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Electrical work in a piston-cylinder filled with refrigerant

  1. Feb 12, 2012 #1

    JJBladester

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    Gold Member

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

    0.8kg of saturated liquid R-134a with an initial temperature of -5 °C is contained in a well-insulated, weighted piston-cylinder device. This device contains an electrical resistor to which 10 volts are applied causing a current of 2 amperes to flow through the resistor. Determine the time required for the refrigerant to be converted to a saturated vapor, and the final temperature.

    2. Relevant equations

    Assumption: The system is at constant pressure throughout the process since both the atmospheric pressure and the weight of the piston remain constant throughout.

    [tex]Q_{in}+W_{e,in}-W_{b}=\Delta U+\Delta KE+ \Delta PE[/tex]

    3. The attempt at a solution

    [tex]Q_{in}=\Delta KE= \Delta PE=0[/tex]

    [tex]W_{e,in}=\Delta U+W_{b}=\Delta H[/tex]

    [tex]VI\Delta t=m(h_{2}-h_{1})[/tex]

    [tex]\Delta t=\frac{m(h_2-h_1)}{VI}[/tex]

    State 1
    P1=Psat @ -5 °C = 243.5kPa
    Saturated Liquid
    Thus, h1=hf @ 243.5kPa = 45.143 kJ/kg

    State 2
    P2=P1=243.5kPa
    Saturated Vapor
    Thus, h2=hg @ 243.5kPa = 247.49 kJ/kg

    T2 = Tsat @ 243.5 kPA = -5 °C

    Rearranging the energy balance equation for t yields 135 minutes for the time it takes to change the saturated liquid refrigerant into saturated vapor state.

    I am having doubts about my calculation for T2. It seems like the temperature would increase as that is the nature of a resistance heater. Any thoughts?
     
  2. jcsd
  3. Feb 12, 2012 #2
    Hi,
    I don't think your steam tables consider the circumstances that the problem gives you, the temperature would probably increase slightly (I'm just a student, not nearly as good as other people on this forum).

    However, looking through my steam tables, I found that hf @ 243.3kPa = 193.32kJ/kg.

    Same with hg, I found that hg @ 243.3kPa = 395.49kJ/kg.
     
  4. Feb 13, 2012 #3

    JJBladester

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    Gold Member

    Hey there TaxOnFear. The problem deals with refrigerant R-134a, not water, so the h values I posted should be correct.

    Perhaps the temperature does stay the same from state 1 to state 2, but the energy that the resistor circuit provides to the system goes into the increasing volume?
     
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