Temperature is a measure of the average internal kinetic energy of a substance. The higher the temperature, the more the atoms of a substance move around. Possible modes of motion include translation, rotation, and vibration. In situations of thermal equilibrium (when all parts of the system are at the same temperature) each mode of motion will have, on average, the same kinetic energy as evey other mode (called Equipartition of Energy).
When a substance gets hotter it will in general expand (yes, there are exceptions such as water between 0°C and
4°C) and, at least over moderate temperature ranges, we find that the amount of expansion is proportional to the temperature change. So for objects with well defined linear dimensions (solids or liquid in tubes) we find that the change in length ΔL cuased by a change in temperature ΔT is given by ΔL=αL0ΔT,
where L0 is the original length and α is a number called the Coefficient of Thermal Expansion with units of 1/temperature.
Because temperature is a measure of internal kinetic energy, there is a minimum possible temperature found ny removing all possible internal energy from a system. This occurs at -273°C, a temperature called absolute zero. We can use this to define a new, physically meaningful, temperature scale, the Kelvin scale, whose zero point is at absolute zero and whose unit is the same size as 1°C. We call this absolute or thermodynmic temperature measured in Kelvins. 0K=-273°C and so
Temp in K = Temp in °C + 273.
As a direct result of kinetic theory, gases at temperatures well above the temperature at which they turn to liquids (or, occasionally, solids) obey simple laws.
Boyle's Law: At constant temperature, the product of pressure and volume is constant: PV=constant.
Charles's Law: At constant pressure, voume is proportional to absolute temperature: V∝T.
Gay-Lussac's Law: At constant volume, pressure is proportional to temperature: P∝T.
Together these form the universal gas law PV=nRT where n is the number of moles of material and R is a universal constant.
As a result, under standard conditions (pretty much room temperature and pressure) 1 mole of any gas occupies 22.4 litres.
According to the kinetic theory gases well above boiling point behave as if they were made of small, non-interacting, particles that bounce off each other and the walls elastically. In this case the gas pressure arises from the average effect of all the collisions between the gas molecules and the walls and it is related to the volume and the internal velocity of the molecules by PV=Nm<v2> where N is the number of molecules, m the mass of a molecule, and <v2> the average squared velocity of a gas molecule.
From that we find that the temperature is a measure of the average kinetic energy where ½m<v2>=3kT/2, so we can relate the mean squared velocity uniquely to the temperature..