# Thermodynamics problem: Piston in cylinder

1. Mar 24, 2017

1. The problem statement, all variables and given/known data

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 ?

2. Relevant equations

My Tries: just this figure and same irrelevant ecuations like PV=nRT and i think P0V0=P1V1, but i dont know why. Thank you very much, i am at begining with thermodynamics.

2. Mar 24, 2017

### 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.

3. Mar 24, 2017

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

4. Mar 24, 2017

### 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.

5. Mar 24, 2017

### Staff: Mentor

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

6. Mar 24, 2017

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 !

Last edited: Mar 24, 2017
7. Mar 24, 2017

### Staff: Mentor

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

8. Mar 24, 2017

### 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.

9. Mar 24, 2017

### Staff: Mentor

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