Specific volumes of a saturated substance due to pressure

In summary: Atoms and molecules in liquids are constantly interacting with each other. This means that you can't simply treat liquids the same way that you would treat solids. For example, you can't just assume that the thermal expansion of a liquid is the same as the thermal expansion of a solid.
  • #1
mech-eng
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I cannot understand why specific volume of a saturated liquid rises when pressure rises, specific volume of saturated vapor reduces when pressure rises. This made me remember buckingham-pi theorem. Is there any equational approach or formulation that show this?

Thank you.
 
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  • #2
The specific volume of a liquid is typically expressed according to $$dV=V(-\kappa dP+\alpha dT)$$where ##\alpha## is the coefficient of thermal expansion and ##\kappa## is the bulk compressibility. If the specific volume of a saturated liquid increases with saturation vapor pressure, it means that $$\frac{dP_{sat}(T)}{dT}<\frac{\alpha}{\kappa}$$So the thermal expansion wins out over the bulk compression.

The specific volume of a vapor that can be approximated by the ideal gas law is given by:
$$V=\frac{RT}{P}$$
So, $$dV=\frac{V}{T}dT-\frac{V}{P}dP=V\left(-\frac{dP}{P}+\frac{dT}{T}\right)$$ So the coefficient of thermal expansion of an ideal gas is 1/T and the bulk compressibility is 1/P. If the specific volume of the saturated vapor increases with the saturation vapor pressure, it means that $$\frac{dP_{sat}(T)}{dT}>\frac{P_{sat}}{T}$$From the Clausius-Clapeyron equation, all that this requires is for the heat of vaporization to be positive (which it is).
 
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  • #3
are bulk compressibility and bulk module the same things?
Chestermiller said:
The specific volume of a liquid is typically expressed according to
dV=V(−κdP+αdT)​
dV=V(-\kappa dP+\alpha dT)where α\alpha is the coefficient of thermal expansion and κ\kappa is the bulk compressibility
What is the name of above equation? I cannot remember if I ever saw it in undergraduate thermodynamics books?

Thank you.
 
  • #4
mech-eng said:
are bulk compressibility and bulk module the same things?

What is the name of above equation? I cannot remember if I ever saw it in undergraduate thermodynamics books?

Thank you.
In freshman physics, you learned about thermal expansion and bulk compressibility of solids and liquids. This equation is just the combination of the two.
 
  • #5
Chestermiller said:
The specific volume of a liquid is typically expressed according to
dV=V(−κdP+αdT)​
dV=V(-\kappa dP+\alpha dT)where α\alpha is the coefficient of thermal expansion and κ\kappa is the bulk compressibility. If the specific volume of a saturated liquid increases with saturation vapor pressure, it means that
dPsat(T)dT<ακ​

Above you have done a very instructive proof but for that proof we have already assumed that "specific volume of a saturated liquid increases with saturatino vapor pressure." Is this an experimental knowledge, being similar to natural laws being known by only experience with no counter situations against observed such as four laws of thermodynamics and Newton's three laws of motion?

Thank you.
 

1. What is the definition of specific volume?

Specific volume is the volume occupied by a unit mass of a substance at a specific temperature and pressure.

2. How does pressure affect the specific volume of a saturated substance?

As pressure increases, the specific volume of a saturated substance decreases. This is because the molecules of the substance are pushed closer together, occupying less space.

3. What is a saturated substance?

A saturated substance is one that exists in both its liquid and vapor phase at a given temperature and pressure. At these conditions, the substance is in equilibrium and any additional heat added will result in a phase change rather than an increase in temperature.

4. How is specific volume of a saturated substance calculated?

The specific volume of a saturated substance can be calculated by dividing the volume of the substance by its mass, or by using the ideal gas law equation: v = V/m = RT/P, where v is specific volume, V is volume, m is mass, R is the gas constant, T is temperature, and P is pressure.

5. Why is specific volume an important property of a substance?

Specific volume is an important property because it helps determine the density and compressibility of a substance. It also plays a role in various thermodynamic calculations and is used in the design of many industrial processes.

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