Conduction heat transfer mechanisms

[Jennifer001]

1. Homework Statement [/b
the ends of a 20cm long,2cm diameter rod are maintained at 0degrees and 100degrees by immersion in an ice-water bath and boiling water. heat is conducted through the rod at 4.5x10^4J/h. of what material is the rod made?

Homework Equations

Q/dt=k(A/L)dT

The Attempt at a Solution

i first changed the heat energy conducted into watts which is = J/s

4.5x10^4J/h*1h/60min*1min/60s=12.5J/s

then i found the surface area of the rod

A=2(pi0.01^2)+(2pi0.01)0.2=0.01319m^2

now plug it into Q/dt=k(A/L)dT

12.5=k(0.01319)/0.2(100-0)
k=1.895

with this number i found that the rod is made of ice which has a k value of 1.7 (the closest number) but i checked the back and it suppose to be iron which has a k value of 80.. what did i do wrong?

 

[physics girl phd]

Your area is incorrect:
A in this equation is the cross sectional area of the conducting rod... not the entire surface area.