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Heat pump question

  1. Jun 13, 2013 #1
    1. The problem statement, all variables and given/known data
    The electrical energy supplied to a heater can be turned with 100% efficiency into thermal energy (room heating).Assume you use a heat pump with a COP of 4 instead to reach the same temperature
    increase in the room.How much electrical energy will you save ?


    2. Relevant equations
    COP(heating)=Qh/W=Qc+W/W;

    3. The attempt at a solution
    Firstly i thought about getting the percentage of energy used which is equal to the work and then getting the percentage of energy saved by subtraction (100%-%ofUsedEnergy).

    since temperature is constant then Qh is constant(am i correct?)
    W=1/4 Qh (i guess something is wrong here)
    ∴the percentage of energy used=100*1/4=25%

    ∴the percentage of energy saved=75%
     
  2. jcsd
  3. Jun 13, 2013 #2

    rude man

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    Gold Member

    Why?
    Your conclusion is correct. (That's why I run a heat pump myself! Unfortunately, if Tc drops too far then the Carnot efficiency drops: Qh/W = Th/(Th - Tc) so for the same Th the colder Tc the lower the COP. Of course, refrigerators in general do not use a Carnot cycle. Part of the cycle is via a throttling process {"expansion valve"} which is an irreversible part of the refrigeration cycle.)
     
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