- #1
zenterix
- 688
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- Homework Statement
- A container with rigid, well-insulated walls is divided into two parts by a partition. One part contains a gas, and the other is evacuated. If the partition suddenly breaks, show that th einitial and final internal energies of the gas are equal. (Note: this process is called an adiabatic free expansion).
- Relevant Equations
- ##\Delta U = Q+W##
Let's consider the system as both internal chambers together, ie everything inside the adiabatic walls.
We have ##Q_{sys}=Q_{gas}+Q_{evac}=0## because we have adiabatic walls and ##W_{gas}+W_{evac}=0## because of the rigid walls.
##\Delta U = U_f-U_i=Q_{gas}+Q_{evac}+W_{gas}+W_{evac}=0##.
How do we reason about ##W_{gas}## and ##W_{evac}## individually? Their sum is zero because it represents work done on the system as a whole. But when the gas expands suddenly into the chamber with no gas, what is the work done on the evacuated chamber for example (of course this is just the negative of the work done by the chamber with the gas).