Chapter 6.4, Problem 60E

Thermodynamics

The magnitude of the range $R$ of exhaust temperatures (in degrees Fahrenheit) in an experimental diesel engine is approximated by the model

$R=\frac{5000\left(4-3x\right)}{\left(11-7x\right)\left(7-4x\right)},0<x\le 1$

where $x$ is the relative load (in foot-pounds).

(a) Write the partial fraction decomposition of the equation.

(b) The decomposition in part (a) is the difference of two fractions. The absolute values of the terms give the expected maximum and minimum temperatures of the exhaust gases for different loads.

$Y\max =\left|1\text{st term}\right|$ $Ymin=\left|\text{2nd term}\right|$

Write the equations for $Y\max$ and $Y\min$

(c) Use a graphing utility to graph each equation from part (b) in the same viewing window.

(d) Determine the expected maximum and minimum temperatures for a relative load of $0.5$.