حرارة وديناميكا حرارية المحاضرة الرابعة د/عبدالرحمن لاشين قسم الفيزياء - كلية العلوم التطبيقية – جامعة أم القرى - المملكة العربية السعودية قسم الفيزياء - كلية العلوم – جامعة المنصورة – جمهورة مصر العربية

Compressibility Factor is a Measure of Deviation from Ideal-Gas Behavior  Compressibility Factor, Z Z = Pv/RT Z = v actual /v ideal  Ideal gas: Z = 1  Real gases: Z > 1 Z = 1 Z < 1  Compressibility Factor, Z Z = Pv/RT Z = v actual /v ideal  Ideal gas: Z = 1  Real gases: Z > 1 Z = 1 Z < 1

Real Gases P 1 Z T1T1 T2T2 T3T3 T 1 < T 2 < T 3 Ideal Gas

Virial equation of state We search about a general equation of state: Expand PV/RT in power series From Van der Waal’s equation

Compare equation 1,2

Boyle temperature T B The second virial coefficient B B = b-(a/RT) a, b are van der Waals parameters when B=0 b = a/RT  T B = (a/bR) Ex. For carbon dioxide a= 3.59 L 2 atm/mol 2 ; b=0.043 L/mol what is the Boyle temperature ? Boyle temperature T B = 3.59 / (0.043 x 0.082) = 1018 K

The reduced equation of state Define: P r is reduced pressure V r is the reduced volume T r is the reduced temperature

The van der Waals equation: may be expressed in reduced form: Substituting values for the critical constants in terms of the van der Waals parameters:

simplifying: This expression has the same form as the van der Waals equation, except the van der Waals parameters have disappeared, indicating that the expression does not depend on the identify of the gas.

The adiabatic compressibility We can define

The P-V-T surface

Properties of Pure Substances

Pure Substance  A substance that has a fixed chemical composition throughout is called a Pure Substance.  Pure Substance: such as: N 2, O 2, gaseous Air -  A substance that has a fixed chemical composition throughout is called a Pure Substance.  Pure Substance: such as: N 2, O 2, gaseous Air -

Phases of a Pure Substance  Solid -The molecules in a solid are kept at their positions by the large intermolecular forces. -The attractive and repulsive forces between the molecules tend to maintain them at relatively constant distances from each other.  Liquid: Groups of molecules move about each other.  Gas: Molecules move about at random.  Solid -The molecules in a solid are kept at their positions by the large intermolecular forces. -The attractive and repulsive forces between the molecules tend to maintain them at relatively constant distances from each other.  Liquid: Groups of molecules move about each other.  Gas: Molecules move about at random.

Phase-Change Processes of Pure Substance  Compressed liquid or a subcooled liquid : A liquid that is not about to vaporize.  Saturated liquid: A liquid that is about to vaporize.  Saturated vapor : A vapor that is about to condense.  Saturated liquid-vapor mixture: the liquid and vapor phases coexist in equilibrium.  Superheated vapor: if the vapor is not heated beyond the saturated vapor  Compressed liquid or a subcooled liquid : A liquid that is not about to vaporize.  Saturated liquid: A liquid that is about to vaporize.  Saturated vapor : A vapor that is about to condense.  Saturated liquid-vapor mixture: the liquid and vapor phases coexist in equilibrium.  Superheated vapor: if the vapor is not heated beyond the saturated vapor

Once the boiling point is reached, the water’s temperature stays the same until all the water is vaporized. The water goes from a liquid state to a vapor state and receives energy in the form of “latent heat of vaporization”. As long as there’s some liquid water left, the steam’s temperature is the same as the liquid water’s. When all the water is vaporized then we get saturated vapor., any subsequent addition of heat raises the steam’s temperature. Steam heated beyond the saturated steam level is called superheated vapour. T-v diagram for the heating process of water at constant pressure. Saturated liquid Saturated vapor

Phase-Change Processes of Pure Substance  Saturated temperature, T sat : At a given pressure, the temperature at which a pure substance changes phase.  Saturated pressure, P sat : At a given temperature, the pressure at which a pure substance changes phase.  Latent heat: the amount of energy absorbed or released during a phase-change process.  Latent heat of fusion: the amount of energy absorbed during melting.  Latent heat of vaporization: the amount of energy absorbed during vaporization.  Saturated temperature, T sat : At a given pressure, the temperature at which a pure substance changes phase.  Saturated pressure, P sat : At a given temperature, the pressure at which a pure substance changes phase.  Latent heat: the amount of energy absorbed or released during a phase-change process.  Latent heat of fusion: the amount of energy absorbed during melting.  Latent heat of vaporization: the amount of energy absorbed during vaporization.

The p-V-T surface for water Solid in equilibrium with vapor (0 o C) Solid in equilibrium with vapor and liquid (0 o C) Liquid and vapor in equilibrium ( 0 < T < 100 o C) Saturated Vapor (T = 100 o C) Superheated Vapor (T > 100 o C)

Property Diagrams for Phase- Change Processes  The T-v diagram:  -Critical point: the point at which the saturated liquid and saturated vapor states are identical.  The critical-point properties of water : (P cr = 22.09MPa, T cr = C, v cr = m 3 /kg)  The T-v diagram:  -Critical point: the point at which the saturated liquid and saturated vapor states are identical.  The critical-point properties of water : (P cr = 22.09MPa, T cr = C, v cr = m 3 /kg)

T-v diagram of constant-pressure phase-change processes of a pure substance at various pressures (numerical values are for water).

T-v diagram of a pure substance.

Property Diagrams for Phase- Change Processes  The P-v diagram: - The triple line: three phases of a pure substance coexist in equilibrium, these triple-phase states forms a line. - The triple point: the triple line appears as a point on the P-T diagrams. -The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium, (For water, 0.01C & kPa)temperaturepressurephasesgas liquidsolid thermodynamic equilibrium  The P-v diagram: - The triple line: three phases of a pure substance coexist in equilibrium, these triple-phase states forms a line. - The triple point: the triple line appears as a point on the P-T diagrams. -The triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium, (For water, 0.01C & kPa)temperaturepressurephasesgas liquidsolid thermodynamic equilibrium

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 2-6 P-v diagram of a substance that expands on freezing (such as water).

The p-T plane for water, Phase diagram Liquid Vapor- Liquid Critical Point Vapor Triple PointpT Solid

P-v-T surface of a substance that expands on freezing (like water).

The p-V-T surface for ideal gas

 Equation of state: Any equation that relates the pressure, temperature, and specific volume of a substance.  Gas: The vapor phase of a substance  Vapor: A gas that is not far from a state of condensation  Equation of state: Any equation that relates the pressure, temperature, and specific volume of a substance.  Gas: The vapor phase of a substance  Vapor: A gas that is not far from a state of condensation

Phase Change Condensation: gas to liquid Vaporization liquid to gas Freezing liquid to solid Melting (fusion) solid to liquid Sublimation Solid to gas Deposition Solid to liquid