Question

How do I calculate the new pressure of liquid water using its isothermal compressibility κ and expansion coefficient α?

Answer 1

I'm given that the isothermal compressibility κ=4.7×10−5atm−1 and expansion coefficient α=1.7×10−4K−1 at 17∘C. The rest of the question states:

closed rigid container filled with liquid water at an initial temperature of 14∘C and initial pressure of 1 atm.

The temperature is changed to 20∘C, and the new pressure is to be found.

Assume that α and κ are negligibly different whether it's 17∘C or 14∘C or 20∘C.

What is this new pressure? I know it is 23 atm, but I don't know how to do the problem.

Here are the definitions you need to know, and the calculus you may need to know:

α=1V(∂V∂T)P⇒αdTP=1VdVP

κ=−1V(∂V∂P)T⇒κdPT=−1VdVT

(∂V∂P)T is the partial derivative of the volume with respect to the pressure at a constant temperature.

(∂V∂T)P is the partial derivative of the volume with respect to the temperature at a constant pressure.

Note that 1VdVP and