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Homework Help: A qns on Thermodynamics Relations

  1. Sep 8, 2010 #1
    1. The problem statement, all variables and given/known data

    We propose to study simple processes of liquid alcohol. At T_1, the molar volume of alcohol is V_1 and its molar heat capacity at constant pressure is C_p,m. We assume that its isobaric coefficent of thermal expansion a, and the isothermal compressibilty coefficient B are constant.

    a. Find the molar heat capacity (C_v,m) at constant volume and T_1, and the variation of the pressure with temperature at constant volume.

    b. starting from an initial state (T_1, V_1), alcohol receives an amt. of heat at constant pressure P, and its final temp. is T_2. Evaluate the work received by alcohol during the process.

    c. Find a formal expression for the rate of change with temperature of the internal energy of the liquid at constant pressure.


    2. Relevant equations

    isothermal coefficient of thermal expansion, a = 1/V * (dV/dT)_p
    isothermal compressibilty coefficient B, -1/V * (dV/dP)_T

    C_p = C_v + TVa^2/B ------ eqn (1)

    3. The attempt at a solution

    For qns a, i have no idea how to go about finding C_v,m. So i simply used the direct relatonship in eqn (1) to find C_v,m which i highly doubt its correct.
    for the second part of the qns,
    I used P=P(T,V)
    -> dP = MdT + NdV
    doing some algebric manipulation: dV = (1/N * dP) - (M/N * dT)
    by comparing coefficients from the derived eqn of V=V(T,P)...
    i got my final dP = (a/B * dT) - (1/VB *dV)
    at constant volume: (dP/dt)_V = a/B

    is this correct?

    For qns b, here's what i attempted:

    (T_1, V_1) ----> (T_2, V_2) at constant P.
    Using U=U(T,P) thermodynamics relationship and letting dP=0
    i get dU = (C_p - PVa)*dT
    by integrating from T_1 to T_2, i will get the change in U.
    then to find the Q received, i used H=H(T,P)
    where in the end i get dH=Q=C_p * dT
    again i integrate to find Q.
    then finally i use first law U= Q+W to find W.
    is this correct?

    For qns c,

    i used U=U(T,P)
    at constant P, i get dU=(C_P-PVa)*dT

    im not sure if this is correct or not...

    thanks a lot for helping me out
     
  2. jcsd
  3. Sep 9, 2010 #2
    is there any kind soul who can help me?

    Thanks!
     
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