Thermodynamics problem: Piston in cylinder

[Adrian379]

Homework Statement

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A horizontal cylinder with length L=1m and section S=2*10^(-3) is divided in two parts by a piston. In theese compartments is air at pressure p0=10^5N/m^2 and same temperature.
The piston move with h=0,4m from initial position. Which is force to hold piston in this position ?

Homework Equations

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My Tries: just this figure and same irrelevant ecuations like PV=nRT and i think P0V0=P1V1, but i don't know why. Thank you very much, i am at beginning with thermodynamics.

 

[John Morrell]

I'll give some hints. The first step is going to be finding the new pressures on both sides in the piston after you move the piston. For that, you'll be using P₀V₀=P₁V₁.

After you know the pressure on both sides, you need to find the net force on the dividing wall between the two sides. If you know the pressure, and you know the area, how do you find the force exerted by either side? Look at the units for pressure and area.

 

[Adrian379]

Yeah but can you explain me why p0v0=p1v1 ? Thanky you for response.

 

[John Morrell]

I'm not an expert here so you might want to double check this, but in my understanding it is a consequence of the law of conservation of energy.

Pressure times volume is a form of energy. So if you change the volume, you must also change the pressure. Energy can be neither created nor destroyed. However, this is only valid if you don't add energy from an outside source.

 

[Chestermiller]

Yeah but can you explain me why p0v0=p1v1 ? Thanky you for response.

It follows from the ideal gas law, assuming that the temperature and number of moles don't change.$$nRT_0=P_0V_0=P_1V_1$$

 

[Adrian379]

It follows from the ideal gas law, assuming that the temperature and number of moles don't change.$$nRT_0=P_0V_0=P_1V_1$$

Yes but, if the piston move, the temperature from compartments don't change ?

I've found P1 & P2:
P1= P0L/L-2h

P2=P0L/L+2h

Now, i must to found the force.

F=P*S but what P i must multiply to S to found force ?

I solve it ! F=(p2-p1)*S = 888N
Thank you very much !

 

[Chestermiller]

Yes but, if the piston move, the temperature from compartments don't change ?

Apparently they expect you to assume that the cylinder and piston are not insulated. So, when the system equilibrates, the temperature will be unchanged.

 

[John Morrell]

Am I right in thinking that without the assumption that the process is Isothermal, there is no way to find the pressure or temperature? It's been a while since I solved this sort of thing.

 

[Chestermiller]

Am I right in thinking that without the assumption that the process is Isothermal, there is no way to find the pressure or temperature? It's been a while since I solved this sort of thing.

It could also be done if the two chambers and the piston were adiabatic, and the piston were moved very slowly.