Temperature is a measure of the average kinetic energy of the particles in a substance and is a fundamental physical quantity in the study of science and everyday life. The measurement of temperature is essential in a wide range of activities, from meteorology to cooking, and it is recorded using different scales.
The Fahrenheit and Celsius scales are the most commonly used temperature scales in daily life. Fahrenheit is often used in the United States for weather forecasts and in households for cooking, while Celsius is used in scientific contexts and is the standard in most other parts of the world. Each scale has its own set of reference points: the freezing and boiling points of water.
temperature scales
Fahrenheit and Celsius are two different scales for measuring temperature.
On the Fahrenheit scale, water freezes at [latex]32[/latex] degrees and boils at [latex]212[/latex] degrees. On the Celsius scale, the freezing and boiling points of water are [latex]0[/latex] degrees and [latex]100[/latex] degrees, respectively.
In this section, you’ll need to use the 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 acronym PEMDAS.
Converting Between Temperature Scales
By looking at the two thermometers shown, you can make some general comparisons between the scales. 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.
Water freezes at [latex]32^{\circ}F[/latex]. On the Celsius scale, what temperature is this?
A Fahrenheit temperature is given. To convert it to the Celsius scale, using the formula below.
[latex]C=\frac{5}{9}(F-32)[/latex]
Substitute [latex]32[/latex] for F and subtract.
[latex]C=\frac{5}{9}(32-32)[/latex]
Any number multiplied by [latex]0[/latex] is [latex]0[/latex].
[latex]C=\frac{5}{9}(0)[/latex]
[latex]C=0[/latex]
The freezing point of water is [latex]0^{\circ}\text{C}[/latex].
The next example shows how these formulas can be used to solve a real-world problem using different temperature scales.
Two scientists are doing an experiment designed to identify the boiling point of an unknown liquid. One scientist gets a result of [latex]120^{\circ}C[/latex]; the other gets a result of [latex]250^{\circ}F[/latex]. Which temperature is higher and by how much?
One temperature is given in [latex]^{\circ}C[/latex], and the other is given in [latex]^{\circ}F[/latex]. To find the difference between them, we need to measure them on the same scale.What is the difference between [latex]120^{\circ}C[/latex] and [latex]250^{\circ}F[/latex]? Use the conversion formula to convert [latex]120^{\circ}C[/latex] to [latex]^{\circ}F[/latex]. (You could convert [latex]250^{\circ}F[/latex] to [latex]^{\circ}C[/latex] instead; this is explained in the text after this example.)
[latex]F=\frac{9}{5}C+32[/latex]
Substitute [latex]120[/latex] 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 [latex]5[/latex].
[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 [latex]248^{\circ}F[/latex] and [latex]250^{\circ}F[/latex], subtract.
[latex]250^{\circ}F[/latex] is the higher temperature by [latex]2^{\circ}F[/latex].
You could have converted [latex]250^{\circ}F[/latex] to [latex]^{\circ}C[/latex] instead, and then found the difference in the two measurements. (Had you done it this way, you would have found that [latex]250^{\circ}\text{F}=121.1^{\circ}\text{C}[/latex], and that [latex]121.1^{\circ}C[/latex] is [latex]1.1^{\circ}C[/latex] higher than [latex]120^{\circ}C[/latex].) Whichever way you choose, it is important to compare the temperature measurements within the same scale, and to apply the conversion formulas accurately.
