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Math 241
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MATH 241, Calculus III
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Thursday, October 23 Solutions Transformations of R2 .
Starting point: Here we consider a variety of transformations T : R2 R2 . Previously, we have used
such functions to describe vector fields on th
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One difficulty we found was that the drawings were difficult to decipher. Because the
drawings are from the early 1900s it is
213 Midterm coming up
Midterm: Monday July 24 12:00-1:15 here.
Covers Lectures 1-11
Extra OHs: See the web.
Lecture 9 Pg 1
Exercise
Energy exchange between 3 oscillators
Three oscillators have total e
How to Achieve Carnot Efficiency
To achieve Carnot efficiency, we must replace the isochors (irreversible)
with reversible processes. Lets use adiabatic processes, as shown:
Processes 1 and 3 are now
Lecture 13
Heat Engines
Thermodynamic processes and entropy
Thermodynamic cycles
Extracting work from heat
- How do we define engine efficiency?
- Is there an efficiency limit?
- Stirling Cycle
Rea
213 Midterm coming up
Midterm: Next Monday (July 24)
12:00-1:15 here.
Covers Lectures 1-11
Lecture 10, p 1
Lecture 7
Entropy and Exchange between Systems
Counting microstates of combined systems
Vol
The Diffusion Constant
The solution to the 3-D random walk, with varying and v, is similar
(but the math is messier).
The mean square displacement along x is still proportional to t:
2
x= 2 D t , wher
213 Midterm coming up
Time and place: Monday July 24 12:00-1:15 here.
Coverage:
Lectures
1-10
(Note the change!)
Extra OHs: See the web.
Lecture 12, p1
Heat Capacity & Harmonic Oscillators
We can use
iClicker info
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https:/community.macmillan.com/docs/DOC-7326-where-do-i-find-my-remote-idand-what-if-it-has-worn-off
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and not at the i
213 Midterm coming up
Time and place: Monday July 24 12:00-1:15 here.
Coverage:
Lectures
1-10
(Note the change!)
Extra OHs: See the web.
Lecture 10, p 1
Lecture 10
The Boltzmann Distribution
Concept
Office hours are posted online.
They are (mostly) held in 64
Loomis.
Mine are held in my office (390Q
Loomis).
Lecture 2, p 1
ACT 1: Ideal gas behavior
Consider a fixed volume of an ideal gas. Beca