The fixed temperature at which a substance in the solid state changes into the liquid state is called its melting point. The fixed temperature at which a substance in the liquid state changes into the gas state is called its boiling point. These two fixed points are what every temperature scale is built on.
Because of the effect of heat, a substance in the solid state changes into a liquid and a substance in the liquid state changes into a gas. At sea level, ice changes into water at a temperature of 0 degrees Celsius, so the melting point of ice is 0 degrees Celsius. At sea level, water boiling at 100 degrees Celsius changes into steam, so the boiling point of water is 100 degrees Celsius.
Three scales, two pegs
The melting point of ice and the boiling point of water, given in the three different scales Celsius, Fahrenheit and Kelvin, are shown in the table below.
| Substance / Scale | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Melting point of ice | 0 °C | 32 °F | 273 K |
| Boiling point of water | 100 °C | 212 °F | 373 K |
| Size of the gap between them | 100 divisions | 180 divisions | 100 divisions |
Look at that table again and notice what the three scales actually are. They are three different rulers laid against the same two physical events. Ice melting and water boiling do not care what numbers we write next to them, and every scale simply chooses its own pair of numbers for those two pegs and divides the gap between them differently. Celsius calls them 0 and 100 and cuts the gap into a hundred parts. Fahrenheit calls them 32 and 212 and cuts the same gap into a hundred and eighty parts. Kelvin calls them 273 and 373 and cuts it into a hundred, exactly like Celsius. That is the whole story, and it means you never have to memorise the conversion formula. Ask instead: how far up from the lower peg is this temperature, as a fraction of the whole gap? That fraction must be identical in all three scales, because all three are describing one physical hotness, and writing that sentence in symbols gives you the formula.
The conversion formula
Using the formula given below, a temperature can be converted from one unit into another.
| \( \dfrac{C - 0}{100 - 0} = \dfrac{F - 32}{212 - 32} = \dfrac{K - 273}{373 - 273} \) |
| which simplifies to \( \dfrac{C - 0}{100} = \dfrac{F - 32}{180} = \dfrac{K - 273}{100} \) |
Here, although there are three scales in temperature, at one time the temperature of any one scale can be changed into another scale. When changing a Celsius temperature into Fahrenheit, the part of the formula that must be used is the one connecting C and F.
Notice one useful thing before you start calculating. The Celsius part and the Kelvin part have the same denominator, 100, and their numerators differ only by the fixed number 273. That is why converting between Celsius and Kelvin needs no fractions at all: \( K = C + 273 \), and \( C = K - 273 \). Only Fahrenheit has the awkward 180, and that is because its degree is a smaller step than the other two.
Worked example 1: body temperature into Celsius
In the normal state the temperature of the human body is 98.6 degrees Fahrenheit. Change this into the Celsius scale.
| Step | Working |
|---|---|
| Given | F = 98.6, C = ? |
| Formula | \( \dfrac{C - 0}{100} = \dfrac{F - 32}{180} \) |
| Substitute | \( \dfrac{C}{100} = \dfrac{98.6 - 32}{180} = \dfrac{66.6}{180} \) |
| Cross multiply | \( C \times 180 = 100 \times 66.6 \) |
| Answer | \( C = \dfrac{6660}{180} = 37 \) °C |
So on the Celsius scale the temperature of the human body is 37 degrees Celsius. That is a pair worth memorising outright, because it appears constantly: 98.6 degrees Fahrenheit and 37 degrees Celsius are the same temperature, and in Kelvin the same body is at 310.
Worked example 2: one reading into two scales
At some place the temperature of the air was 50 degrees Fahrenheit. Convert this into the Kelvin and Celsius units.
| Step | Working |
|---|---|
| Given | F = 50, K = ?, C = ? |
| Formula | \( \dfrac{K - 273}{100} = \dfrac{F - 32}{180} \) |
| Substitute | \( \dfrac{K - 273}{100} = \dfrac{50 - 32}{180} = \dfrac{18}{180} = \dfrac{1}{10} \) |
| Rearrange | \( K = \dfrac{100}{10} + 273 = 10 + 273 = 283 \) K |
| Then for Celsius | \( \dfrac{C - 0}{100} = \dfrac{K - 273}{100} \), so \( C = K - 273 = 283 - 273 = 10 \) °C |
So 50 degrees Fahrenheit converted into Kelvin is 283 K, and converted into degrees Celsius is 10 degrees Celsius. Notice the shortcut in the last line: once you have the Kelvin value, the Celsius value is simply 273 less, with no fraction needed at all.
Before you write a converted temperature down, hold it against a fact you already have. Water freezes at 0 °C, 32 °F and 273 K. Water boils at 100 °C, 212 °F and 373 K. The body sits at 37 °C, 98.6 °F and 310 K. Now suppose a calculation gave you 500 °C for a room. Rooms are nowhere near boiling, so something has gone wrong. Or suppose it gave you 5 K for a warm day. Kelvin values near zero are colder than anything on Earth, so again something is wrong. Two mistakes cause almost all of these. Using 32 with the Kelvin part of the formula instead of 273, and dividing by 100 where the Fahrenheit part needs 180. If your answer fails the sensibility check, look at those two lines first.
The relationship between temperature and heat
Why do hot things to eat and drink, such as tea and coffee, cool down after a little while? Why is the water in the tap extremely cold in winter? Have you ever thought about these questions?
The temperature of hot tea is much greater than the temperature around us. While the tea was being made, it absorbed the heat energy that was given to it and its temperature rose. After the hot tea has lost heat energy it cools, that is to say its temperature falls. Heat energy moves from an object with a higher temperature towards an object with a lower temperature. If any object gains heat energy its temperature rises, but if it loses heat its temperature falls.
| Object with a HIGHER temperature | → direction in which heat moves → | Object with a LOWER temperature |
In winter the temperature around us is low. The temperature of the water in the tap becomes equal to the temperature of the environment. A person's body temperature in the normal state is always steady at 98.6 degrees Fahrenheit. When we touch cold water, the heat energy of our body moves into the water and the water feels cold to us. In the same way, when the water is hot, heat from that water moves into our skin and the water feels hot to us.
Read that last sentence about cold water again, because it says something most people have never noticed. When you put your hand into cold water, nothing called cold enters your hand. What happens is that heat leaves your hand and goes into the water, because heat always moves from the hotter thing to the colder one. The feeling we call cold is not the arrival of anything. It is the sensation of losing heat. This explains a puzzle you have met without thinking about it. Why does a metal railing feel colder than a wooden bench on the same winter morning, when both have been in the same air all night and must be at the same temperature? They are at the same temperature. Metal simply takes heat out of your hand much faster than wood does, so more heat leaves you per second and your skin reports colder. Your hand was never measuring temperature at all. It was measuring how quickly it was losing heat.
In winter, before bathing, hot or boiled water is mixed with cold water to make it just lukewarm for bathing. The lukewarm water made in this way has a temperature less than that of the hot water and more than that of the cold water. In this process heat moves from the hotter water into the colder water.
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