Temperature Scales
Learning Outcomes
- Convert from one temperature scale to the other, using conversion formulas
Measuring Temperature on Two Scales
Fahrenheit and Celsius are two different scales for measuring temperature.A thermometer measuring a temperature of 22° Celsius is shown here.On the Celsius scale, water freezes at 0° and boils at 100°. If the United States were to adopt the Celsius scale, forecast temperatures would rarely go below -30° or above 45°. (A temperature of -18° may be forecast for a cold winter day in Michigan, while a temperature of 43° may be predicted for a hot summer day in Arizona.) Most office buildings maintain an indoor temperature between 18°C and 24°C to keep employees comfortable. | A thermometer measuring a temperature of 72° Fahrenheit is shown here.On the Fahrenheit scale, water freezes at 32° and boils at 212°. In the United States, forecast temperatures measured in Fahrenheit rarely go below -20° or above 120°. (A temperature of 0° may be forecast for a cold winter day in Michigan, while a temperature of 110° may be predicted for a hot summer day in Arizona.) Most office buildings maintain an indoor temperature between 65°F and 75°F to keep employees comfortable. | ||
Celsius |
Fahrenheit |
order of operations
In this section, you'll need to use order of operations carefully to obtain correct results. Recall that we do operations in parentheses first, then handle exponents, then multiply or divide from left to right as encountered, then add or subtract from left to right as encountered. The order is sometimes represented using the acroynim PEMDAS.Try It
A cook puts a thermometer into a pot of water to see how hot it is. The thermometer reads 132°, but the water is not boiling yet. Which temperature scale is the thermometer measuring?Answer: Fahrenheit scale
Converting Between the Scales
By looking at the two thermometers shown, you can make some general comparisons between the scales. For example, many people tend to be comfortable in outdoor temperatures between 50°F and 80°F (or between 10°C and 25°C). If a meteorologist predicts an average temperature of 0°C (or 32°F), then it is a safe bet that you will need a winter jacket. Sometimes, it is necessary to convert a Celsius measurement to its exact Fahrenheit measurement or vice versa. For example, what if you want to know the temperature of your child in Fahrenheit, and the only thermometer you have measures temperature in Celsius measurement? Converting temperature between the systems is a straightforward process as long as you use the formulas provided below.Temperature Conversion Formulas
To convert a Fahrenheit measurement to a Celsius measurement, use this formula.[latex] C=\dfrac{5}{9}(F-32)[/latex]
To convert a Celsius measurement to a Fahrenheit measurement, use this formula.[latex] F=\dfrac{9}{5}C+32[/latex]
Example
The boiling point of water is 100°C. What temperature does water boil at in the Fahrenheit scale? A Celsius temperature is given. To convert it to the Fahrenheit scale, use the formula at the left.[latex]F=\frac{9}{5}C+32[/latex]
Substitute 100 for C and multiply.[latex]F=\frac{9}{5}(100)+32[/latex]
[latex]F=\frac{900}{5}+32[/latex]
Simplify [latex]\frac{900}{5}[/latex] by dividing numerator and denominator by 5.[latex]F=\frac{900\div 5}{5\div 5}+32[/latex]
[latex]F=\frac{180}{1}+32[/latex]
Add [latex]180+32[/latex].[latex]F=212[/latex]
The boiling point of water is 212°F.Try It
[ohm_question]1011[/ohm_question]Example
Water freezes at 32°F. On the Celsius scale, what temperature is this?Answer: A Fahrenheit temperature is given. To convert it to the Celsius scale, use the formula at the left.
[latex] C=\frac{5}{9}(F-32)[/latex]
Substitute 32 for F and subtract.[latex] C=\frac{5}{9}(32-32)[/latex]
Any number multiplied by 0 is 0.[latex] C=\frac{5}{9}(0)[/latex]
[latex] C=0[/latex]
The freezing point of water is [latex]0^{\circ}\text{C}[/latex].Try It
[ohm_question]1010[/ohm_question]Example
Two scientists are doing an experiment designed to identify the boiling point of an unknown liquid. One scientist gets a result of 120°C; the other gets a result of 250°F. Which temperature is higher and by how much?Answer: One temperature is given in °C, and the other is given in °F. To find the difference between them, we need to measure them on the same scale. What is the difference between 120°C and 250°F? Use the conversion formula to convert 120°C to °F. (You could convert 250°F to °C instead; this is explained in the text after this example.)
[latex] F=\frac{9}{5}C+32[/latex]
Substitute 120 for C.[latex] F=\frac{9}{5}(120)+32[/latex]
Multiply.[latex] F=\frac{1080}{5}+32[/latex]
Simplify [latex] \frac{1080}{5}[/latex] by dividing numerator and denominator by 5.[latex] F=\frac{1080\div 5}{5\div 5}+32[/latex]
Add [latex]216+32[/latex].[latex] F=\frac{216}{1}+32[/latex]
You have found that [latex]120^{\circ}\text{C}=248^{\circ}\text{F}[/latex].[latex] F=248[/latex]
To find the difference between 248°F and 250°F, subtract.[latex]250^{\circ}\text{F}-248^{\circ}\text{F}=2^{\circ}\text{F}[/latex]
250°F is the higher temperature by 2°F.Try It
Tatiana is researching vacation destinations, and she sees that the average summer temperature in Barcelona, Spain is around 26°C. What is the average temperature in degrees Fahrenheit?Answer: 78.8 degrees Fahrenheit.
Summary
Temperature is often measured in one of two scales: the Celsius scale and the Fahrenheit scale. A Celsius thermometer will measure the boiling point of water at 100° and its freezing point at 0°; a Fahrenheit thermometer will measure the same events at 212° for the boiling point of water and 32° as its freezing point. You can use conversion formulas to convert a measurement made in one scale to the other scale.Licenses & Attributions
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Question ID 1011, 1010. Authored by: Lippman, David. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.