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Entropy of a system water-reservoir

  1. Feb 26, 2014 #1
    Hello,
    I'm studying for my exam for tomorrow and we solved an exercise in class , but a question was not answered and I don't know how to solve it.
    1. The problem statement, all variables and given/known data

    1 Kg of water is heated at 0 degree C is brought into contact with a large heat reservoir at 100 degrees C. When the water has reached 100 degrees C, what has been the change in entropy of the water? And of the heat reservoir ? what has been the change in the entire system consisting of both water and the heat reservoir?

    Show that we can heat water ( from 0°c to 100°C) without changing the entropy of the whole system.
    2. Relevant equations



    3. The attempt at a solution
    For the first questions we have
    ΔS(water)=4180*ln(373/273) J
    ΔS(reservoir)=-418000/373 J

    I don't get it how we can heat the water without changing the entropy ..? :confused:
     
  2. jcsd
  3. Feb 26, 2014 #2
    Suppose, rather than having just one hot reservoir, you had a sequence of hot reservoirs at temperatures running from 0 to 100 C. Could you figure out a way of transferring the heat so that the overall change in entropy of the 1 Kg of water plus all the reservoirs totaled zero?

    Chet
     
  4. Feb 26, 2014 #3
    Is it that we have to make a chain of heat baths ?
     
  5. Feb 26, 2014 #4
    Pretty much. You use at heat bath at 1C to raise the temperature from 0C to 1 C, you use a heat bath at 2 C to raise the temperature from 1C to 2C, etc. This will give a total entropy change for the water plus the reservoirs very close to zero. In the limit as the temperature increments get smaller, the total entropy change approaches zero.
     
  6. Feb 26, 2014 #5
    Thank you !
     
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