Express this temperature in degrees Celsius.<br />

3. The average surface temperature on Saturn is 134K. Express this temperature in degrees Celsius.<br />

4. The average surface temperature on the dwarf planet Pluto is 50K. Express this temperature in degrees<br />

Celsius.<br />

5. The Sun has several regions. The apparent surface that we can see from a distance is called the photosphere.<br />

<strong>Temperature</strong>s of the photosphere range from 5,000 °C to 8,000 °C. Express this temperature range in<br />

Kelvin.<br />

6. The chromosphere is a hot layer of plasma just above the photosphere. Chromosphere temperatures can<br />

reach 10,000 °C. Express this temperature in Kelvin.<br />

7. The outermost layer of the Sun’s atmosphere is called the corona. Its temperatures can reach over<br />

1,000,000 °C. Express this temperature in Kelvin.<br />

8. Nuclear fusion takes place in the center, or core, of the Sun. <strong>Temperature</strong>s there can reach 15,000,000 °C.<br />

Express this temperature in Kelvin.<br />

9. Challenge! Surface temperatures on Mercury can reach 660 °F. Express this temperature in Kelvin.<br />

10. Challenge! Surface temperatures on Venus, the hottest planet in our solar system, can reach 755K. Express<br />

this temperature in degrees Fahrenheit.<br />

<strong>8.2</strong>