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Meteor impact - Heat vaporization and capacity

  1. Mar 9, 2016 #1
    I believe my attempt below is correct but I'm not 100% sure, any guidance welcome.

    1. The problem statement, all variables and given/known data

    Suppose a meteor of volume 1000 km3, density 5000 kg m-3 and speed 30000 km hr-1 crashed into the ocean and 10% of the impact energy was converted directly into heat.

    i) Estimate the volume of water that would be evaporated.
    ii) Given that the area of the oceans is 3.9 × 1015 m2, estimate the resulting change in their depth.

    (The specific latent heat of vaporization for water is 2257 kJ kg-1 and the specific heat capacity of water is 4.18 kJ kg-1K-1. Assume that the mean ocean temperature is 4°C and that seawater has a density of 1000 kg m-3. Indicate clearly any further assumptions you make.)

    2. Relevant equations
    i) Kinetic Energy = 0.5 mv^2
    ii) Latent Heat Q = m l (m is the mass and l is the latent heat of vaporization)
    iii) Heat Capacity = m c ΔT (m is the mass, ΔT is change in temp and c is the specific heat capacity)

    3. The attempt at a solution
    Work the mass of the meteor : M = ρV = (5000)(1000x10^3) = 5x10^9 kg
    Kinetic energy of meteor: 0.5(5x10^9)(3x10^7)^2 = 2.25x10^24 Joules
    10% of kinetic energy turns to heat : 10%(2.25x10^24) = 2.25x10^23 Joules

    ΔT (Change in temp required from 4C to 100C degrees or 277.15K to 373.15) : 96K
    Energy required to heat 1kg of salt water by 96K.
    Qheat = Mwater c ΔT = 1kg x (4.18) 96 = 401.28 kJ

    Energy required to vapourize the salt water = 2257kJ/kg
    Total energy required to heat and vapourize 1 kg of water = 2257 + 401.28 = 2658.28kJ

    Determine the mass of water that is evaporated : 2.25x10^23 / 2658.28x10^3 = 8.46 x 10^16 kg
    Convert this mass into volume: V = M/ρ = (8.46 x 10^16) / 1000 = 8.46 x 10^13 m3

    Answer 1) Volume of sea water vaporized = 8.46 x 10^13 m3

    Answer 2) Change in Ocean depth: (8.46 x 10^13)/ (3.9 x 10^15) = .022 m or 2.2cm
     
    Last edited: Mar 9, 2016
  2. jcsd
  3. Mar 9, 2016 #2

    SteamKing

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    How many cubic meters are in 1 cubic kilometer?

    Remember, 1 cubic kilometer has the same volume as a cube which measures 1000 m on each edge.

    What are the units of the velocity of the meteor on impact? Do those units produce joules for kinetic energy?

    A temperature difference of 1° C = a temperature difference of 1° K.

    There is no need to convert to absolute temperature when calculating temperature differences.
    You've got some serious errors in your unit calculations which need fixing.
     
  4. Mar 10, 2016 #3
    Thanks for your reply and for pointing out my mistakes.

    Here are my corrections. For the last section "Energy required to heat 1kg..." you said I have serious unit calculations.
    But apart from the ones that were carried through from my earlier mistakes I couldn't spot new ones?

    I am however not sure about my answer to part 2) of the question.


    3. The attempt at a solution
    Convert the volume of the meteor from km^3 to m^3
    1000 km^3 = 1x10^12 m

    Work the mass of the meteor : M = ρV = (5000)(1x10^12) = 5x10^15 kg
    Convert the velocity of the meteor from km/hr to m/s.
    30,000 km/hr = 8333m/s
    Kinetic energy of meteor: 0.5(5x10^15)(8333)^2 = 1.7x10^23 Joules


    10% of kinetic energy turns to heat : 10%(1.7x10^23) = 1.7x10^22 Joules

    ΔT is difference in temperate from 4 to 100 degrees which is 96 degrees
    Energy required to heat 1kg of salt water by 96 degrees
    Qheat = Mwater c ΔT = 1kg x (4.18) 96 = 401.28 kJ

    Energy required to vapourize the salt water = 2257kJ/kg
    Total energy required to heat and vapourize 1 kg of water = 2257 + 401.28 = 2658.28kJ

    Determine the mass of water that is evaporated : (1.7x10^22) / (2658.28x10^3) = 6.53 x 10^15 kg
    Convert this mass into volume: V = M/ρ = (6.53 x 10^15) / 1000 = 6.53 x 10^12m3

    Answer 1) Volume of sea water vaporized = 6.53 x 10^12 m3

    Answer 2) Change in Ocean depth: (6.53 x 10^12)/ (3.9 x 10^15) = 1.67x10^-3 m
     
  5. Mar 10, 2016 #4

    SteamKing

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    Corrections look good.

    The change in ocean depth due to vaporization of the water due to meteor impact < 2 mm.
     
  6. Mar 10, 2016 #5
    Thanks for you help. Greatly appreciated.
     
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