MS&E 303 – Fall 2004Homework #1 – Due Friday, September 3Thermodynamics is an abstract science which seeks to explain the behavior of heat and equilibriumaround us. As we jump into the abstract, we will also try to relate it to physical problems in everyday life.However, the first step is to understand and work with the mathematics of thermodynamics which is basedon total (exact) differentials and the Legendre Transform.1. For the functionz=x2y3+x3y2, determine the following differentials:(a)∂z∂x¶y(b)∂z∂y¶x(c)∂z∂y¶z(d)∂x∂y¶z(e) The relative change in the x with respect to motion in y required in order to remain on the surfacewhile traveling along a path wherex2+zis constant.(f) The rate of change of z with respect to the total distance traveledpx2+y2under conditionsmaintaining a constantx+z.2. The surfacez=x2-y2is called the saddle function. (a) Sketch the function. (b) Determine the slopeof the function with respect to changes inx
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