What is its diameter when the temperature is raised to 100 degrees Celsius? (b) What temperature change is required to increase its volume

Question

What is its diameter when the temperature is raised to 100 degrees Celsius? (b) What temperature change is required to increase its volume

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Adela 4 years 2021-08-17T14:06:23+00:00 1 Answers 30 views 0

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  1. Doris
    0
    2021-08-17T14:08:17+00:00
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    The question is incomplete, the complete question is;

    A spherical steel ball bearing has a diameter of 2.540cm at 25.00∘C.

    (a) What is its diameter when it’s temperature is raised to

    100∘C?

    (b) What temperature change is required to increase its volume by

    1.000% ?

    Answer:

    a) 2.542 cm

    b) 303.03°C

    Explanation:

    Given;

    Diameter of the ball= 2.540cm

    Initial temperature= 25.0°C

    Final temperature= 100.0°C

    Percentage increase in volume = 1.000%

    Temperature coefficient of expansion for steel =11.0×10^−6/∘C

    d2= d1[1 + α(T2-T1)]

    d2= 2.540[1 + 11.0×10^−6(100-25)]

    d2= 2.540[1 + 8.25×10^-4]

    d2= 2.542 cm

    From;

    %V ×1/100 = V ×3α ×∆T/ V

    Substituting values;

    1.000 ×1/100= 3× 11.0×10^−6 × ∆T

    ∆T= 0.01/3× 11.0×10^−6

    ∆T= 303.03°C

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