Lecture5Ch161Feb9

Lecture5Ch161Feb9 - Summary of last lecture Density of...

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Summary of last lecture Density of states – the key property of a statistical system Sphere analogy for density of states of an ideal gas. Quantum indistinguishability of particles. Reversible and irreversible processes, Second law of Thermodynamics Balance of energy in heat exchange Absolute Temperature

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Key Concepts and Lessons: a) Entropy and Temperature b) Heat reservoir c) Mechanical Interactions and Work Reading: Reif, Ch3
Energy partitioning at equilibrium This simple example shows that certain amount of heat exchange would lead to highest number of states. Now we are ready to find this value using usual tools: The last relation comes from our common sense observation that when two systems are in thermal exchange their temperatures are the same! Note T - is absolute temperature in Kelvins! E Ω 0 = E Ω A E ( ) Ω A ' E ' ( ) ( ) = E Ω A E ( ) Ω A ' E 0 E ( ) ( ) = 0 Ω A ' E 0 E ( ) E Ω A E ( ) + Ω A E ( ) E Ω A ' E 0 E ( ) = 0 E ln Ω A E ( ) = E ' ln Ω A ' E ' ( ) S A ( E ) E = S A ' ( E ') E ' = β = 1 kT !!! Note: the + sign in the second line is CORRECT!

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Does that work for an ideal Gas? Remember an expression for entropy of an ideal gas which we obtained before: S = kN ln 2 π m h 2 3/2 VE 3/2 kN ln N / e ( ) + const + O (1) A straightforward calculation gives us: E = 3 2 NkT S E = 1 T i.e. a very familiar (from high school) result!
Is it really temperature? Our common sense tells us that heat should flow from a more heated (higher T) to a less heated (lower T) object. Does our definition of T comply with that common sense requirement?) Consider again two systems A and A’ which were brought into contact with subsequent heat exchange. Now consider the relationships: Δ S A + Δ S A ' 0 Δ Q = Δ E A = E A f E A i = −Δ E A ' = E A ' f E A ' i ( ) ; Δ Q is the amount of heat transfered from A' to A . if

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Lecture5Ch161Feb9 - Summary of last lecture Density of...

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