Compressing a Gas
An ideal gas is kept in a cylinder fitted with a movable piston.
- The gas is compressed suddenly by moving the piston downwards.
- Then, the piston is fixed at the final position and the gas is left in compressed state.
How does the pressure change as the time passes after the gas is left compressed?
Assume : The gas is initially at the same temperature as the surroundings and that the container can exchange heat with the surroundings
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If the piston was lowered very slowly, then you could do the compression reversibly. But if you lower the piston quickly, then the piston does more work than is required only to compress the gas. Since you compress the gas suddenly, that heat stays in the gas without leaving( adiabatic compression) ,with the result being that the gas in the piston is hotter than the surroundings. So after the gas is left compressed , it tries to acquire thermal equilibrium with the surroundings (which now have lower temperature than the gas), therefore it will lose temperature. Since volume of the container is fixed (since the piston is fixed in its position) , from ideal gas equation : PV =nRT
,the pressure is directly proportional to temp for fixed volume and amount of gas. Since temp of the gas decreases therefore its pressure also decreases after the gas is left compressed.