An adiabatic piston of mass m .

[zorro]

An adiabatic piston of mass m...

Homework Statement

An adiabatic piston of mass m equally divides a diathermic container of volume V and length l. A light spring connects the piston to the right wall. In equilibrium pressure on each side of the piston is P. The container starts moving with acceleration a towards right. Find the stretch of the spring assuming x<< l

I just have one doubt in this question.
Is the expansion of the gas in the right part of the container adiabatic or isothermic?

 

[Andrew Mason]

Homework Statement

An adiabatic piston of mass m equally divides a diathermic container of volume V and length l. A light spring connects the piston to the right wall. In equilibrium pressure on each side of the piston is P. The container starts moving with acceleration a towards right. Find the stretch of the spring assuming x<< l

I just have one doubt in this question.
Is the expansion of the gas in the right part of the container adiabatic or isothermic?

The piston is adiabatic so no heat goes from one side to the other in the container. But the container is diathermic, so the gas in both sides remains at the same temperature as the surroundings.

AM

 

[zorro]

So the equation to be employed is that for adiabatic process or Boyle's Law ?

 

[Andrew Mason]

So the equation to be employed is that for adiabatic process or Boyle's Law ?

If a gas is compressed adiabatically, does the temperature of the gas change? In this case, if the gas on the right is compressed, does its temperature change?

AM

 

[zorro]

In this case, there is no change in temperature on either side. But in an adiabatic expansion, the temperature of the gas decreases. So the expansion of the gas in the right container is not adiabatic. Both the parts are in thermal equilibrium with surroundings and with each other, so there is no use of the 'adiabatic' piston here.

Is there anything wrong with my analysis?

 

[Andrew Mason]

In this case, there is no change in temperature on either side. But in an adiabatic expansion, the temperature of the gas decreases. So the expansion of the gas in the right container is not adiabatic. Both the parts are in thermal equilibrium with surroundings and with each other, so there is no use of the 'adiabatic' piston here.

Is there anything wrong with my analysis?

No. But the question is not clear. It does not say how long the acceleration lasts. I assume that it lasts indefinitely and that there was a reason for making the container diathermic.

AM

 

[zorro]

I think we can assume it lasts indefinitely and the stretch that we have to find is when the acceleration of the piston equals that of the container.

Can't we use the equation for adiabatic process PV^k-1= constant assuming temperature to be constant?

 

[Andrew Mason]

I think we can assume it lasts indefinitely and the stretch that we have to find is when the acceleration of the piston equals that of the container.

Can't we use the equation for adiabatic process PV^k-1= constant assuming temperature to be constant?

??Not if the process is not adiabatic! That is the adiabatic condition. Temperature is not constant in an adiabatic compression or expansion.

AM