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General Physics(ppt) Ch 20-1 - Chapter Chapter 20...

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Unformatted text preview: Chapter Chapter 20 Thermodynamics III Entropy Entropy and the 2nd law of thermodynamics thermodynamics Ch 20 Reversible Reversible and irreversible processes Idea Idea of entropy The The 2nd law of thermodynamics Opening Opening story The The popcorn ‘pops’ in an oven. Can we retrieve the original unpopped corn by put the popcorn back into a refrigerator? What in the world gives direction to time? Direction of time Why Why time has direction? Why oneWhy one-way processes are irreversible From From energy conservation? Hot Hot coffee cup and cold hand Popped Popped helium balloon Entropy Entropy postulate If If an irreversible process occurs in a closed closed system, the entropy S of the system always increases; it never decreases. What What is entropy? A state property state Start Start from a Carnot engine An An ideal engine Extracts Extracts heat from environment and and does useful work All All processes are reversible Similar Similar to frictionless in motion Heat Heat flow can be driven by infinitesimal T difference Is Is there any property invariable in a Carnot cycle? What is entropy? a → b & c → d : isothermal∴ ∆Eint = 0, b b dV V QH = Qa →b = Wa →b = ∫ pdV = ∫ NkTH = NkTH ln b a a V Va V QL = Qc→d = NkTL ln d Vc b → c & d → a : adiabatic∴TV γ-1 = const , γ = C p / CV ∴ TH Vb γ-1 = TLVc ; TH Va γ-1 γ-1 = TLVd γ-1 ⇒ Vb / Va = Vc / Vd QH QL =S ⇒ = TH TL Entropy! Change Change in entropy ∆S = S f − S i = ∫ i f dQ T (J/K) Free Free expansion: irreversible Can Can be modeled by a reversible process with same i and f state Free Free expansion isothermal isothermal Vf 1f Q ∆S = ∫ dQ = = nR ln Vi Ti T refe For For 1 mol He ∆S = (1 mol)(8.31 J/mol ⋅ K)ln2 = 5.76 J/K Change in entropy What What is ∆S of a popped popcorn? 1. Water in pericarp vaporized at 180 oC (water 1. mass = 4 mg) 1f Q Lm ∆S1 = ∫ dQ = = V ≈ 0.02 J/K Ti T T 2. Adiabatic expansion of the vapor ∆S 2 = 0 ∆S = ∆S1 + ∆S 2 ≈ 0.02 J/K Corresponding to each audible pop http://www.buetzer.info/fileadmin/pb/HTML-Files/Popcorn.htm Quick Quick quiz Water Water is heated on a stove. Rank the entropy changes of the water when its temperature 1. 2. 3. From 20 oC to 30 oC From 30 oC to 35 oC From 80 oC to 85 oC ∆S = S f − Si = ∫ i f dQ Q ≈ T Tavg Quick quiz Is Is the entropy change along the path to state a larger than, smaller than, or the same as that along the path to state b? Entropy Entropy as a state function For For a reversible process A slow series of small steps slow dEint = dQ − dW p= dQ = pdV + nCV dT dQ dV dT = nR + nCV T V T ∆S = nR ln ⇒∫ i Vf Vi f nRT V f f dQ dV dT = ∫ nR + ∫ nCV i i T V T + nCV Tf Ti Only depends on initial and final states, not path-dependent Entropy and 2nd law of dQ = dS thermodynamics T In In a reversible process, there is no gain or loss of Q/T Entropy Entropy remains constant For For irreversible processes The The entropy of the world is increased No No conservation of entropy ∆S ≥ 0 !! refe Example Example of irreversibility Work Work done on an object by friction Q=W Entropy Entropy of the world increase by W/T Hot Hot stone in cold water ∆S of stone? –Q/T1 ∆S of water? Q/T Q/T2 ∆S of the world? Q/T Q/T2–Q/T1>0 refe Entropy of reversible processes In In a Carnot engine ∆S = 0 for the reversible cycle How How about a single reversible process such as as c d? d? ∆S = -QL/T < 0?? Need Need to consider the whole system, including the heat reservoir. ∆S = -QL/T + QL/T = 0 Entropy Entropy and time Entropy Entropy is the arrow of time For For irreversible processes, the entropy always increases the the forward direction of time To To return in time requires an entropy decrease decrease Not Not allowed by thermodynamics Efficiency of an engine W energy we get = ε= energy we pay for QH For For a Carnot engine εC = QH − QL QH = 1− QL QH TL = 1− TH ...
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