How Does Heat Transfer Through Different Metals?

AI Thread Summary
Heat transfer through the lead and copper rods is calculated using the formula Q=kA(ΔT/L)t, where k represents thermal conductivity. The correct interpretation of "square cross section" means the ends of the rods are square, with a side length of 1.50 cm, not a diameter. The area used in calculations should be the square of the side length, leading to Q values that incorporate this area. There is confusion regarding the length of the rods, as the problem states L = 0.525 m, not 0.0150 m. Accurate application of these principles is crucial for determining the total heat flow through the rods.
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Two 0.525 m rods, one lead and the other copper, are connected between metal plates held at 2.00°C and 106°C. The rods have a square cross section of 1.50 cm on a side. How much heat flows through the two rods in 1.0 s? Assume no heat is exchanged between the rods and the surroundings.

Relevant equations
Q=kA(ΔT/L)t
k for Pb is 34.3
k for Cu is 395

My attempt
I set up the equation for the rods in the exact same manner.
Q=(34.3)(1.77e-4)(104/.0150)(1)
Q=(395)(1.77e-4)(104/.0150)(1)

I know what is incorrect about these equations is the area I am using. I took the square cross section to mean diameter, which evidently it is not. The answers given in the text are:
Q=(34.3)(.0151)^2(104/.0150)(1)
Q=(395)(.0151)^2(104/.0150)(1)

How should I interpret square cross section in the future?
To finish this problem I am aware that Qtotal=QPb+QCu
Thanks!
 
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A cross section is the surface you get when an object is cut (or intersected by a plane). If you cut a round rod at 90 degrees to the axis the cross section is circular. If you cut it at say 30 degrees to the axis the cross section would be an elipse. If in doubt assume it's cut at 90 degrees.

So when it says the rods have a "square cross section", that means the cut ends look like a square. When it says "1.50 cm on a side" that means the cross section has sides (so can't be round).

If it had said "the rods have a triangular cross section of 1.50 cm on a side" then the cross section would be an equilateral triangle of area 1.255 cm2.
 
The answers given in the text are:
Q=(34.3)(.0151)^2(104/.0150)(1)
Q=(395)(.0151)^2(104/.0150)(1)

Are you sure?

They seem to have L = 0.0150m = 1.5cm but the problem says L = 0.525m.
 
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