- #1

Hiero

- 322

- 68

- Homework Statement
- A cylinder of cross section A is divided into two chambers 1 and 2 by means of a frictionless piston. The piston as well as the walls of the cylinder are heat insulating, and the chambers initially have equal length L. Both chambers are filled with 1 mol of helium gas, with pressures ##P_0## and ##2P_0## respectively. The piston is then allowed to slide freely, whereupon the gas in chamber 1 pushed the piston a distance “a” to equalize the pressure. Find a.

- Relevant Equations
- ##PV^\gamma =## constant

I was puzzling over how to solve this and finally peeked at the solution. They used the relevant equation above.

I disagree with this though. The problem specifically says “the piston is allowed to slide freely!” This means that we don’t let it happen slowly. So then we are not in quasi-static equilibrium throughout the expansion. Thus the pressure is not well defined at each moment, and so the relevant equation does not apply! (It is derived from dU = -PdV which seems to me to rely on the pressure being well defined and hence the process being reversible, unlike in this problem.)

Do you agree with me that the relevant equation only applies for reversible (quasi-equilibrium) adiabatic processes, and not irreversible adiabatic processes?

(And if so, how would you solve this problem as it stands?)

I disagree with this though. The problem specifically says “the piston is allowed to slide freely!” This means that we don’t let it happen slowly. So then we are not in quasi-static equilibrium throughout the expansion. Thus the pressure is not well defined at each moment, and so the relevant equation does not apply! (It is derived from dU = -PdV which seems to me to rely on the pressure being well defined and hence the process being reversible, unlike in this problem.)

Do you agree with me that the relevant equation only applies for reversible (quasi-equilibrium) adiabatic processes, and not irreversible adiabatic processes?

(And if so, how would you solve this problem as it stands?)