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18 February, 08:36

Early in the morning, when the temperature is 5.0°C, gasoline is pumped into the 51-liter steel tank of a car until it is filled to the top. Later in the day the temperature rises to 25°C. Given that the coefficient of volume expansion is 0.95 * 10-3 °C-1 for gasoline and 0.036 * 10-3 °C-1 for steel, how much gasoline spills out of the tank?

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  1. 18 February, 11:21
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    gasoline spills out of the tank is 0.93228 L

    Explanation:

    Given data

    temperature T1 = 5.0°C

    temperature rises T2 = 25°C

    volume = 51 L

    coefficient of volume expansion gasoline = 0.95 * 10-3 °C-1

    coefficient of volume expansion steel = 0.036 * 10-3 °C-1

    to find out

    how much gasoline spills out of the tank

    solution

    we know that

    the volume of liquid spills out from tank is given by expression as

    change in volume in gas - change in volume in tank

    so

    change in volume of gas

    ΔV = V * ΔT * β

    put value

    ΔV = 51 * (20) * 950 * 10^-6

    ΔV = 0.969 L

    and

    change in volume of steel tank

    ΔV = V * ΔT * β

    ΔV = 51 * (20) * 36 * 10^-6

    ΔV = 0.03672 L

    so gasoline spills out of the tank is = 0.969 - 0.03672

    gasoline spills out of the tank is 0.93228 L
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