o - number of oxygen molecules in the room Average kinetic energy of total hydrogen molecules = N kT H where N H - number of hydrogen molecules in the room. It is given that the number of oxygen molecules is times more than number of hydrogen molecules in the room. So the ratio of average kinetic energy of oxygen molecules with average kinetic energy of hydrogen molecules is : . .
. Mean (or) average speed ( v ) It is defined as the mean (or) average of all the speeds of molecules If v , v , v …..v N are the individual speeds of molecules then N RT M kT n ........ π π ( . ) Here M- Molar Mass and m – mass of the molecule.
kT = ( . ) - - - - Unit Kinetic theory of gases we calculated the rms speed of each molecule and not the speed of each molecule which is rather difficult. In this scenario we can find the number of gas molecules that move with the speed of m s − to m s − or m s − to m s − etc. In general our interest is to find how many gas molecules have the range of speed from v to v + dv .
This is given by Maxwell’s speed distribution function. N N kT v e mv kT π π ( . ) The above expression is graphically shown as follows N v v mp v avg v rms d v N v The number of molecules having speeds ranging from v to v + d v equals the area of the rectangle, N v d v Figure . Maxwell’s molecular speed distribution From the Figure .
, it is clear that, for a given temperature the number of molecules having lower speed increases parabolically ( v ) but decreases exponentially ( e mv kT - ) after reaching most probable speed. The rms speed, average speed and most probable