number of molecules per unit volume N . We have assumed that the number density is the same throughout the cube. Figure . Number of molecules hitting the wall - - - - Unit Kinetic theory of gases molecules on the wall is independent of area of the wall (A).
. . Kinetic interpretation of temperature To understand the microscopic origin of temperature in the same way, Rewrite the equation ( . ) N V mv = PV Nmv = ( .
) Comparing the equation ( . ) with ideal gas equation PV=NkT , NkT= Nmv kT= mv ( . ) Multiply the above equation by / on both sides, kT mv ( . ) R.H.S of the equation ( .
) is called average kinetic energy of a single molecule ( KE ). The average kinetic energy per molecule KE = ∈ = kT ( . ) Equation ( . ) implies that the temperature of a gas is a measure of the average translational kinetic energy per molecule of the gas.
Compare this with the definition of temperature studied in lower classes: Temperature is the degree of hotness or coldness! Note Equation . is a very important result from kinetic theory of gas. We can infer the following from this equation.
P = nm v x ( . ) Since the gas is assumed to move in random direction, it has no preferred direction of motion (the effect of gravity on the molecules is neglected). It implies that the molecule has same average speed in all the three direction. So, v x = v y z .
The mean square speed is written as x y z x x Using this in equation ( . ), we get nmv = or P N V mv = ( . ) as n N The following inference can be made from the above equation. The pressure exerted by the molecules depends on (i) Number density n N .
It implies that if the number density