Calculation of Kinetic Energy-
According to kinetic theory of gases, the pressure P exerted by a gas is given by
\(P =\frac 13 \frac{Mu^2}V\) or \(PV = \frac 13 Mu^2\)
According to gas equation, PV = RT
\(\therefore \frac 13 mu^2 = RT \quad ....(1)\)
\(u^2 = \frac{3RT}{M}\)
\(u^2 \propto T\) (\(\because\) R and M are constants)
\(u \propto \sqrt T\)
Thus, the root mean square velocity of an ideal gas is directly proportional to the square root of the absolute temperature.
Also from eq. (1)
\(\frac13 mu^2 = KT\) (\(\because \frac RN = K\) Boltzmann constant)
or \(\frac13 mu^2 = \frac 32KT\)
But \(\frac 12 mu^2\) is average kinetic energy per molecule of the gas
\(\therefore \) Average K.E. = \(\frac 32 KT\) or Average K.E. \(\propto\) T (\(\because\) K is constant)
Thus, average kinetic energy of one mole of any gas is directly proportional to its absolute temperature.
Again from equation (1), when u = 0
T = 0 (Absolute zero)
Hence absolute zero may be defined as the temperature at which the velocities of the gas molecules reduce to zero i.e. molecular motion ceases at absolute zero. However, note that this is true only in case of an ideal or perfect gas. The gases used in practice are far from the perfect, particularly at such low temperature.
