Heat and Thermodynamics


   
 
Root Mean Square Speed in Terms of Temperature
We are now in a position to write the rms speed of the molecules in terms of the absolute temperature. From equation (vi),
 
 
And from equation (x),
 
 
From these two,
 
 
 
This can also be written as,
 
 
 
 
Average Kinetic Energy of a Molecule
Average kinetic energy of a molecule is
 
 
 
The total kinetic energy of all the molecules is
 
 

The average speed    is somewhat smaller than the rms speed. It can be shown that

 
 
  
     
   
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