A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling water. How long will it take the bar to

Question

A small metal bar, whose initial temperature was 30° C, is dropped into a large container of boiling water. How long will it take the bar to reach 70° C if it is known that its temperature increases 2° during the first second? (The boiling temperature for water is 100° C. Round your answer to one decimal place.)

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Nick 2 weeks 2021-07-22T20:52:49+00:00 1 Answers 1 views 0

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    2021-07-22T20:53:54+00:00

    Answer:

    Explanation:

    We shall solve this problem on the basis of averaging , otherwise it will require integration which is a complex operation .

    According to newton’s law of cooling

    dQ / dt = k ( T₁ – T₂ )

    T₁ is temperature of surrounding  and T₂ is temperature of object .

    For the heating by 2 degree

    dQ = ms x ΔT , m is mass , s is specific heat and ΔT is rise of

    = ms x 2

    dt = 1 second

    T₁ the average temperature of object = (30 + 32)  / 2 = 31

    dQ = ms x ΔT

    ms x 2 = k ( 100 – 31 )

    k = 2 ms / 69

    In the second case bar’s temperature rises from 32 to 70

    average temperature = 32 + 70 / 2 = 51

    If t be the time required

    dQ = ms x ( 70 – 32 ) = 38ms

    38ms / t = k ( 100 – 51 )

    38ms / t = (2ms / 69) x 49

    t = 38 x 69 / (2 x 49)

    = 26.75 s .  

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )