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Jenkz
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Homework Statement
Derive an equation for the change in entropy that occurs in an isolated (micro-canonical) system containing N particles, if an adiabatic expansion from volume V1 to volume V1 takes place. Show that the number of microstates is given by V^N.
Homework Equations
Entropy S = K[itex]_{b}[/itex] ln [itex]\Omega[/itex]
Where [itex]\Omega[/itex] is multiplicity, the number of microstates for distinguishable partciles= N!/[itex]\Pi[/itex][itex]_{i}[/itex]n[itex]_{j}[/itex]!
The Attempt at a Solution
Ok I'm not too sure where to start. I know that dQ = 0 as this is an adiabatic expansion.
Meaning dU = dW = - NK[itex]_{b}[/itex]T ln (V2/V1), but I'm not sure if this helps anything.
I also know that a microcanonical system is thermally isolated and has a fixed N. So would thermally isolated mean dT = 0? in which case dU = 0 ... confused.
please help!