MS&E 303 – Fall 2004
Homework #1 – Due Friday, September 3
Thermodynamics is an abstract science which seeks to explain the behavior of heat and equilibrium
around 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 based
on total (exact) differentials and the Legendre Transform.
1. For the function
z
=
x
2
y
3
+
x
3
y
2
, 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 surface
while traveling along a path where
x
2
+
z
is constant.
(f) The rate of change of z with respect to the total distance traveled
p
x
2
+
y
2
under conditions
maintaining a constant
x
+
z
.
2. The surface
z
=
x
2

y
2
is called the saddle function. (a) Sketch the function. (b) Determine the slope
of the function with respect to changes in
x
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 Fall '04
 THOMPSON
 Derivative, 10%, 4000 hours, page summary discussion, 3400 hours

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