# Thermodynamics maximum and minimum temperatures

1. Sep 27, 2005

### asdf1

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...
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2. Sep 27, 2005

### HallsofIvy

Staff Emeritus
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).

3. Sep 27, 2005

### asdf1

during a discussion with a classmate, he suggested to draw a 45 degree angle line through the origin... but why?