# Temperature

All matter is made from particles (atoms or molecules) that are in constant motion. Being in motion, the particles have kinetic energy. The motion of the particles is oscillatory, like a random vibration. The higher the frequency and amplitude of the vibration, the higher is the kinetic energy of the particle.

Image: Thermal vibration of a segment of protein alpha helix

The temperature of the matter is directly related to the kinetic energy of the particles. The higher the kinetic energy of the particles, the higher is the temperature of the matter.

Salt will dissolve faster in hot water than in cold water. That’s because in hot water the molecules move faster which helps mixing together the salt and water molecules.

Temperature is an average measure of the kinetic energy of the particles of a defined quantity of matter (solid, liquid, gas or plasma).

Image: Particles expansion contraction due to temperature (left – cold, right – hot)

At higher temperatures solids, liquids and gases increase in volume, the occupy more space. That’s because the molecules have higher amplitude when vibrating and push away each other.

Two bodies in contact will reach thermal equilibrium. The body with higher temperature will gradually transfer heat (particle’s kinetic energy) to the lower temperature body. After some time they will have the same temperature.

Thermometers are used to measure the average temperature of a body (solid, liquid or gas). Temperature measurement works due to the above mentioned laws:

• at higher temperature liquid increase their volume
• two bodies in contact reach thermal equilibrium

A thermometer contains usually a liquid (alcohol or mercury) in a narrow glass tube. When the thermometer is put in contact with a body, heat transfer starts from the hotter body to the colder body. The liquid within the thermometer starts to expand/contact faster than the glass. The liquid position in the glass tube gives an indication of the body’s temperature.

Image: Celsius and Kelvin scale thermometer

There are different temperature scales used worldwide. The differ mainly in two ways: the point for zero degrees and the resolution (magnitude of incremental units) on the scale.

The Celsius temperature scale is the most common used in the world. It has these main characteristics:

• the symbol is: °C
• the 0 °C point is the freezing point of water (at sea-level atmospheric pressure)
• the 100 °C point is the boiling point of water (at sea-level atmospheric pressure)
• it’s a centigrade scale because of the 100 degree interval

The Kelvin temperature scale is the International System of Units (SI) defined unit for temperature measurement. It has these main characteristics:

• the symbol is: K
• the 0 K point is the lowest physically possible temperature that can occur (it’s called also absolute zero)
• water freezing point is at 275.15 K (at sea-level atmospheric pressure)
• it’s used in science and engineering

Image: Celsius and Fahrenheit temperature scales

The Fahrenheit temperature scale is mainly used in the USA. It has these main characteristics:

• the symbol is: °F
• the 0 °F point is the temperature at which a solution of brine contains equal parts of ice and salt
• the 32 °F point is the freezing point of water (at sea-level atmospheric pressure)
• the 212 °F point is the boiling point of water (at sea-level atmospheric pressure)

The table below contains the mathematical relationships to convert for one temperature scale to another.

 °C K °F $T [^\circ C] = T[K] – 273.15$ $T [K] = T[^\circ C]+273.15$ $T [^\circ F] = T[^\circ C] \cdot \frac{9}{5} + 32$ $T[^\circ C]= \left ( T[^\circ F] – 32 \right ) \cdot \frac{5}{9}$ $T[K]= \left ( T[^\circ F] + 459.67 \right ) \cdot \frac{5}{9}$ $T [^\circ F] = T[K] \cdot \frac{9}{5} – 459.67$

Example 1. Convert the temperature -15 °C in K and °F.

$\begin{equation*} \begin{split} T [K] &= -15 + 273.15 = 258.15\\ T [^\circ F] &= -15 \cdot \frac{9}{5} + 32 = 5 \end{split} \end{equation*}$

Example 2. Convert the temperature 0 °F in K and °C.

$\begin{equation*} \begin{split} T[K] &= \left ( 0 + 459.67 \right ) \cdot \frac{5}{9} = 255.37\\ T[^\circ C] &= \left ( 0 – 32 \right ) \cdot \frac{5}{9} = -17.78 \end{split} \end{equation*}$

Example 3. Convert the temperature 100 K in °F and °C.

$\begin{equation*} \begin{split} T [^\circ F] &= 100 \cdot \frac{9}{5} – 459.67 = −279.67\\ T [^\circ C] &= 100 – 273.15 = -173.15 \end{split} \end{equation*}$

Test your knowledge regarding Temperature by taking the quiz below:

QUIZ! (click to open)

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