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

Unlock Document

Washington University in St. Louis

University College - Chemistry

University College - Chemistry Chem 402

Barnes Alexander

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

More
Less
Related notes for University College - Chemistry Chem 402