assignment Homework
Task: Draw a right triangle. Put a circle around the right angle, that is, the angle that is \(\frac\pi2\) radians.
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assignment Homework
Instructions for 2022: You will need to complete this assignment in a 15 minute appointment on Zoom or in person with one of the members of the teaching team between 1/21 and 10 pm on 1/26. Here is a link to a sign-up page.
You are required to watch a sample video for how to make symmetry arguments here. As demonstrated in the video you should bring with you to the meeting a cylinder, an observer, and a vector.
Use good symmetry arguments to find the possible direction for the electric field due to a charged wire. Also, use good symmetry arguments to find the possible functional dependence of the electric field due to a charged wire. Rather than writing this up to turn in, you should find a member of the teaching team and make the arguments to them verbally.
face Lecture
30 min.
assignment Homework
Consider one mole of an ideal monatomic gas at 300K and 1 atm. First, let the gas expand isothermally and reversibly to twice the initial volume; second, let this be followed by an isentropic expansion from twice to four times the original volume.
How much heat (in joules) is added to the gas in each of these two processes?
What is the temperature at the end of the second process?
Suppose the first process is replaced by an irreversible expansion into a vacuum, to a total volume twice the initial volume. What is the increase of entropy in the irreversible expansion, in J/K?
face Lecture
30 min.
assignment Homework
assignment Homework
assignment Homework
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assignment Homework
In economics, the term utility is roughly related to overall happiness. Many things affect your happiness, including the amount of money you have and the amount of coffee you drink. We cannot directly measure your happiness, but we can measure how much money you are willing to give up in order to obtain coffee or bagels. If we assume you choose wisely, we can thus determine that your happiness increases when you decrease your amount of money by that amount in exchange for increasing your coffee consumption. Thus money is a (poor) measure of happiness or utility.
Money is also a nice quantity because it is conserved---just like energy! You may gain or lose money, but you always do so by a transaction. (There are some exceptions to the conservation of money, but they involve either the Fed, counterfeiters, or destruction of cash money, and we will ignore those issues.)
In this problem, we will assume that you have bought all the coffee and bagels you want (and no more), so that your happiness has been maximized. Thus you are in equilibrium with the coffee shop. We will assume further that you remain in equilibrium with the coffee shop at all times, and that you can sell coffee and bagels back to the coffee shop at cost.*
Thus your savings \(S\) can be considered to be a function of your bagels \(B\) and coffee \(C\). In this problem we will also discuss the prices \(P_B\) and \(P_C\), which you may not assume are independent of \(B\) and \(C\). It may help to imagine that you could possibly buy out the local supply of coffee, and have to import it at higher costs.
The prices of bagels and coffee \(P_B\) and \(P_C\) have derivative relationships between your savings and the quantity of coffee and bagels that you have. What are the units of these prices? What is the mathematical definition of \(P_C\) and \(P_B\)?
Write down the total differential of your savings, in terms of \(B\), \(C\), \(P_B\) and \(P_C\).
assignment Homework
Find the course syllabus and schedule on Canvas. Read through them carefully and bring your questions to the second day of class.