Fluids - Internal Energy and Pressure Energy

If you take a cylinder filled with a fluid and place a piston on top so that no liquid can escape and heat the fluid, several things can happen.

As you add heat the internal energy increases; the fluid will expand, if the piston is restricted pressure will increase. The point is the pressure does not have to increase as the energy is increased if the volume is not restricted.

Saying that, a liquid will not compress much before pressure destroys the vessel. This principal is more applicable to gasses where they can compress as internal energy increases if the volume is restricted, but if volume is not restricted pressure will not increase.

Drew

There's some confusion here, Captain. Internal energy is one measurement, which is related to the phase, pressure and the temperature of the fluid. Pressure is another parameter. There is no such thing as "pressure energy".

You can look up the internal energy, the enthalpy, of steam in Steam Tables.

You can apply energy to the system with heat or pressure, either way you are doing work on the system right? If work is done on the system its internal energy increases. If the only work done is by applying pressure the energy of the system still increases.

As I understand it if compressible it will increase pressure, if not much compressible, it's temp will increase. Either way doing work on the system increases its overall energy level.

Drew

If you squeeze a gas like steam, then the pressure will increase, as will the temperature, and its volume will decrease. Its internal energy will go up, as it's in a position to do more work for you than before it got squeezed.

If you squeeze a liquid like water, then the pressure will go up but its volume and temperature will remain the same. Its internal energy will stay the same as it's in no better position to do any work for you compared to before it got squeezed. Which is sort-of-why liquids are used in hydraulic systems, and is very-much-why liquids are used for pressure-testing of things like pressure vessels and pipelines.

As I understand it, if you increase the temp of a liquid, solid, or a gas it's volume increases. If the volume is not allowed to increase, the pressure increases.

So inversely if you increase the pressure on a solid, liquid or gas it's temperature will increase. This is much more difficult to see or visualize because solids and liquids do not generally compress well.

But if you look at it on a molecular scale temperature is caused by collisions of the molecules or atoms, if you reduce the volume there will be more collisions and the temperature will rise.

Drew

just to be technically correct- work is energy acting on something over some distance within some time frame.

If you ADD energy to some system, you increase its ability to do work or increase the amount of work that it can do.

Whether a fluid pressure increases with the addition of heat depends totally on whether the volume is restrained. If the volume is restrained, the pressure AND temperature will rise regardless or whether the fluid is compressible or not. If it is not compressible, the vessel will rupture as soon as the internal pressure exceeds the pressure limitation of the vessel. If the vessel is not volume restrained, the temperature of the fluid will increase and the volume will also increase but the pressure will not change.

What Raj probably means as 'pressure energy' is potential energy stored in a fluid in the form of pressure.

Bernoulli's equation says that a fluid's 'hydraulic energy' (so 'mechanical energy', disregarding chemical energy, etc.) is the sum of one half the fluid's velocity squared times a coefficient, plus pressure times a coefficient, plus the change in 'gravitic energy' caused by raising or lowering the fluid flow in a gravity field (say by pumping fluid up a vertical pipe).

Total hydraulic energy, if we neglect energy losses in the fluid flowing say in a pipe system (i.e., losses from friction), remains constant at all points in the pipe system (i.e., preservation of energy). The relative proportions of 'velocity energy', 'pressure energy', and 'gravitic energy', can all be changed (assuming no fluid-phase change), but they'll always add up to the same hydraulic energy.

'Velocity energy' is the fluid's kinetic energy.

'Pressure energy' is a potential energy stored in the form of fluid pressure.

'Gravitic energy' is a potential energy stored in the form of gravitational-potential differences between points in the pipe system.

So, concerning 'pressure energy' ... it's a form of potential energy.

Cheers! DZ

Oops! Forgot to say ... Increasing pressure increases a fluid's internal energy.

If the fluid is stationary and is kept stationary, doubling its pressure will double its internal energy. That's because the fluid's being stationary means that there's no influence from fluid velocity and no influence from changing the fluid's potential energy by raising or lowering it in a gravitational field. Bernoulli's equation says that in the case, internal energy equals pressure times a coefficient.

If the fluid is in motion, then doubling its pressure from the outside will increase its internal energy, all other factors being the same.

Cheers! DZ

Bear in mind that bernoulli's equation is meant for fluids that are in a state of relative thermal equilibrium and relatively incompressible, such as water. However, it is used as the basis for hydraulic designs, particularly for water and similar fluids conveyance. Other terms have to be accounted for in compressible fluids and thermally instable environments (though such effects can be rolled into resistance factors and changes in head or pressure through application of things like the ideal gas law).