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1. All the gas molecules (1028of them) are compressed so that they only fill 1/3rdof the...

1. All the gas molecules (1028of them) are compressed so that they only fill 1/3rdof the room.They are then allowed to expand to fill the whole room. First, why do they expand to fill theroom, and what is the increase in entropy of this system, as well as the increase in entropy ofthe “universe” during this expansion?

Solutions

Expert Solution

Let N be the number of atoms, N = 1028. Let V be the volume of the room. So,

V1 = V/3

After the expansion, V2 = V. As the gas molecules are compressed they frequently collide with each. So They move randomly after the collision and because of diffusion they completely fill the room. This reason is justified because random motion is diffusive and gas molecules perform random motion after every collision with each other.

Change in entropy:  Number of microstates proportional to the total volume of N molecules so,

before expansion,

after expansion,

Change in entropy,

  

  

  

So if the walls of the room are insulating so that no heat exchange takes place, the entropy of the environment is constant during the expansion. So increase in entropy of the universe is equal to the increase in the entropy of the gas.

genius_generous answered 1 year ago
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