Consider a metal rod that has 10 W of heat conduction between its two ends, which are maintained at temperatures of 200 K and 400 K. If we raise the temperature of the hot end from 400 K to 500 K, what is the new rate of heat conduction along the rod? Group of answer choices

heat conduction along the rod (Q/Δt):

⇒ Q/Δt = 15 W

Explanation:

heat conduction:

Q/Δt = k. A. (T1 - T2) ... fourier law

∴ 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