Calculate Pressure of Gas with Light Piston

[thereddevils]

Homework Statement

A cylinder is vertically placed with its frictionless ,light and moveable piston facing the top. A mass of known value is placed on it, and its distance from the bottom of the cylinder is known. What is the pressure of the gas ?

Homework Equations

The Attempt at a Solution

The potential energy of the mass is the work done by the gas. Since the system is in equilibrium , the gas must do work against the compressing effect of the piston.But the problem is there is no change in the volume of the gas.

W=p dV is simply zero since dV is 0 . That doesn't make sense ??

 

[irycio]

I don't catch it. The question says "what is the pressure of the gas?" and you are considering work.
Anyway, since the topic is entitled "work done by gas", than there is no work done by gas in this situation. If the gas is compressed, the work is done on it. And since the mass is placed on the piston, the gas is compressed; if the volume changes, it decreases, so that the work done by gas equales 0 no matter what :)

 

[ehild]

.

The potential energy of the mass is the work done by the gas. Since the system is in equilibrium , the gas must do work against the compressing effect of the piston.But the problem is there is no change in the volume of the gas.

W=p dV is simply zero since dV is 0 . That doesn't make sense ??

Work is done during a process, not in equilibrium. There is no displacement during equilibrium, so there is no work. The gas has to exert force against the compressing effect of the piston.

ehild

 

[thereddevils]

Thanks all , so how do i calculate pressure in this case ?

Also , the volume of the cylinder is also known.

P=F/A

F=PA

where F=mg and A=(volume/height)

is it just like that ?

 

[irycio]

Yep, it's that simple :)

 

[ehild]

And you are that smart :)