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Thermodynamics - Entropy

  1. Feb 8, 2013 #1
    1. The problem statement, all variables and given/known data

    A 2.3kg aluminum pan at 135° is plunged into 3.0kg of water at 15°. The specific heat of aluminum is 900 J/(kg K).



    Part A
    Find the final Celsius temperature of the aluminum and water.
    T_f = °Celsius

    Part B
    Find the entropy change of the aluminum pan.
    ΔS_Al = J/K

    Part C
    Find the entropy change of the water.
    ΔS_H20 = J/K

    Part D
    Find the entropy change in the system of particles consisting of all the particles in the aluminum plus all the particles in the water.
    ΔS = J/K





    2. Relevant equations

    Q=mCΔT
    ΔS=Q/T



    3. The attempt at a solution


    So my first couple attempts was that we use the equation Q=mC(T_f-T_i)

    other related equations i know is DeltaS=Q/T but, how can i find the temperature final of both Water and aluminum.

    I tried setting it up like this

    m_water*C_water(T_f-T-i) + m_aluminum*C_aluminum(T_f-T_i) = Q_total

    but i don't know how to get anything done from there.

    Please help me with the first part and i should be able to most of it done on my own.
     

    Attached Files:

  2. jcsd
  3. Feb 9, 2013 #2
    I found the answer to the first two. And the first two will eventually help you with the rest.

    attached in this form is a file showing the integration for part b.

    Part A
    Q_water+Qaluminum=0
    m_waterC_water(T_f-T_water)+m_aluminumC_aluminum(T_f-T_aluminum)=0
    using distribution from algebra and algebraically solving for T_F,
    T_f=(m_waterC_waterT_water+m_aluminumCaluminumT_aluminum)/(m_waterC_water+m_aluminumC_aluminum)
    you get Tf = 31.96 degrees Celsius.

    Where, if your values were,
    m_aluminum=2.3kg
    T_aluminum=135 degrees Celsius
    C_aluminum=900J/kg*k
    m_water=3kg
    T_water=15 degrees celsius
    C_water=4190J/kg*k


    Part B


    =(2.3kg)(900J/kg*k)ln((31.96+273)/(135+273))=-602.549J/K

    Part C
    use the same format, as b, but with different mass and specific heat, and T_i values, T_f is the same.

    Part D is the sum of part B and C.
     

    Attached Files:

    Last edited: Feb 9, 2013
  4. Feb 9, 2013 #3

    rude man

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    Homework Helper
    Gold Member

    This all looks good.
     
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