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17 September, 09:38

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

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  1. 17 September, 09:42
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    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
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