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Homework Help: Common temperature for thermal equilibrium

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data
    One mole of copper at a uniform temp. of 0 Celsius is placed in thermal contact with a second mole of copper which, initially, is at a uniform temperature of 100 Celsius. The pressure in the system is maintained at 1 atm. The two moles of copper are thermally insulated from the surroundings. Temperature dependence of the constant pressure heat capacity of solid copper can be described by:
    Cp = 33.64 + 6.28x10^-3*T J/mol*K

    a) Calculate the common temperature of the 2 mole system, which is contained in an adiabatic enclosure, when thermal equilibrium is attained.

    2. Relevant equations

    dH = cp*dt
    dS = dq/T

    3. The attempt at a solution

    Since it is in an adiabatic enclosure, dq = 0.
    ΔH= H2 - H1 = dq = 0

    but in the solution, it says ΔH = H1 + H2 = 0
    273Tfcp*dT = - ∫373Tfcp*dT

    I don't understand why this approach is correct.
  2. jcsd
  3. Mar 5, 2013 #2
    For the combined system of two moles,
    ΔH=∫273Tfcp*dT +∫373Tfcp*dT=0

    where the first term represents the change in enthalpy of the mole initially at 0 C, and the second term represents the change in enthalpy of the mole initially at 100 C.
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