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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!