KAHIBARO
Table of Contents
Measuring temperature on different scales
Temperature scales give numbers to how hot or cold something is. A scale is built by choosing reference points and deciding how large one degree should be. Different scales use different reference points, so the same physical temperature can have different numerical values.
In physics, the most important idea is that temperature is a measurable quantity, and a temperature scale is a system for assigning values to it. The physical state of an object does not depend on whether we describe it in Celsius, Fahrenheit, or Kelvin. Only the number changes.
Common temperature scales
The three most common temperature scales are Celsius, Fahrenheit, and Kelvin.
The Celsius scale is widely used in daily life and in science. It is based on the freezing and boiling points of water at standard atmospheric pressure. On this scale, water freezes at $0^\circ \mathrm{C}$ and boils at $100^\circ \mathrm{C}$.
The Fahrenheit scale is used mainly in some countries for everyday temperature measurements. On this scale, water freezes at $32^\circ \mathrm{F}$ and boils at $212^\circ \mathrm{F}$.
The Kelvin scale is the standard scientific temperature scale. It is called an absolute scale because it begins at absolute zero, the lowest possible temperature. On this scale, water freezes at about $273.15\ \mathrm{K}$ and boils at about $373.15\ \mathrm{K}$.
| Scale | Freezing point of water | Boiling point of water | Degree size |
|---|---|---|---|
| Celsius | $0^\circ \mathrm{C}$ | $100^\circ \mathrm{C}$ | Same as Kelvin |
| Fahrenheit | $32^\circ \mathrm{F}$ | $212^\circ \mathrm{F}$ | Smaller than Celsius degree |
| Kelvin | $273.15\ \mathrm{K}$ | $373.15\ \mathrm{K}$ | Same as Celsius |
Celsius and Kelvin
Celsius and Kelvin have the same size degree. A change of $1^\circ \mathrm{C}$ is exactly the same size as a change of $1\ \mathrm{K}$. The difference is only where zero is placed.
The conversion is
$$
T(\mathrm{K}) = T(^\circ \mathrm{C}) + 273.15
$$
and
$$
T(^\circ \mathrm{C}) = T(\mathrm{K}) - 273.15
$$
For example, a room temperature of $25^\circ \mathrm{C}$ is
$$
25 + 273.15 = 298.15\ \mathrm{K}
$$
Absolute zero is
$$
0\ \mathrm{K} = -273.15^\circ \mathrm{C}
$$
Important rule: Kelvin temperatures are written without the degree symbol.
Write $300\ \mathrm{K}$, not $300^\circ \mathrm{K}$.
Celsius and Fahrenheit
The Fahrenheit and Celsius scales do not have the same zero point, and their degree sizes are different. A temperature interval of $100^\circ \mathrm{C}$ corresponds to $180^\circ \mathrm{F}$. Therefore,
$$
1^\circ \mathrm{C} = 1.8^\circ \mathrm{F}
$$
The conversion from Celsius to Fahrenheit is
$$
T(^\circ \mathrm{F}) = \frac{9}{5}T(^\circ \mathrm{C}) + 32
$$
The conversion from Fahrenheit to Celsius is
$$
T(^\circ \mathrm{C}) = \frac{5}{9}\left[T(^\circ \mathrm{F}) - 32\right]
$$
For example, to convert $20^\circ \mathrm{C}$ to Fahrenheit,
$$
T(^\circ \mathrm{F}) = \frac{9}{5}(20) + 32 = 36 + 32 = 68^\circ \mathrm{F}
$$
To convert $68^\circ \mathrm{F}$ back to Celsius,
$$
T(^\circ \mathrm{C}) = \frac{5}{9}(68 - 32) = \frac{5}{9}(36) = 20^\circ \mathrm{C}
$$
Fahrenheit and Kelvin
Sometimes it is useful to convert directly between Fahrenheit and Kelvin. This can be done by first converting to Celsius, or by using a direct formula:
$$
T(\mathrm{K}) = \frac{5}{9}\left[T(^\circ \mathrm{F}) - 32\right] + 273.15
$$
and
$$
T(^\circ \mathrm{F}) = \frac{9}{5}\left[T(\mathrm{K}) - 273.15\right] + 32
$$
Temperature differences
A very important point is the difference between a temperature value and a temperature change.
If a temperature rises from $20^\circ \mathrm{C}$ to $30^\circ \mathrm{C}$, the change is
$$
\Delta T = 10^\circ \mathrm{C}
$$
The same change in Kelvin is
$$
\Delta T = 10\ \mathrm{K}
$$
So for temperature differences,
$$
\Delta T(\mathrm{K}) = \Delta T(^\circ \mathrm{C})
$$
But Fahrenheit is different. A change of $10^\circ \mathrm{C}$ corresponds to
$$
\Delta T(^\circ \mathrm{F}) = \frac{9}{5}\Delta T(^\circ \mathrm{C}) = 18^\circ \mathrm{F}
$$
Important rule: Use care with differences.
For absolute temperatures,
$$
T(\mathrm{K}) = T(^\circ \mathrm{C}) + 273.15
$$
For temperature changes,
$$
\Delta T(\mathrm{K}) = \Delta T(^\circ \mathrm{C})
$$
Do not add $273.15$ to a temperature difference.
Why Kelvin is used in physics
The Kelvin scale is especially important in physics because many formulas work naturally with absolute temperature. Since Kelvin starts at absolute zero, it avoids negative values for ordinary thermal systems and connects directly to microscopic physical behavior.
For example, gas laws and thermodynamic equations typically require temperature in Kelvin, not Celsius or Fahrenheit. If Celsius were used directly in such formulas, the results would be wrong because the zero point is not absolute.
In physics formulas involving temperature, always check whether temperature must be in Kelvin. In thermodynamics, this is usually required.
Visual comparison of scales
Worked examples
Suppose a laboratory sample has a temperature of $37^\circ \mathrm{C}$. In Kelvin,
$$
T = 37 + 273.15 = 310.15\ \mathrm{K}
$$
In Fahrenheit,
$$
T = \frac{9}{5}(37) + 32 = 66.6 + 32 = 98.6^\circ \mathrm{F}
$$
Now suppose the sample is heated by $5^\circ \mathrm{C}$. Its temperature increase is also $5\ \mathrm{K}$, not $278.15\ \mathrm{K}$. The new temperature is
$$
42^\circ \mathrm{C} = 315.15\ \mathrm{K}
$$
Summary formulas
| Conversion | Formula |
|---|---|
| Celsius to Kelvin | $T(\mathrm{K}) = T(^\circ \mathrm{C}) + 273.15$ |
| Kelvin to Celsius | $T(^\circ \mathrm{C}) = T(\mathrm{K}) - 273.15$ |
| Celsius to Fahrenheit | $T(^\circ \mathrm{F}) = \frac{9}{5}T(^\circ \mathrm{C}) + 32$ |
| Fahrenheit to Celsius | $T(^\circ \mathrm{C}) = \frac{5}{9}\left[T(^\circ \mathrm{F}) - 32\right]$ |
| Fahrenheit to Kelvin | $T(\mathrm{K}) = \frac{5}{9}\left[T(^\circ \mathrm{F}) - 32\right] + 273.15$ |
Core facts to remember:
$$
0\ \mathrm{K} = -273.15^\circ \mathrm{C}
$$
$$
\Delta T(\mathrm{K}) = \Delta T(^\circ \mathrm{C})
$$
Kelvin is the preferred scale in physics equations.