5.2: Temperature Units and Conversions: Review

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Learning Objectives

Identify the different scales used for measuring temperature.
Apply equations to convert temperature units from one scale to another.

The primary objective of this chapter is to quantify the amount of heat that is transferred during physical and chemical changes. However, the equations that must be employed to determine these values are complex, as each consists of several variables. Therefore, the next several sections of this chapter are dedicated to the discussion of fundamental concepts and mathematical quantities that must be understood, in order to successfully complete the heat transfer calculations.

As discussed previously, temperature, T, which is defined as a measure of how hot an object is, can be measured on three different scales, degrees Fahrenheit, which is abbreviated as °F, degrees Celsius, °C, and Kelvin, K. Notice that there is no "degree" used in a Kelvin temperature designation. Unlike the Fahrenheit and Celsius scales, in which temperatures are referred to as "degrees Fahrenheit" or "degrees Celsius", temperatures in the Kelvin scale are simply designated as "kelvins."

Converting between Temperature Scales

Temperatures are converted using equations, which must contain both an equal sign and a variable. When performing temperature conversions, using appropriately-formatted variables is important. The quantity that is being measured should be written as the primary variable, and any qualifiers or information about that quantity should be written as a subscript. For example, the phrase "temperature in degrees Celsius" should be written as "T_C". A capital "T" should be used, as a lower-case "t" represents time. Simply using a capital "C" is not appropriate, as "C" does not refer to temperature at all, but rather to a quantity called "heat capacity."

The equations that can be applied to convert between the Kelvin scale and the Celsius scale and between the Celsius scale and the Fahrenheit scale are

T_K = T_C + 273.15

and

T_F = 1.8T_C + 32

respectively. When using the first equation, the appropriate number of significant digits must be applied to the answer using addition and subtraction rules. Recall that value of "1.8" in the second equation is an exact number and, therefore, does not impact the number of significant figures that are present in the final answer. However, since multiple mathematical operations are involved in this equation, both multiplication and division rules and addition and subtraction rules must be applied, in order to report a scientifically-correct final answer.

When using these equations, the given value, which includes the number and its associated unit, replace the relevant variable in the equation.

Example \(\PageIndex{1}\)

Convert the melting point of gallium, 29.76 °C, to degrees Fahrenheit and Kelvin.

Solution

In order to convert from degrees Celsius to degrees Fahrenheit, the given information must be incorporated into the second equation that is shown above, as follows.

T_F = 1.8(29.76 °C) + 32

Order of operations dictates that multiplication must occur first, followed by addition. Applying the correct number of significant figures to the calculated quantity results in the final answer that is shown below.

T_F = 85.568 °F ≈ 85.57 °F

In order to convert from degrees Celsius to Kelvin, the given information must be inserted into the first equation. Applying the correct number of significant figures to the calculated quantity results in the final answer that is shown below.

T_K = 29.76 °C + 273.15
T_K = 302.91 K

Exercise \(\PageIndex{1}\)

Convert the boiling point of molecular nitrogen, -320.4 °F, to degrees Celsius and Kelvin.

Answer

In order to convert from degrees Fahrenheit to degrees Celsius, the given information must be incorporated into the second equation that is shown above, as follows.

-320.4 °F = 1.8T_C + 32

Order of operations dictates that subtraction must occur first, followed by division. Applying the correct number of significant figures to the calculated quantity results in the final answer that is shown below.

T_C = -195.77777... °C ≈ -195.7 °C

This answer can then be converted to Kelvin by inserting the calculated value into the first equation. Applying the correct number of significant figures to the calculated quantity results in the final answer that is shown below.

T_K = -195.7 °C + 273.15
T_K = 77.45 K ≈ 77.5 K