notes_Lecture_07_101510

# notes_Lecture_07_101510 - Lecture 7 Thermo Def of Entropy...

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Lecture 7: Thermo. Def. of Entropy Reading: Zumdahl 10.2, 10.3 and 10.13 Outline – Isothermal processes; Isothermal gas expansion and work, Reversible processes (10.2) – Entropy is a state function

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General Expression for Entropy • Note that in the previous example, weight was directly proportional to volume. • Generalizing: ( ) ( ) B B S = ln ln f i k k Δ Ω - Ω B = ln f i k Ω Ω B = N ln f i k Ω Ω B S = N ln f i V k V Δ For one particle… For N particles… Since number of available positions scales linearly with volume…
Isothermal Processes • Recall: Isothermal means Δ T = 0. • Since Δ E = nC V Δ T, then Δ E = 0 for an isothermal process. • Since Δ E = q + w: q = –w (for an isothermal process)

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Example: Isothermal Expansion Consider a mass connected to a ideal gas contained in a “piston.” Piston is submerged in a constant T bath so that the temperature of the system and surroundings are the same and constant at all times ( Δ T = 0). • Initially, V = V i P = P i • Pressure of gas is equal to that created by mass: P i = force/area = (M i . g)/A where A = piston area & g = gravitational acceleration (9.8 m/s 2 )
One-Step Expansion We change the object to one with mass = M i /4, then P ext = (M i /4)g/A = P i /4 The object will be lifted until the internal pressure equals the external pressure, during which the volume will increase: V final = 4V i w 1 = -P ext Δ V = -(P i /4) (4V i - V i ) = - ¾ P i V i

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notes_Lecture_07_101510 - Lecture 7 Thermo Def of Entropy...

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