# Homework Help: Thermodynamics: Calculating Final Pressure from Volume Differential

1. Mar 17, 2012

### waters

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.