17.72. You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that
will conduct 150.0 J/s from a furnace at 4000.0°C to a container of boiling water under 1
atmosphere. What must the rod’s diameter be?
Identify:
Apply Eq.(17.21) and solve for A.
Set Up: The area of each circular end of a cylinder is related to the diameter D by
A   R2   ( D / 2)2 .
For steel, k  50.2 W/m  K. The boiling water has T  100°C, so
T  300 K.
Execute:
 300 K 
Q
T
150 J/s   50.2 W/m  K  A 
 kA
.
3
2
 0.500 m  This gives A  4.98 10 m , and
t
L and
D  4 A/  4(4.98 103 m2 )/  8.0 102 m  8.0 cm.
Evaluate:
H increases when A increases.