PHYS 330 Homework
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   Homework #5: Due Friday, September 26 by 5:30pm
  1. problem 4.3. Remember, you can switch back and forth between the variables volume and mass using the density ρ. This problem is done quite nicely by thinking about the units of things.
  2. problem 4.4
  3. Note: This is a fairly long and involved problem--don't start it at the last minute. You should be able to work most any problem like this with these cycles. They are all conceptually the same and you should get to the point that you recognize this.

    I want you to work with the Diesel cycle on page 133 with some numbers. And some are freakishly huge and unrealistic, but that's OK--just go with it. Let P1=1.0 atm, V1=0.50 L, T1=300K. Let the compression ratio of 20:1 mean that V2=(1/20)V1. Then, the cutoff ratio is V3/V2, and accounts for what happens during injection of the gas/air mix and its subsequent ignition. Take the cutoff ratio to be 5, so that V3=5V2. As usual, for (mostly) diatomic air, let γ=1.4.
    Note: In this problem, only the four steps shown in the cycle on page 133 are relevant. Label your curves in the following manner for clarity: Step (1) is the adiabat from V1 to V2; step (2) is the dP=0 line from V2 to V3; step (3) is the adiabat from V3 to V1; and step (4) is the dV=0 line at V1.
       (a) Calculate the work done in each of the four steps in this cycle. Show your work for each of these calculations, even if W=0 for a step.
       (b) Assume CV=(5/2)nR for an ideal diatomic gas. Calculate the net heat gained or lost--include the correct sign--for the gas in each of the four steps in this cycle.
       (c) Calculate the net change in internal energy, ΔU, for each of the four steps in this cycle.

  4. You should be reading chapter 4, sections 1 & 3, with the goal of recognizing the commonalities in all cycles.
   That's all for homework #5.