A Thermometer Gives a Reading of 96.1 F

Learning Objectives

By the end of this section, you will exist 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 yous place one hand in hot h2o and the other in cold water, and then place both hands in tepid water, the tepid water volition feel cool to the hand that was in hot h2o, and warm to the one that was in common cold water. The scientific definition of temperature is less cryptic 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. Nosotros shall see later on how temperature is related to the kinetic energies of atoms and molecules, a more physical caption.) Two accurate thermometers, ane placed in hot water and the other in cold water, will show the hot h2o to have a higher temperature. If they are and so placed in the tepid h2o, both will give identical readings (within measurement uncertainties). In this department, we hash out temperature, its measurement by thermometers, and its relationship to thermal equilibrium. Again, temperature is the quantity measured by a thermometer.

Misconception Alert: Homo Perception vs. Reality

On a cold winter morning, the woods on a porch feels warmer than the metal of your bike. The wood and wheel are in thermal equilibrium with the outside air, and are thus the aforementioned temperature. They feel different because of the departure in the fashion that they conduct heat abroad from your pare. The metal conducts heat abroad from your body faster than the wood does (run across more than about conductivity in Conduction). This is simply one example demonstrating that the human being sense of hot and cold is not determined by temperature alone.

Another gene that affects our perception of temperature is humidity. Most people feel much hotter on hot, humid days than on hot, dry out days. This is considering on humid days, sweat does non evaporate from the pare as efficiently as it does on dry days. Information technology is the evaporation of sweat (or h2o from a sprinkler or pool) that cools us off.

Figure 1. The curvature of a bimetallic strip depends on temperature. (a) The strip is directly at the starting temperature, where its ii components have the aforementioned length. (b) At a higher temperature, this strip bends to the right, considering the metal on the left has expanded more than the metallic on the correct.

Any concrete property that depends on temperature, and whose response to temperature is reproducible, tin can exist used equally the basis of a thermometer. Considering many physical backdrop depend on temperature, the multifariousness of thermometers is remarkable. For case, 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 i).

Other backdrop used to measure temperature include electrical resistance and color and the emission of infrared radiation.

Ane 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 ii contains a pic of a dissimilar heat-sensitive liquid crystal material Beneath 95ºF, all six squares are black. When the plastic thermometer is exposed to temperature that increases to 95ºF, the offset liquid crystal square changes color. When the temperature increases above 96.8ºF the second liquid crystal square too changes color, and then along.

Effigy 2. A plastic (liquid crystal) thermometer. (credit: Arkrishna, Wikimedia Commons)

Effigy 3. Fireman Jason Ormand uses a pyrometer to check the temperature of an shipping carrier's ventilation organization. (credit: Lamel J. Hinton/U.S. Navy)

An example of emission of radiation is shown in the utilize of a pyrometer (Figure iii). Infrared radiation (whose emission varies with temperature) from the vent in Figure iii is measured and a temperature readout is quickly produced. Infrared measurements are also frequently used as a measure of body temperature. These mod thermometers, placed in the ear canal, are more than accurate than alcohol thermometers placed under the tongue or in the armpit.

Temperature Scales

Thermometers are used to measure out temperature according to well-defined scales of measurement, which use pre-divers reference points to assistance compare quantities. The 3 almost common temperature scales are the Fahrenheit, Celsius, and Kelvin scales. A temperature calibration can exist created by identifying two easily reproducible temperatures. The freezing and humid temperatures of water at standard atmospheric pressure level are usually used.

The Celsius scale (which replaced the slightly different centigrade scale) has the freezing point of h2o at 0ºC and the boiling bespeak at 100ºC. Its unit is the caste Celsius(ºC). On the Fahrenheit scale (still the nearly oft used in the Usa), the freezing point of water is at 32ºF and the boiling point is at 212ºF. The unit of temperature on this calibration is the degree Fahrenheit(ºF). Note that a temperature difference of ane degree Celsius is greater than a temperature difference of i degree Fahrenheit. Only 100 Celsius degrees span the same range as 180 Fahrenheit degrees, thus 1 caste on the Celsius calibration is 1.8 times larger than one degree on the Fahrenheit scale 180/100=ix/5.

The Kelvin scale is the temperature calibration that is usually used in science. It is an absolute temperature scale divers to have 0 K at the everyman possible temperature, chosen accented cypher. 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.xv M and 373.15 K, respectively. Thus, the magnitude of temperature differences is the aforementioned in units of kelvins and degrees Celsius. Unlike other temperature scales, the Kelvin scale is an absolute scale. Information technology 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 piece of work.

Figure 4. Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales, rounded to the nearest caste. The relative sizes of the scales are also shown.

The relationships between the three common temperature scales is shown in Figure iv. Temperatures on these scales tin can exist converted using the equations in Tabular array 1.

Table ane. Temperature Conversions
To convert from . . .	Utilise this equation . . .	Besides written as . . .
Celsius to Fahrenheit	[latex]T\left(^{\circ}\text{F}\right)=\frac{9}{five}T\left(^{\circ}\text{C}\right)+32\\[/latex]	[latex]T_{^{\circ}\text{F}}=\frac{nine}{five}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}\correct)-32\right)\\[/latex]	[latex]T_{^{\circ}\text{C}}=\frac{v}{nine}\left(T_{^{\circ}\text{F}}-32\right)\\[/latex]
Celsius to Kelvin	T(K) =T(ºC) + 273.15	T K =T ºC + 273.15
Kelvin to Celsius	T(ºC) =T(Chiliad) − 273.xv	T ºC =T K − 273.15
Fahrenheit to Kelvin	[latex]T\left(Grand\correct)=\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.xv\\[/latex]
Kelvin to Fahrenheit	[latex]T\left(^{\circ}\text{F}\right)=\frac{nine}{v}\left(T\left(Chiliad\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 uncomplicated combinations of the conversions betwixt Fahrenheit and Celsius, and the conversions between Celsius and Kelvin.

Example ane. Converting betwixt Temperature Scales: Room Temperature

"Room temperature" is generally divers to be 25ºC.

1. What is room temperature in ºF?
2. What is it in K?

Strategy

To respond these questions, all nosotros need to practise is choose the right conversion equations and plug in the known values.

Solution for Part 1

1. Choose the correct equation. To catechumen from ºC to ºF, apply the equation [latex]T_{^{\circ}\text{F}}=\frac{9}{5}T_{^{\circ}\text{C}}+32\\[/latex].
2. 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

1. Choose the correct equation. To catechumen from ºC to Yard, use the equationT _Grand =T _ºC + 273.15
2. Plug the known value into the equation and solve:T _K = 25ºC + 273.15 = 298 K.

Instance ii. 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 bespeak of water is 0ºR and the humid temperature is 80ºR. If "room temperature" is 25ºC on the Celsius scale, what is it on the Reaumur scale?

Strategy

To reply this question, we must compare the Reaumur scale to the Celsius scale. The difference between the freezing point and boiling point of h2o 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, and so we can derive a elementary formula to catechumen between temperatures on the two scales.

Solution

1. Derive a formula to convert from one calibration to the other: [latex]T_{^{\circ}\text{R}}=\frac{0.viii^{\circ}\text{R}}{^{\circ}\text{C}}\times{T}_{^{\circ}\text{C}}\\[/latex]
2. Plug the known value into the equation and solve: [latex]T_{^{\circ}\text{R}}=\frac{0.eight^{\circ}\text{R}}{^{\circ}\text{C}}\times25^{\circ}\text{C}=20^{\circ}\text{R}\\[/latex]

Temperature Ranges in the Universe

Effigy 6 shows the wide range of temperatures found in the universe. Human beings have been known to survive with torso temperatures within a small range, from 24ºC to 44ºC (75ºF to 111ºF). The boilerplate normal body temperature is usually given as 37.0ºC (98.6ºF), and variations in this temperature tin can indicate a medical status: a fever, an infection, a tumor, or circulatory problems (see Figure 5).

Figure 5. This epitome of radiation from a person's body (an infrared thermograph) shows the location of temperature abnormalities in the upper body. Dark blue corresponds to common cold areas and reddish to white corresponds to hot areas. An elevated temperature might be an indication of malignant tissue (a malignant tumor in the breast, for example), while a depressed temperature might be due to a decline in claret flow from a clot. In this case, the abnormalities are caused by a condition chosen hyperhidrosis. (credit: Porcelina81, Wikimedia Eatables)

The lowest temperatures ever recorded accept been measured during laboratory experiments: 4.5 × 10⁻¹⁰ Thou at the Massachusetts Institute of Applied science (U.s.), and ane.0 × 10⁻¹⁰ K at Helsinki Academy of Technology (Finland). In comparison, the coldest recorded place on Globe'south surface is Vostok, Antarctica at 183 G (–89ºC), and the coldest place (exterior the lab) known in the universe is the Boomerang Nebula, with a temperature of 1 K.

Effigy 6. Each increment on this logarithmic calibration indicates an increment past a cistron of ten, and thus illustrates the tremendous range of temperatures in nature. Annotation that zilch on a logarithmic scale would occur off the lesser of the page at infinity.

Making Connections: Absolute Nothing

What is accented zero? Accented null 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 abiding volume decreases as temperature decreases. Various scientists accept noted that the pressures of gases extrapolate to nil at the aforementioned temperature, –273.15ºC. This extrapolation implies that at that place is a lowest temperature. This temperature is called absolute naught. Today we know that nigh gases first liquefy and and so freeze, and information technology is non really possible to reach absolute zilch. The numerical value of absolute aught temperature is –273.15ºC or 0 K.

Thermal Equilibrium and the Zeroth Police of Thermodynamics

Figure seven. Graph of pressure versus temperature for various gases kept at a constant volume. Note that all of the graphs extrapolate to naught pressure at the same temperature.

Thermometers actually take their own temperature, non the temperature of the object they are measuring. This raises the question of how we can be certain that a thermometer measures the temperature of the object with which information technology is in contact. It is based on the fact that any two systems placed in thermal contact (meaning rut transfer can occur between them) will reach the same temperature. That is, estrus volition menstruation from the hotter object to the cooler i until they take exactly the aforementioned temperature. The objects are then in thermal equilibrium, and no further changes will occur. The systems interact and change because their temperatures differ, and the changes stop one time their temperatures are the same. Thus, if enough time is allowed for this transfer of rut to run its course, the temperature a thermometer registers does represent the system with which information technology is in thermal equilibrium. Thermal equilibrium is established when two bodies are in contact with each other and can freely exchange energy.

Furthermore, experimentation has shown that if two systems, A and B, are in thermal equilibrium with each some other, and B is in thermal equilibrium with a third system C, then A is also in thermal equilibrium with C. This decision may seem obvious, because all 3 accept the same temperature, but it is basic to thermodynamics. It is called the zeroth law of thermodynamics.

The Zeroth Police force of Thermodynamics

If two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system, C, and then A is also in thermal equilibrium with C.

This law was postulated in the 1930s, afterward the showtime and second laws of thermodynamics had been adult and named. It is called the zeroth law because it comes logically before the first and second laws (discussed in Thermodynamics). An example of this law in action is seen in babies in incubators: babies in incubators normally have very few clothes on, so to an observer they look as if they may not exist warm enough. However, the temperature of the air, the cot, and the babe is the same, because they are in thermal equilibrium, which is achieved past maintaining air temperature to proceed the baby comfy.

Check Your Understanding

Does the temperature of a body depend on its size?

Solution

No, the organisation can be divided into smaller parts each of which is at the same temperature. We say that the temperature is an intensive quantity. Intensive quantities are independent of size.

Section Summary

• Temperature is the quantity measured by a thermometer.
• Temperature is related to the average kinetic energy of atoms and molecules in a system.
• Absolute nix is the temperature at which in that location is no molecular motion.
• There are three main temperature scales: Celsius, Fahrenheit, and Kelvin.
• Temperatures on one scale tin be converted to temperatures on another calibration using the following equations:
  • [latex]T_{^{\circ}\text{F}}=\frac{9}{five}T_{^{\circ}\text{C}}+32\\[/latex]
  • [latex]T_{^{\circ}\text{C}}=\frac{5}{9}\left(T_{^{\circ}\text{F}}-32\right)\\[/latex]
  • T _Grand = T _ºC + 273.15
  • T _ºC = T _K − 273.15
• Systems are in thermal equilibrium when they accept the aforementioned temperature.
  Thermal equilibrium occurs when two bodies are in contact with each other and can freely substitution energy.
  The zeroth law of thermodynamics states that when two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third organization, C, then A is likewise in thermal equilibrium with C.

Conceptual Questions

1. What does it mean to say that two systems are in thermal equilibrium?
2. Requite an example of a concrete holding that varies with temperature and depict how it is used to measure temperature.
3. When a cold booze thermometer is placed in a hot liquid, the cavalcade of alcohol goes downwardly slightly before going up. Explain why.
4. If you add together humid water to a loving cup at room temperature, what would you expect the final equilibrium temperature of the unit to be? You will need to include the surroundings as function of the system. Consider the zeroth law of thermodynamics.

Issues & Exercises

1. What is the Fahrenheit temperature of a person with a 39.0ºC fever?
2. Frost damage to most plants occurs at temperatures of 28.0ºF or lower. What is this temperature on the Kelvin scale?
3. To conserve free energy, room temperatures are kept at 68.0ºF in the wintertime and 78.0ºF in the summer. What are these temperatures on the Celsius calibration?
4. A tungsten light bulb filament may operate at 2900 K. What is its Fahrenheit temperature? What is this on the Celsius scale?
5. The surface temperature of the Sun is nearly 5750 K. What is this temperature on the Fahrenheit scale?
6. 1 of the hottest temperatures ever recorded on the surface of World was 134ºF in Death Valley, CA. What is this temperature in Celsius degrees? What is this temperature in Kelvin?
7. (a) Suppose a cold front end blows into your locale and drops the temperature by forty.0 Fahrenheit degrees. How many degrees Celsius does the temperature subtract when at that place is a 40.0ºF decrease in temperature? (b) Show that whatever alter in temperature in Fahrenheit degrees is nine-fifths the modify in Celsius degrees.
8. (a) At what temperature do the Fahrenheit and Celsius scales have the same numerical value? (b) At what temperature do the Fahrenheit and Kelvin scales accept the same numerical value?

Glossary

temperature: the quantity measured by a thermometer

Celsius calibration: temperature scale in which the freezing point of water is 0ºC and the boiling betoken of water is 100ºC

degree Celsius: unit on the Celsius temperature scale

Fahrenheit scale: temperature scale in which the freezing point of water is 32ºF and the humid bespeak of water is 212ºF

degree Fahrenheit: unit on the Fahrenheit temperature calibration

Kelvin scale: temperature scale in which 0 G is the lowest possible temperature, representing absolute zilch

absolute zero: the lowest possible temperature; the temperature at which all molecular motion ceases

thermal equilibrium: the status in which heat no longer flows between two objects that are in contact; the ii objects have the same temperature

zeroth constabulary of thermodynamics: police that states that if two objects are in thermal equilibrium, and a tertiary object is in thermal equilibrium with 1 of those objects, it is also in thermal equilibrium with the other object

Selected Solutions to Bug & Exercises

i. 102ºF

3.  20.0ºC and 25.6ºC

v. 9890ºF

7.  (a) 22.2ºC; (b)

[latex]\brainstorm{assortment}{lll}\Delta T\left(^{\circ}\text{F}\right)& =& {T}_{ii}\left(^{\circ}\text{F}\right)-{T}_{1}\left(^{\circ}\text{F}\right)\\ & =& \frac{9}{5}{T}_{2}\left(^{\circ}\text{C}\correct)+\text{32}\text{.}0^{\circ}-\left(\frac{nine}{five}{T}_{ane}\left(^{\circ}\text{C}\right)+\text{32}\text{.}0^{\circ}\correct)\\ & =& \frac{ix}{5}\left({T}_{2}\left(^{\circ}\text{C}\right)-{T}_{1}\left(^{\circ}\text{C}\correct)\right)\text{}=\frac{9}{five}\Delta T\left(^{\circ}\text{C}\correct)\terminate{array}\\[/latex]

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Source: https://courses.lumenlearning.com/physics/chapter/13-1-temperature/

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