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Question

Kinetic theory of gases proves 
  1. Both a and b
  2. None of these
  3. Only Boyle's law 
  4. Only Charles' law


Solution

The correct option is A Both a and b
Explanation of the gas laws on the basis of Kinetic Molecular Model 
One of the postulates of kinetic theory of gases is Average K.E.T
or, 12mnC2rmsT or ,12mnC2rms=23kT
Now, PV=13mnC2rms=23×12mnC2rms=23kT
(i) Boyle's Law: 
Constant temperature means that the average kinetic energy of the gas moleculea remains constant. 
This means that the rms velocity of the molecules, Crms remains unchanged. 
If the rms velocity remains unchanged, but the volume increases, this means that there will be fewer collisions with the container walls over a given time. 
Therefore, the pressure will decrease i.e., P1V or PV = constnat. 

(ii) Charles' Law: 
An increase in temperature means an increase in the average Kinetic energy of the gas molecules, thus an increase in Crms. 
There will be more collisions per unit time, furthermore, the momentum of each collision increases (molecules strike the wall harder).
Therefore, there will be an increase in pressure. 
If we allow the volume to change to maintain constant pressure, the volume will increase with increasing temperature (Charle's law).

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