# Ideal Gas Equation and Absolute Temperature

The notion of absolute temperature is suggested by observations in the behavior of gases with change in temperature. In particular, the volume of a fixed mass of gas at constant pressure increases linearly with temperature t as

V = A (t - T

_{o}) ------(i)

The significant thing about this is that T

_{o}is independent of the gas but depends only on the temperature scale chosen. For the Celsius scale T

_{o}= -273.15

^{ o }C. This suggests that we define a new temperature T given by

T = t + 273.15 -------(ii)

So that equation (i) can be put in the simple form

**V = AT**

This is known as Charles' Law. We have a similar relation for pressure versus temperature at constant volume (P Î± T). These relations and the Boyle's law, PV = const. (at constant temperature) are contained, as we know, in the ideal gas equation PV = Î¼ RT. Real gases obey these relations only approximately, the approximation being better for low pressures and high temperatures.

The Charles' Law suggests the physical interpretation of the temperature T, introduced above. As T Â® 0, the volume of an ideal gas goes to zero. T = 0 thus represents the absolute lowest temperature possible, since below T = 0, V would be negative, which is unphysical. For this reason T is known as absolute temperature. Of course, since ideal gas is a hypothetical entity and real gases do not follow Charles' Law for all T, this is only a suggestive argument for the existence of absolute zero of temperature where every substance in nature has the least possible molecular activity.

The unit of the absolute temperature scale has the same size as the unit of the Celsius scale: the two scales only differ in their origin. The absolute temperature T in Equation (ii) is called the Kelvin temperature, denoted by K. The absolute zero of temperature is thus 0 K or -273.15

^{ o }C. We should note that the Kelvin scale is not the only absolute temperature scale possible. We can have different absolute temperature scales by choosing different sizes of the unit of the scale. The zero of all such absolute scales will, however, be the same, namely the lowest possible temperature in nature.

We mentioned earlier that two fixed points are needed to define a temperature scale. In modern thermometry, the triple point of water is chosen to be one of the fixed points. The triple point of water is the state where the solid, liquid and vapour phases of water co-exist in equilibrium.

It is characterized by a unique temperature and pressure. This is why it is preferred over the conventional fixed points (melting point of ice and boiling point of water), which depend on pressure. To construct the absolute temperature scale, we take the triple point of water as one fixed point. On this scale, the absolute zero may be regarded as the other fixed point! We need to assign some numbers for temperatures of these two fixed points. The lowest temperature, the absolute zero, has T = 0.

What value of absolute temperature shall we assign to the triple point of water? The value that we choose will determine the size of the unit of the absolute temperature scale. The triple point of water on the Celsius scale is 0.01

^{ o }C. From the Kelvin, the absolute temperature that we assign to the triple point is 273.16 K.

To summarize, the Celsius temperature t

_{ c}is related to the absolute temperature on the Kelvin scale (T) by t = T - 273.15; T = 273.16 K (triple point of water).

The next task is to see how to determine the temperature T for different bodies in a way that is as independent of the particulars of the measuring device as possible.

Heat energy causes changes in temperature, volume and pressure of gases.

**Boyle's Law**

Sir Robert Boyle stated that at constant temperature, the pressure of a given mass of gas is inversely proportional to its volume. Let P be the pressure and V the volume of a gas at a constant temperature T, then

(at constant temperature) or

(at constant temperature) or

**PV = a constant**

**
**