if it is within the distance v x ∆ t from the wall. That is, all molecules within the volume Av x ∆ t only can hit the wall in time ∆ t . But, on the average, half of these are moving towards the wall and the other half away from molecule with a different initial velocity which after a collision acquires the velocity ( v x , v y , v z ). If this were not so, the distribution of velocities would not remain steady.
In any case we are finding . Thus, on the whole, molecular collisions (if they are not too frequent and the time spent in a collision is negligible compared to time between collisions) will not affect the calculation above. . .
Kinetic Interpretation of Temperature Equation ( . ) can be written as PV = ( / ) nV m ( .15a) PV = ( / ) N x ½ m ( .15b) where N (= nV ) is the number of molecules in the sample. The quantity in the bracket is the average translational kinetic energy of the molecules in the gas. Since the internal energy E of an ideal gas is purely kinetic * , E = N × ( / ) m ( .
) Equation ( . ) then gives : PV = ( / ) E ( . ) We are now ready for a kinetic interpretation of temperature. Combining Eq.
( . ) with the ideal gas Eq. ( . ), we get E = ( / ) k B NT ( .
) or E/ N = ½ m = ( / ) k B T ( . ) i.e., the average kinetic energy of a molecule is proportional to the absolute temperature of the gas; it is independent of pressure, volume or the nature of the ideal gas. This is a fundamental result relating temperature, a macroscopic measurable parameter of a gas (a thermodynamic variable as it is called) to a molecular quantity, namely the average kinetic energy of a molecule. The two domains are connected by the Boltzmann constant.
We note in passing that Eq. ( . ) tells us that internal energy of an ideal gas depends only on temperature, not on pressure or