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7 February, 13:06

At 3 p. m., a hot coal was pulled out of a furnace and allowed to cool at room temperature (75°F). If, after 10 minutes, the temperature of the coal was 475°F, and after 20 minutes, its temperature was 395°F, find the following.

(a) The temperature of the furnace.

°F

(b) The time when the temperature of the coal was 105°F. (Round your answer to the nearest minute.)

: p. m.

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  1. 7 February, 13:56
    0
    A. This can be solved using Newton's Law of Cooling

    T - To = (Tb - To) e^kt

    From the given conditions

    T = 475 F

    To = 75 F

    t = 10 min

    475 - 75 = (Tb - 75) e^k (10)

    For the second condition

    T = 395 F

    To = 75 F

    t = 20 min

    (395 - 75) = (Tb - 75) e^k (20)

    There are two unknowns and two equations, solve for

    k and Tb

    You can then use this to solve for the time until the T = 105 F
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