Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Thermodynamics maximum and minimum temperatures

  1. Sep 27, 2005 #1
    In the following question,

    "two moles of an ideal gas, in an initial state P=10 atm, V=5 liters, are taken reversibly in a clockwise direction around a circular path given by (V-10)^2 + (P-10)^2 =25. Calculate the amount of work done by the gas as a result of the process, and calculate the maximum and minimum temperatures attained by the gas during the cycle."

    how do you find the max/min temperatures? at first, i thought of trying to take the first derivative of the path, but the results are weird...
  2. jcsd
  3. Sep 27, 2005 #2


    User Avatar
    Science Advisor

    The graph of (V-10)2+ (P-10)2= 25 is a circle, in the PV-plane, with center at (10,10) and radius 5. Since PV= NRT, T= PV/NR. Maximum temperature occurs on that circle where PV is a maximum, Minimum Temperature where PV is a minimum. It should be clear where that occurs from the graph. If not, maximize (and minimize) PV with the constraint (V-10)2+ (P-10)2= 25 (Lagrange Multiplier method probably is best).
  4. Sep 27, 2005 #3
    during a discussion with a classmate, he suggested to draw a 45 degree angle line through the origin... but why?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook