If our atmosphere had a uniform density of 1.25 kg/m3 all the way up to a border with empty space above, that border would be Answer km abov

Question

If our atmosphere had a uniform density of 1.25 kg/m3 all the way up to a border with empty space above, that border would be Answer km above sea level. The pressure at sea level is 1 atm = 105 N/m2 and g = 10 m/s2. Enter your answer as an integer.

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Lệ Thu 1 year 2021-09-03T03:01:17+00:00 1 Answers 23 views 0

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    2021-09-03T03:02:19+00:00

    Answer:

    The border is 8km above sea level.

    Explanation:

    We know that:

    Density = 1.25 kg/m^3

    Pressure = 10^5 N/m^2

    g = 10m/s^2

    Now, suppose that we have a virtual rectangle, such that its bases have an area of 1m^2 and the rectangle has a height equal to H.

    This virtual figure has a volume V = 1m^2*H, and it is filled with air (which we know that has a density 1.25 kg/m^3)

    Then the total mass inside that volume is:

    M = (1.25 kg/m^3)*V = (1.25 kg/m^3)*(1m^2*H)

    The weight of this mass is:

    W = g*M = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)

    And if we divide the weight in a given surface, let’s say 1 m^2, we get the pressure per square meter, which we know is equal to  10^5 N/m^2

    then:

    P = 10^5 N/m^2 = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)*(1/m^2)

    Whit this equation we can find the value of H.

    10^5 N/m^2 = (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)*(1/m^2)

    10^5 N =  (10m/s^2)*(1.25 kg/m^3)*(1m^2*H)

    (10^5 N)/(10 m/s^2) = (1.25 kg/m^3)*(1m^2*H)

    (10^4 kg) = (1.25 kg/m^3)*(1m^2*H)

    (10^4 kg)/( 1.25 kg/m^3) = 1m^2*H

    8,000 m^3 = 1m^2*H

    (8,000 m^3)/(1m^2) =H

    8,000 m = H

    And we want this answer in km, knowing that 1,000m = 1km

    8,000m = 8km = H

    The border is 8km above sea level.

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