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Homework Help: First Law of Thermodynamics and automobile

  1. Mar 20, 2010 #1
    1. The problem statement, all variables and given/known data

    An automobile battery that is originally fully charged gradually discharges while sitting on a shelf at a constant temperature of 40C, producing no electric work but resulting in a heat transfer of 1000kJ to its enviroment.
    The battery is then recharged to its initial state by means of a process involving work input of 440Wh.
    Find the heat interaction of the battery during this charging process. Justify your answer thermodynamically.

    2. Relevant equations

    The first law of thermodynamics
    ΔE = Q -W

    3. The attempt at a solution


    in the first step, heat is moving out of the system and no work is done, so:
    Q12 = -1000kJ
    W12 = 0

    in the charging process, the is done on the system, so:
    W21 = -440Wh = -440[Wh]*3.6[kJ/Wh] = -1584kJ

    The battery is charged to its initial state, so:
    ΔE = 0
    ΔE12 + ΔE21 = 0
    (Q12 - W12) + (Q21 - W21) = 0
    -1000kJ + Q21 +1584kJ = 0
    and
    Q21 = -584kJ

    the answer in the book is +440kJ. Why? What have I done wrong?
     
  2. jcsd
  3. Mar 22, 2010 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    I am not sure what is meant by "heat interaction" of the battery.

    If the battery in its initial state can supply 1000KJ of energy to its environment by discharging, and if 1584KJ (440Wh) of work is needed to recharge it to its original state (original charge and temperature), then the battery must dissipate 584KJ of heat to the environment in the charging process. [itex]\Delta Q = \Delta U + W = 1000KJ - 1584KJ = -584KJ[/itex] (W = +work done BY the battery)

    I would say the answer given is wrong and you are correct.

    AM
     
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