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Chapter 8 and 9

# Chapter 8 and 9 - L29 Entropy under different conditions...

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L29: Entropy under different conditions Gibbs Free Energy (G) a. Calculating entropy for different processes 1. Entropy change for T=const (isothermal) - isothermal gas expansion/compression - phase transition 2. Entropy for Q=0 (adiabatic processes) 3. Entropy change for V=const (isochoric) 4. Entropy change for P=const (isobaric) - standard molar entropies = Δ f i r T dQ S

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1. Isothermal ideal gas expansion/compression T Q S r Δ = Δ In reversible isothermal gas expansion Δ E=0 Thus, W = -Q (The 1st Law) = Δ 1 2 ln V V nR S 2. Adiabatic process: Δ Q=0 Δ S=0 Example: Expansion of CO 2 from gas cylinder causes increase in kinetic energy and therefore decrease in internal energy.
3. Isochoric processes: V=const Heating/cooling at V=const: = Δ f i r T dQ S dT nc dQ v r = = = = Δ 1 2 ln 2 1 2 1 T T nc T dT nc T dT nc S v T T v T T v T is not constant: cannot be taken out of integral From chapter 7

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4. Isobaric processes: P=const Heating/cooling at P=const: = Δ f i r T dQ S dT nc dQ p r = = = = Δ 1 2 ln 2 1 2 1 T T nc T dT nc T dT nc S p T T p T T p
Iron has a heat capacity ( c p ) of 25.1 J/(K mol), independent of T between 0 and 100 C. (a) Calculate the enthalpy and entropy changes of 1 mol of Fe as it is cooled at atmospheric pressure (P=const) from 100 C to 0 C. Cooling: Entropy at P=const: (b) A piece of Fe weighing 55.85 g (1 mol) at 100C is placed in large reservoir of water held at 0 C. It cools irreversibly until its temperature equals that of the water. Assuming that the water reservoir temperature remains at 0 o C, calculate the entropy changes for the Fe and the water and the total entropy changes in this process. J T nc H p 2510 ) 373 273 ( 1 . 25 = = Δ = Δ 1 1 2 83 . 7 373 273 ln 1 . 25 ln = = = Δ K J T T nc S p 1 19 . 9 273 2510 = = Δ = Δ K J K J T H S water 1 83 . 7 = Δ K J S Fe 1 36 . 1 19 . 9 83 . 7 = + = Δ + Δ = Δ K J S S S water Fe tot

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Various Possible Combinations of Δ H and Δ s for a Process (system) and the Resulting Dependence of Spontaneity on Temperature
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Chapter 8 and 9 - L29 Entropy under different conditions...

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