Question $2$

A liquid is compressed and heated from State $1$ to State $2.$ At

both states, water at $4C$ and $1$ atm is used as the reference

density. Here are the given properties:

At State $1$ the specific gravity of the liquid is $1\mathrm{.}114$

At the average temperature and pressure of the two states,

the volume expansion coefficient is $0\mathrm{.}16{10}^{-3}\frac{1}{K}$

The change in temperature from State $1$ to State $2$ is $20\mathrm{.}71C$

The change in pressure from State $1$ to State $2$ is $1,628$kPa

The density at State $2$ is $1,164k\frac{g}{m^3}$

You may approximate that the coefficient of compressibility and

the volume expansion coefficient remain constants throughout

the process of heating and compression. Approximate the

coefficient of compressibility at the average temperature and

pressure of the two states in units of atm. Can you show all work on how to get to correct answer.