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Saving a Town from Lava Thermodynamics Problem

  1. Dec 30, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-12-30_10-32-15.png

    2. Relevant equations
    Q1 + Q2 = 0

    3. The attempt at a solution
    I found the mass of water needed to cool the lava to a solid. I'm not sure how to find the rate of water needed to stop the lava.

    https://lh3.googleusercontent.com/HTrvgt1wh2amrK8pZkIgNXe3HUaQ8lUPQHugcY-7NzMPqAZ1jAiB8ws4V4G_E60yfYe03KX23qTVAmIDJuXK7UYo3d685xqE5b0VxHk81jFFbijZbFhwrAP5OcGJV3EDHVH3F72QSP9x1rnut92wI3J-wRRGdXAG43ONxSehJns78s8QTpbIDqU0PT2dLxdQmvd4S6fxPRe4bqtLQG3g34A3aULY6daVs_c7wIFw0N7yQ3pQy1vt9ib6c0CN-rN54HAE8Vdv_yPFA0VMhPx219qiJkE1U5feFCZLKLH16J_ZW4ELwQ5q7eeJnFaZ1mJJsFFv2lmeZU94-WWUiUqUolKMTe1su0a6ejG-ElQLnHBAmzP7-O9briknyffQYrUoeW3T9OANjI21Sa2E73_PUByRrFxrdsHns4L0MARbTys-nXTVReSk1W_RTiFNvWK6mbPk5ChLxZ0uvjq-spgOINTkjj5y615fPGDQ0DKBnWwwssw8mSuso_BGrItJFAWEYhLwmIqIEy42yInjUPnUreOMqJ3hZjDSqhY2Dp654zeCbyUmKr4biZN7g9FFZv0SVxNLgowMuID6t1A1QiqgCwbfk0Rlf7639-l8D3DrAb5AK6UqaYII=w497-h662-no
     
  2. jcsd
  3. Dec 30, 2016 #2
    What happens to the water when it reaches 100 deg C?
    The mass of lava you calculated (350000 kg) was the mass of lava that arrives every minute. So the mass of water needed every minute would have to cool that lava down from 1200 to 800 deg C and then freeze it. So it looks like that is what your mass of water is attempting to represent. But like I mentioned at the beginning, water doesn't increase in temp. from 20 to 800 deg C.

    Edit: By the way, it looks like your 1.4 e11 and 1.54 e11 numbers are correct.
     
  4. Dec 30, 2016 #3
    OK I see. So I need to add MwLv because the water is going to evaporate. Then I need to add nCΔT for water in the gas state until it reaches 800 deg C, right? But what should I use for C for water in the gas phase?
     
  5. Dec 30, 2016 #4
    That's the part I was wondering about. I was thinking that once the water turns to steam, it doesn't hang around to be heated up by the lava; it just rises upward never to be heard from again. At least that's what I think would happen.
     
  6. Dec 30, 2016 #5
    OK you're right. You get the right answer if you just add MwLv. So basically, the Lava is heating up the water to boiling point and then the rest of the energy is removed when the water evaporates to a gas. The steam then "just rises upward never to be heard from again." Thanks!
     
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