Thermodynamic Properties: Water, R-134a, and Ideal Gases

Introduce the concept of a pure substance.
Discuss the physics of phase-change processes.
Illustrate the P-v, T-v, and P-T property diagrams.
Demonstrate the procedures for determining thermodynamic properties of water and R-134a from property tables.
Describe the hypothetical substance “ideal gas” and the ideal-gas equation of state.
Apply the ideal-gas equation of state in the solution of typical problems.
Introduce the compressibility factor, which accounts for the deviation of real gases from ideal-gas behavior.

Pure substance: A substance that has a fixed chemical composition throughout.
Air is a mixture of several gases but is considered a pure substance (exception).
This module focuses solely on pure substances.

The molecules in a solid are kept at their positions by the large springlike intermolecular forces.

Compressed liquid (subcooled liquid): A substance that is not about to vaporize.
Saturated liquid: A liquid that is about to start to vaporize.
Saturated vapor: A vapor that is about to start to condense (partially).
Saturated liquid–vapor mixture: The state at which the liquid and vapor phases coexist in equilibrium.
Superheated vapor: A vapor that is not about to condense (i.e., not a saturated vapor).

Saturated liquid: A liquid that is about to vaporize.
Compressed liquid (subcooled liquid): A substance that is not about to vaporize.
Saturated vapor: A vapor that is about to condense.
Saturated liquid–vapor mixture: The state at which the liquid and vapor phases coexist in equilibrium.
Superheated vapor: A vapor that is not a saturated vapor.
During heating at 1 atm, the temperature remains constant at 100°C until the last drop of liquid is vaporized (saturated vapor).
Further heating causes the temperature of the vapor to rise (superheated vapor).

Reversing the heating process by cooling the water while maintaining constant pressure retraces the same path, releasing the same amount of heat added during heating.

Variations of properties during phase-change processes are studied using property diagrams such as T-v, P-v, and P-T diagrams.
Saturation temperature $T_{sat}$ : The temperature at which a pure substance changes phase at a given pressure.
Saturation pressure $P_{sat}$ : The pressure at which a pure substance changes phase at a given temperature.

Saturated liquid line
Saturated vapor line
Compressed liquid region
Superheated vapor region
Saturated liquid–vapor mixture region (wet region)
Critical point: The point at which the saturated liquid and saturated vapor states are identical.

Illustrates regions for compressed liquid, saturated liquid, saturated vapor, saturated liquid-vapor mixture, and superheated vapor.
Shows lines of constant temperature (T1, T2) where $T2 > T1$ .

Relationships among thermodynamic properties are complex and often presented in tables.
Some properties are measured, while others are calculated using relations between measurable properties.
Enthalpy is defined as $h = u + Pv$ , where u is internal energy, P is pressure, and v is specific volume; the product of pressure and volume has energy units.

Table A–4: Saturation properties of water under temperature.
Table A–5: Saturation properties of water under pressure.
Enthalpy of vaporization, $h_{fg}$ (Latent heat of vaporization): The amount of energy needed to vaporize a unit mass of saturated liquid at a given temperature or pressure.

Quality, x: The ratio of the mass of vapor to the total mass of the mixture. $x = mg/mt$ , Values range between 0 and 1 (0: sat. liquid, 1: sat. vapor).
Properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor.
The relative amounts of liquid and vapor phases in a saturated mixture are specified by the quality x.
A two-phase system can be treated as a homogeneous mixture for convenience.
Temperature and pressure are dependent properties for a mixture.

$v{avg} = vf + x \cdot v{fg}$ , where $v{fg} = vg - vf$
$u{avg} = uf + x \cdot u{fg}$ , where $u{fg} = ug - uf$
$h{avg} = hf + x \cdot h{fg}$ , where $h{fg} = hg - hf$
$x = \frac{AB}{AC} = \frac{v{avg} - vf}{v_{fg}}$
The v value of a saturated liquid-vapor mixture lies between the $vf$ and $vg$ values at the specified T or P ( $vf < v < vg$ ).

In the region to the right of the saturated vapor line, a substance exists as superheated vapor.
In this region, temperature and pressure are independent properties.
At a specified P, superheated vapor exists at a higher h than the saturated vapor.
Compared to saturated vapor, superheated vapor is characterized by lower pressures, lower specific volumes, higher temperatures and higher internal energies.

Compressed liquid is characterized by y → v, u, or h.
For low pressures, a compressed liquid may be approximated as a saturated liquid at the given temperature.
The compressed liquid properties depend on temperature much more strongly than they do on pressure.

Equation of state: Any equation that relates the pressure, temperature, and specific volume of a substance.
The simplest and best-known equation of state for substances in the gas phase is the ideal-gas equation of state.
Ideal gas equation of state: $Pv = RT$ , $P = \frac{RT}{v}$ , Different substances have different gas constants.
Ideal gas equation at two states for a fixed mass: $\frac{P1v1}{T1} = \frac{P2v2}{T2}$
Although a good approximation, water in the superheated phase can’t be assumed as an ideal gas.

Phases of a pure substance
Phase-change processes of pure substances
- Compressed liquid, Saturated liquid, Saturated vapor, Superheated vapor
- Saturation temperature and Saturation pressure
Property diagrams for phase change processes
- The T-v diagram, The P-v diagram
Property tables
- Enthalpy
- Saturated liquid, saturated vapor, Saturated liquid vapor mixture, Superheated vapor, compressed liquid
The ideal gas equation of state