# Summary

• The ideal gas equation connecting pressure (P),volume(V) and absolute temperature (T) is
• PV=Î¼RT=kBNT
•  Where Î¼ is the number of moles and N is the number of molecules. R and kB are universal constants.
• R= 8.314 J mol-1 K-1, kB= R/NA=1.38x10-23 J K-1
• Real gases satisfy the ideal gas equatin only approximately, more so at low pressures and high temperatures
• Kinetic theory of an ideal gas gives the relation
• P=
• Where n is number density of molecules, m the mass of the molecule and is the mean of squared speed. Combined with the ideal gas equation it yields a kinetic interpretation of temperature
• This tells us that temperature of gas is a measure of the average kinetic energy
• Of a molecule, independent of the nature of the gas or molecule. In a mixture of gases at a fixed temperature the heavier molecule has the lower average speed.
•  The translational kinetic energy
• This leads to a relation
• The law of equipartition of energy states that if a system is in equilibrium at absolute temperature T, the total energy is distributed equally in different energy modes of absorption, the energy in each mode being equal to 1/2 KBT. Each translational and rotational degree of freedom corresponds to one energy mode of absorption and has energy 1/2 KBT. Each vibrational frequency has two modes of energy (kinetic and potential) with corresponding energy equal to
• Using the law of equipartition of energy, the molar specific heats of gases can be determined and the values are in agreement with the experimental values of specific heat of several gases. The agreement can be improved by including vibrational modes of motion.
• The mean free path lis the average distance covered by a molecule between two succesive collision:
• Where n is the number density and d is the diameter of the molecule.