Conduction between a steel/copper cylinder.

[jj5959]

Homework Statement

A steel cylinder of radius 7.0 cm and length 4.0 cm is placed in end-to-end thermal contact with a copper cylinder of the same dimensions. If the free ends of the two cylinders are maintained at constant temperatures of 85°C (steel) and 20°C (copper), how much heat will flow through the cylinders in 19 min?

Homework Equations

Q = (kAtdeltaT)/L

Q=heat
k for steel=66.9
k for copper=395
A=area
t=time
T=temperature
L=length

The Attempt at a Solution

x=temperature in the middle of the cylinders

I set heat transferred through the steel part of the cylinder equal to the heat transferred through the copper part of the cylinder.

(66.9)(85-x) = (395)(x-20)
x=29.4

then using that value, i solved for Q.

Q=((66.9)(.0154)(85-29.4)(1140))/.04
so Q=1.6E6 J

BUT the answer is Q=1.17E6 J
where'd i go wrong?

 

[ideasrule]

Q=1.17E6 J should be right. Perhaps the answer key is wrong?

 

[kerimek]

Your attempt at a solution is correct, but the difference in the final answer is due to rounding errors. When solving for x, you get x=29.4118, but in your calculation for Q, you used x=29.4. This small difference in x leads to a difference in the final answer. To get the correct answer, you can use the more precise value of x (29.4118) in your calculation for Q.