# Heat flow problem (copper pipe)

**1. The problem statement, all variables and given/known data**

A copper bar with a cross sectional area of 4.40 cm^{2} and a length of 0.62 m has one end at 1 °C and the other end at 97 °C. Find the heat flow through the bar if the thermal conductivity of copper is 385 W/(m·K)

**2. Relevant equations**

R = (λ*L)/A

I = ΔT / R

k = 1/λ

R = resistance

λ = thermal resistivity

L = length of pipe

A = cross sectional area

I = thermal current

ΔT = change in temperature

k = thermal conductivity

**3. My attempt**

So first I converted the area 4.40 cm^{2} into 0.044 m^{2}.

Then I converted the thermal conductivity given in the problem to thermal resistivity

k = 1/λ

λ = 1/k = 1/385 W/(m·K) = 0.00259 mK/W

Using this value, the area, and the length from the problem, I used R = (λ*L)/A

R = (0.00259 mK/W)(0.62 m) / 0.044 m^{2}

R = 0.0366 K/W

Now I plugged this R into the thermal current formula I = ΔT/R, where ΔT = 97 °C – 1 °C = 96 °C

The ΔT is measured in Kelvin, but is still a difference of 96 units.

I = 96K / 0.0366 K/W = 2622.95 W = 2622.95 J/s

This is incorrect apparently. Does anybody know where I might have went wrong?

Thanks!

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