What is the correlation of temperature and pressure of a fluid?

Question

Is there a similar law like the Law of Boyle (Robert Boyle 1661) that works for fluids?
I would like to know if the temperature of water increases if I increase the pressure from 1 atm to 10 atm. e.g.

The formula's I could find, but the constants for water I am missing. Is there anybody who can give me more precise directions?

Answer 1

Whatever work you do in compressing the liquid (note: a fluid can be either a gas or a liquid) will go into mechanical potential energy and heat, similarly to a gas. The following is from the referenced web page:
"Liquids are much less compressible than gasses. Even when a liquid is described with an equation similar to a gas equation, the constants in the equation will result in much less dramatic changes in volume with a change in temperature. Like wise at constant volume, a temperature change will give a much larger pressure change than seen in a gas."
You can understand this when you consider not only the relative incompressibility of a liquid but also its much higher specific heat resulting in smaller temperature changes.

Answer 2

The pressure of any medium is a function of its density and temperature. This relationship is called its "Equation of State". Ideal gas has the simplest EoS (the ideal gas law), but everything has one. For liquids and solids, the EoS is usually treated phenomenologically. That means you just have to measure it. This is because calculating from first principles (quantum molecular dynamics) is rather difficult. There has been some success in this recently, though complex computer simulations.

Derivable from the general EoS are adiabatic curves, somethings called the adiabatic EoS. This tells you how the temperature changes with pressure and density during slow compression without heat flow. Yes, the temperature of water will increase with pressure. However, it would be hard to measure at only 10 atm since water is not as compressible as gas. That means little work is done on it. If you compress is to, say, 100,000 atm, though, the temperature (and density) change would be significant. This requires special equipment, such as a diamond anvil.