Department of Physics
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Homework #3: Do not turn this in since there is a test next week. I will post my solutions so that you can check your work.
Note: It's all too easy to fall into the trap of just looking at my solutions first without truly trying to do these problems. You need to work these first--and come to me with questions--just as you would on any assignment. Only then should you look at my solutions.
That's all for homework #3.
- The pressure gradient equation (1 dimension) for an ideal gas fluid is dP/dz=(-)ρg=(-)(m/N)(g/kT)P, as I derived in class. Now, let the temperature vary with height according to T(z)=T0-c*z2 where c is a constant whose units are Kelvin per kilometer2, and To=22°C=294K.
(a) Integrate the barometric equation now (by hand, using Mathematica, using the Wolfram online integrator at http://integrals.wolfram.com/, or whatever), being sure to use the definite integral height limits of zf and zi as I did in class. You should end up with a general expression with a bunch of letters in this part.
(b) Assuming that the value for c is c=7.0 K/km2, find the atmospheric pressure in Ogden, Utah (see problem 1.16 for Ogden's elevation).
- problem 1.33. The "What does this process accomplish?" question is like I was saying in class about conversions between heat and work. Note that there are 5 distinct things for you to answer here: (1) With the first three, parts (a)-(c), you will simply write down the correct thing (+, - or 0) for each. (2) The fourth is the overall sign for each of the two P-V diagrams for work, ΔU, and heat. (3) The fifth thing is what the overall "accomplishment" is (i.e. you need to mention if heat energy is converted to work energy, or whatever).
- problems 1.36. Note that γ=1.40=7/5 for diatomic gases (see Eq.(1.40) right above this problem).
- Substitute the word "isothermally" for "adiabatically" in problem 1.36, and do parts (a) and (b) only.
- As usual, there are many ways to ask basic questions. I know that I have not asked every single homework question to hit every topic in detail that we've covered. So be sure to check the class examples and types of calculations you needed to do, and be sure that you can do them.