Haha thanks for all your effort - this is a qual practice problem from Caltech - my qual is tomorrow. Point being, this is supposed to be solvable in 30 min, so I may be screwed. Anyway your equation looks like what I got - impossible to solve for general γ. Maybe I'll go back to the chemical...
Thanks for the detailed response - it makes more sense now, but..
##P\propto\rho^\gamma\rightarrow P'\propto\rho^{\gamma-1}\rho'\rightarrow -\rho g\propto\rho^{\gamma-1}\rho'\rightarrow\rho'\propto-\rho^{2-\gamma}\rightarrow\rho\sim(-z)^{\frac{1}{\gamma-1}}=(C-Az)^{3/2}## for γ=5/3, where C is...
Ok I see the distinction between adiabatic and isentropic from wikipedia, but this process is reversible since you can just as easily place the cylinder back and it will return to its original state.
Well this was what I was doing with the density distribution - clearly it is more dense toward...
1. I don't think it makes sense to ask for the temperature change if the temperature is not uniform, plus I think it has to be - in equilibrium. Otherwise the particles would just keep exchanging energy until they.. reached equilibrium.
2-4. For the entropy part, the problem also asks to "note...
Homework Statement
A thin, closed, insulated cylinder of length L, filled with ideal gas (temperature T, mass M, total amount 1 mole) lies on a table. It is very gently raised to the vertical, after which equilibrium is reestablished.
Does the entropy change? What is the temperature change (to...