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Lecture 10

# Chem 402 Lecture 10: L10 2:8:17 Premium

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School
Washington University in St. Louis
Department
University College - Chemistry
Course
University College - Chemistry Chem 402
Professor
Barnes Alexander
Semester
Spring

Description
8 February 2017 st L10: The 1 Law of Thermodynamics I. The First Law A. Heat 1. Historically measured in calories a. 1 cal = heat needed to raise 1 g of 2 O 1°C from 14.5°C to 15.5°C • Heat capacity is temperature dependent • Specific heat differs at different temps, may be able to access more rotational states etc. at higher temps b. The modern unit of heat (and work) is the Joule • 1 cal = 4.184 Joules (J) • Before Joule, Count Rumsford was the first to relate heat and work, 1 horsepower x 2.5 hours = heating 27 pounds of ice cold water (0°C) to 100°C 2. Heat Capacity (C) a. Connects heat with temperature, is path dependent ð𝑞 b. 𝐶 𝑝𝑎𝑡ℎ = (𝑑𝑇 𝑝𝑎𝑡ℎ, 𝑞 = ∫𝑝𝑎𝑡ℎ𝐶𝑝𝑎𝑡ℎ 𝑑𝑇 c. If you have q vconstant volume) = C ∆v and q = P ∆T Pconstant pressure) • If qv= qp, ∆T (constant volume) > ∆T (constant pressure) because at constant volume the system cannot do work so all energy is converted to temperature change • At constant pressure, there can be expansion, and thus energy goes into work, so the ∆T (constant pressure) is less than that at constant volume 3. The Joule Experiment a. Showed that it is possible to raise the temp of 2 O with only heat (puts in q in J) or with only work (work in J, weight falling to church propeller) 2 2 b. Since work = strce * distance = mg(h), gives units of kgm /s (= Joules today) c. Relation to 1 law: work and heat have equivalent ability to increase temperature • = U = ∑𝑖𝑝 𝑖 𝑖 d. Both methods give the same final average internal energy • BUT entropy change is not the same • ∆T (from just heat) = ∆T (from just work) • BUT ∆S (just heat) ≠ ∆S (just work) B. The First Law Empirically 1. Empirically it was found that: ∮ð𝑞 + ð𝑤) = 0 a. The integral of a closed path of two path-dependent variables = 0 • Means that for a closed path, these variables define a state variable • Since T is a state variable, if same pressure, equation of state b. The sum (w + q) is independent of path • This implies that there is a state function whose exact differential is ð𝑞 + ð𝑤 • Defined as U, the internal energy, dU = ð𝑞 + ð𝑤 (∆U = q + w) c. For a cyclic process,∮ 𝑑𝑈 = 0 2 • For a change from state 1 to state 2, ∆𝑈 ∫ 𝑑𝑈 = 𝑈 −2𝑈 = 1 + 𝑤 1 • Each q and w depends on path individually, but the sum doesn’t depend on path! d. For fixed n, we just need to know 2 properties (ie T, V) to fully describe the system • So U = U(T, V) • U is an extensi
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