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Thermodynamics: Calculating Final Pressure from Volume Differential

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Liquid water, initially at 25.00 °C & 1.000 bar is heated at constant
    pressure to 95.00 °C, then is compressed at constant temperature to a final
    pressure at which the volume is the same as the original volume (25.00 °C,
    1.000 bar). Calculate the final pressure.

    M = 18.015 g mole-1.
    At 25.00 °C & 1.000 bar: ρ = 0.9970 g cm-3.
    Data from text:
    β = 2.04 x 10-4 K-1. κT = 45.9 x 10-6 bar-1.

    2. Relevant equations

    dV = (∂V/∂T)dT + (∂V/∂P)dP
    β = (∂V/∂T)/V (Thermal Expansion)
    κT = -(∂V/∂P)/V (Isothermal Compressibility)

    3. The attempt at a solution

    You rearrange the equation: dV = (∂V/∂T)dT + (∂V/∂P)dP and solve for the differentials by multiplying β and κT by the volume. The only problem is, I don't know how to get the volume. Should you assume dV ≈ 0 for liquids? The answer is 311.1 bars.
     
  2. jcsd
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