Energy change of apparatus when gaws suddenly expands

[jasoncurious]

Energy change of apparatus when gas suddenly expands

Homework Statement

A gas is confined in a cylinder by a piston. The initial pressure of the gas is 7 bar(700kPa), and the volume is 0.10m^3. The piston is held in place by latches in the cylinder wall.The whole apparatus is placed in a total vacuum. What is the energy change of the apparatus if the restraining latches are removed so that the gas suddenly expands to double its initial volume, the piston striking other latches at the end of the process?

Data known:
P(initial) = 700kPa
V(initial) = 0.10m^3
V(final) = 0.2m^3

Homework Equations

Energy change = W = PΔV

The Attempt at a Solution

Since the gas suddenly expands (not a quasi-equilibrium process), the PV ln (V2/V1) equation cannot used. But still, my lecturer gave me zero. I want to know the right way to solve this problem. God bless you all.

 

[CWatters]

If it's surrounded by a vacuum and the expansion happens rapidly then yes the process is probably adiabatic...

http://en.wikipedia.org/wiki/Adiabatic_process

You didn't actually tell us what answer you gave or showed how you got it.

 

[jasoncurious]

Thanks for the help. I'll confirm with my lecturer. I suggest since it's expansion against vacuum, there should be no energy change.

 

[uart]

I'd assume that the gas is doing work against the (assume finite mass) piston during the expansion, so work done by the gas is converted into KE of the moving piston. This energy is lost with a thud when the piston hits the stop "latch", so no useful work is done, but you can still calculate the work done and the energy lost by the gas (for an adiabatic expansion).

 

[rezeew]

I would approach this problem by considering the different forms of energy present in the system and how they change during the process.

Firstly, the gas in the cylinder has both kinetic and potential energy due to its motion and position within the cylinder. When the latches are removed and the gas expands, the gas molecules will move and collide with the walls of the cylinder, transferring some of their kinetic energy to the walls. This results in a decrease in the kinetic energy of the gas.

Secondly, the piston and latches have potential energy due to their position and the forces acting on them. When the latches are removed, the piston will move and strike the other latches at the end of the process. This results in a decrease in the potential energy of the piston and latches.

Overall, the energy change of the apparatus can be calculated by considering the changes in kinetic and potential energy of the gas, piston, and latches. This can be expressed as:

Energy change = Change in kinetic energy + Change in potential energy

= (Final kinetic energy - Initial kinetic energy) + (Final potential energy - Initial potential energy)

Since the initial and final states of the system are at rest, the change in kinetic energy is zero. Therefore, the energy change of the apparatus can be simplified to:

Energy change = Final potential energy - Initial potential energy

= (Mass of piston + latches) x g x (Final height - Initial height)

= (Mass of piston + latches) x g x (2 x initial height)

= (Mass of piston + latches) x g x (2 x (initial volume/area))

= (Mass of piston + latches) x g x (2 x (0.1m^3/πr^2))

= (Mass of piston + latches) x g x (0.2m^3/πr^2)

= (Mass of piston + latches) x g x (0.2m^3/π(0.04m)^2)

= (Mass of piston + latches) x g x 1256.64m^-3

Therefore, the energy change of the apparatus when the gas suddenly expands is dependent on the mass of the piston and latches, the acceleration due to gravity, and the initial volume of the gas.

I hope this helps!