A copper bar with a cross sectional area of 4.40 cm2 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 cm2 into 0.044 m2.
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 m2
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?