Adiabatic process for water

[JD9]

I was just wondering if there is a relationship between Pressure, Temperature , and Volume like there is for Ideal Gases, but for water.

ie. for Ideal Gas:
TV^(gamma-1) = constant
PV^gamma = constant

Any insight would be greatly appreciated,

Thanks in advance.

 

[Andrew Mason]

I was just wondering if there is a relationship between Pressure, Temperature , and Volume like there is for Ideal Gases, but for water.

ie. for Ideal Gas:
TV^(gamma-1) = constant
PV^gamma = constant

Any insight would be greatly appreciated,

Water in its liquid or solid state is virtually incompressible, so there is little volume change even under very high pressure. So there is not much work that is done when increasing pressure to water. If there is not much work done and no heat added (because it is adiabatic), there is no not much change in internal energy (ie. temperature) with pressure.

Bernoulli's equation explains how the speed of water will change with dynamic pressure when water is flowing.

AM

 

[kyle8921]

Yes, there is a relationship between pressure, temperature, and volume for water in an adiabatic process. The adiabatic process for water follows the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In an adiabatic process, there is no heat transfer, so the change in internal energy is equal to the work done by the system.

This relationship can be expressed as:

dU = -PdV

Where dU is the change in internal energy, P is the pressure, and dV is the change in volume. This equation shows that as the volume of water decreases, the pressure increases, and vice versa. This is known as Boyle's law, which states that at a constant temperature, the pressure and volume of a gas (or liquid in this case) are inversely proportional.

Additionally, the temperature of water in an adiabatic process can also change. This is due to the relationship between temperature and internal energy, which can be expressed as:

dU = Cv dT

Where Cv is the specific heat at constant volume and dT is the change in temperature. This equation shows that as the internal energy of water changes, the temperature will also change.

Combining these two relationships, we can see that in an adiabatic process for water, the pressure, temperature, and volume are all interrelated and can change in response to each other. However, unlike ideal gases, the relationship between these variables is not as simple and cannot be expressed in a single equation. The specific values for these variables in an adiabatic process for water will depend on various factors such as the initial conditions, the properties of the water, and the external environment.

I hope this provides some insight into the relationship between pressure, temperature, and volume for water in an adiabatic process.