Answer:
heat conduction along the rod ( Q/Δt ):
⇒ Q/Δt = 15 W
Explanation:
heat conduction:
∴ Q/Δt : heat trasmitted per unit of time.
∴ k: thermal conductivity
∴ A: contact surface area
∴ T1 - T2: temperature difference between its two ends.
⇒ Q/Δt = 10 W
⇒ T1 = 400K ∧ 500K
⇒ T2 = 200K
∴ 10W = k.A(400K - 200K)
⇒ k.A = 10 W/200K = 0.05 W/K
if T1 = 500K
⇒ Q/Δt = (0.05 W/K)(500K - 200K)
⇒ Q/Δt = (0.05 W/K)(300K)
⇒ Q/Δt = 15 W
This question involves the concepts of Fourier's Law of heat conduction.
The new rate of heat conduction is "15 W".
Fourier's Law of heat conduction gives the rate of heat conduction through this formula:
[tex]Q=-KA\frac{\Delta T}{\Delta x}[/tex]
where,
Q = Rate of heat conduction = 10 W
K = Thermal conductivity of the material of the rod
A = Area of cross-section of rod
ΔT = change in temperature = 400 K - 200 K = 200 K
Δx = length of rod
Therefore,
[tex]\frac{10\ W}{200\ K}=\frac{-KA}{\Delta x}\\\\\frac{-KA}{\Delta x}= 0.05\ W/K\\\\[/tex]
Now, for the changed temperature only the temperature difference will change:
ΔT' = 500 K - 200 K = 300 K
Therefore,
[tex]Q' = \frac{-KA}{\Delta x}(\Delta T)\\\\Q' = (0.05\ W/K)(300\ K)[/tex]
Q' = 15 W
Learn more about Fourier's Law of heat conduction here:
https://brainly.com/question/13253422?referrer=searchResults
The attached picture shows Fourier's Law of heat conduction.
