Learning Objectives
By the end of this section, you will be able to:
- Define temperature.
- Convert temperatures between the Celsius, Fahrenheit, and Kelvin scales.
- Define thermal equilibrium.
- State the zeroth law of thermodynamics.
The concept of temperature has evolved from the common concepts of hot and cold. Human perception of what feels hot or cold is a relative one. For example, if you place one hand in hot water and the other in cold water, and then place both hands in tepid water, the tepid water will feel cool to the hand that was in hot water, and warm to the one that was in cold water. The scientific definition of temperature is less ambiguous than your senses of hot and cold. Temperature is operationally defined to be what we measure with a thermometer. (Many physical quantities are defined solely in terms of how they are measured. We shall see later how temperature is related to the kinetic energies of atoms and molecules, a more physical explanation.) Two accurate thermometers, one placed in hot water and the other in cold water, will show the hot water to have a higher temperature. If they are then placed in the tepid water, both will give identical readings (within measurement uncertainties). In this section, we discuss temperature, its measurement by thermometers, and its relationship to thermal equilibrium. Again, temperature is the quantity measured by a thermometer.
Misconception Alert: Human Perception vs. Reality
On a cold winter morning, the wood on a porch feels warmer than the metal of your bike. The wood and bicycle are in thermal equilibrium with the outside air, and are thus the same temperature. They feel different because of the difference in the way that they conduct heat away from your skin. The metal conducts heat away from your body faster than the wood does (see more about conductivity in Conduction). This is just one example demonstrating that the human sense of hot and cold is not determined by temperature alone.
Another factor that affects our perception of temperature is humidity. Most people feel much hotter on hot, humid days than on hot, dry days. This is because on humid days, sweat does not evaporate from the skin as efficiently as it does on dry days. It is the evaporation of sweat (or water from a sprinkler or pool) that cools us off.
Figure 1. The curvature of a bimetallic strip depends on temperature. (a) The strip is straight at the starting temperature, where its two components have the same length. (b) At a higher temperature, this strip bends to the right, because the metal on the left has expanded more than the metal on the right.
Any physical property that depends on temperature, and whose response to temperature is reproducible, can be used as the basis of a thermometer. Because many physical properties depend on temperature, the variety of thermometers is remarkable. For example, volume increases with temperature for most substances. This property is the basis for the common alcohol thermometer, the old mercury thermometer, and the bimetallic strip (Figure 1).
Other properties used to measure temperature include electrical resistance and color and the emission of infrared radiation.
One example of electrical resistance and color is found in a plastic thermometer. Each of the six squares on the plastic (liquid crystal) thermometer in Figure 2 contains a film of a different heat-sensitive liquid crystal material Below 95ºF, all six squares are black. When the plastic thermometer is exposed to temperature that increases to 95ºF, the first liquid crystal square changes color. When the temperature increases above 96.8ºF the second liquid crystal square also changes color, and so forth.
Figure 2. A plastic (liquid crystal) thermometer. (credit: Arkrishna, Wikimedia Commons)
Figure 3. Fireman Jason Ormand uses a pyrometer to check the temperature of an aircraft carrier’s ventilation system. (credit: Lamel J. Hinton/U.S. Navy)
An example of emission of radiation is shown in the use of a pyrometer (Figure 3). Infrared radiation (whose emission varies with temperature) from the vent in Figure 3 is measured and a temperature readout is quickly produced. Infrared measurements are also frequently used as a measure of body temperature. These modern thermometers, placed in the ear canal, are more accurate than alcohol thermometers placed under the tongue or in the armpit.
Temperature Scales
Thermometers are used to measure temperature according to well-defined scales of measurement, which use pre-defined reference points to help compare quantities. The three most common temperature scales are the Fahrenheit, Celsius, and Kelvin scales. A temperature scale can be created by identifying two easily reproducible temperatures. The freezing and boiling temperatures of water at standard atmospheric pressure are commonly used.
The Celsius scale (which replaced the slightly different centigrade scale) has the freezing point of water at 0ºC and the boiling point at 100ºC. Its unit is the degree Celsius(ºC). On the Fahrenheit scale (still the most frequently used in the United States), the freezing point of water is at 32ºF and the boiling point is at 212ºF. The unit of temperature on this scale is the degree Fahrenheit(ºF). Note that a temperature difference of one degree Celsius is greater than a temperature difference of one degree Fahrenheit. Only 100 Celsius degrees span the same range as 180 Fahrenheit degrees, thus one degree on the Celsius scale is 1.8 times larger than one degree on the Fahrenheit scale 180/100=9/5.
The Kelvin scale is the temperature scale that is commonly used in science. It is an absolute temperature scale defined to have 0 K at the lowest possible temperature, called absolute zero. The official temperature unit on this scale is the kelvin, which is abbreviated K, and is not accompanied by a degree sign. The freezing and boiling points of water are 273.15 K and 373.15 K, respectively. Thus, the magnitude of temperature differences is the same in units of kelvins and degrees Celsius. Unlike other temperature scales, the Kelvin scale is an absolute scale. It is used extensively in scientific work because a number of physical quantities, such as the volume of an ideal gas, are directly related to absolute temperature. The kelvin is the SI unit used in scientific work.
Figure 4. Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales, rounded to the nearest degree. The relative sizes of the scales are also shown.
The relationships between the three common temperature scales is shown in Figure 4. Temperatures on these scales can be converted using the equations in Table 1.
| Table 1. Temperature Conversions | ||
|---|---|---|
| To convert from . . . | Use this equation . . . | Also written as . . . |
| Celsius to Fahrenheit | [latex]T\left(^{\circ}\text{F}\right)=\frac{9}{5}T\left(^{\circ}\text{C}\right)+32\\[/latex] | [latex]T_{^{\circ}\text{F}}=\frac{9}{5}T_{^{\circ}\text{C}}+32\\[/latex] |
| Fahrenheit to Celsius | [latex]T\left(^{\circ}\text{C}\right)=\frac{5}{9}\left(T\left(^{\circ}\text{F}\right)-32\right)\\[/latex] | [latex]T_{^{\circ}\text{C}}=\frac{5}{9}\left(T_{^{\circ}\text{F}}-32\right)\\[/latex] |
| Celsius to Kelvin | T(K) = T(ºC) + 273.15 | TK = TºC + 273.15 |
| Kelvin to Celsius | T(ºC) = T(K) − 273.15 | TºC = TK − 273.15 |
| Fahrenheit to Kelvin | [latex]T\left(K\right)=\frac{5}{9}\left(T\left(^{\circ}\text{F}\right)-32\right)+273.15\\[/latex] | [latex]T_{K}=\frac{5}{9}\left(T_{^{\circ}\text{F}}-32\right)+273.15\\[/latex] |
| Kelvin to Fahrenheit | [latex]T\left(^{\circ}\text{F}\right)=\frac{9}{5}\left(T\left(K\right)-273.15\right)+32\\[/latex] | [latex]T_{^{\circ}\text{F}}=\frac{9}{5}\left(T_{K}-273.15\right)+32\\[/latex] |
Notice that the conversions between Fahrenheit and Kelvin look quite complicated. In fact, they are simple combinations of the conversions between Fahrenheit and Celsius, and the conversions between Celsius and Kelvin.
Example 1. Converting between Temperature Scales: Room Temperature
“Room temperature” is generally defined to be 25ºC.
- What is room temperature in ºF?
- What is it in K?
Strategy
To answer these questions, all we need to do is choose the correct conversion equations and plug in the known values.
Solution for Part 1
- Choose the right equation. To convert from ºC to ºF, use the equation [latex]T_{^{\circ}\text{F}}=\frac{9}{5}T_{^{\circ}\text{C}}+32\\[/latex].
- Plug the known value into the equation and solve: [latex]T_{^{\circ}\text{F}}=\frac{9}{5}25{^{\circ}\text{C}}+32=77^{\circ}\text{F}\\[/latex]
Solution for Part 2
- Choose the right equation. To convert from ºC to K, use the equation TK = TºC + 273.15
- Plug the known value into the equation and solve: TK = 25ºC + 273.15 = 298 K.
Example 2. Converting between Temperature Scales: the Reaumur Scale
The Reaumur scale is a temperature scale that was used widely in Europe in the eighteenth and nineteenth centuries. On the Reaumur temperature scale, the freezing point of water is 0ºR and the boiling temperature is 80ºR. If “room temperature” is 25ºC on the Celsius scale, what is it on the Reaumur scale?
Strategy
To answer this question, we must compare the Reaumur scale to the Celsius scale. The difference between the freezing point and boiling point of water on the Reaumur scale is 80ºR. On the Celsius scale it is 100ºC. Therefore 100º C=80ºR. Both scales start at 0 º for freezing, so we can derive a simple formula to convert between temperatures on the two scales.
Solution
- Derive a formula to convert from one scale to the other: [latex]T_{^{\circ}\text{R}}=\frac{0.8^{\circ}\text{R}}{^{\circ}\text{C}}\times{T}_{^{\circ}\text{C}}\\[/latex]
- Plug the known value into the equation and solve: [latex]T_{^{\circ}\text{R}}=\frac{0.8^{\circ}\text{R}}{^{\circ}\text{C}}\times25^{\circ}\text{C}=20^{\circ}\text{R}\\[/latex]
Temperature Ranges in the Universe
Figure 6 shows the wide range of temperatures found in the universe. Human beings have been known to survive with body temperatures within a small range, from 24ºC to 44ºC (75ºF to 111ºF). The average normal body temperature is usually given as 37.0ºC (98.6ºF), and variations in this temperature can indicate a medical condition: a fever, an infection, a tumor, or circulatory problems (see Figure 5).
Figure 5. This image of radiation from a person’s body (an infrared thermograph) shows the location of temperature abnormalities in the upper body. Dark blue corresponds to cold areas and red to white corresponds to hot areas. An elevated temperature might be an indication of malignant tissue (a cancerous tumor in the breast, for example), while a depressed temperature might be due to a decline in blood flow from a clot. In this case, the abnormalities are caused by a condition called hyperhidrosis. (credit: Porcelina81, Wikimedia Commons)
The lowest temperatures ever recorded have been measured during laboratory experiments: 4.5 × 10−10 K at the Massachusetts Institute of Technology (USA), and 1.0 × 10−10 K at Helsinki University of Technology (Finland). In comparison, the coldest recorded place on Earth’s surface is Vostok, Antarctica at 183 K (–89ºC), and the coldest place (outside the lab) known in the universe is the Boomerang Nebula, with a temperature of 1 K.
Figure 6. Each increment on this logarithmic scale indicates an increase by a factor of ten, and thus illustrates the tremendous range of temperatures in nature. Note that zero on a logarithmic scale would occur off the bottom of the page at infinity.
Making Connections: Absolute Zero
What is absolute zero? Absolute zero is the temperature at which all molecular motion has ceased. The concept of absolute zero arises from the behavior of gases. Figure 7 shows how the pressure of gases at a constant volume decreases as temperature decreases. Various scientists have noted that the pressures of gases extrapolate to zero at the same temperature, –273.15ºC. This extrapolation implies that there is a lowest temperature. This temperature is called absolute zero. Today we know that most gases first liquefy and then freeze, and it is not actually possible to reach absolute zero. The numerical value of absolute zero temperature is –273.15ºC or 0 K.
