حرارة وديناميكا حرارية المحاضرة الرابعة د/ محرز لولو

Compressibility Factor is a Measure of Derivation from Ideal-Gas Behavior Compressibility Factor, Z Z = Pv/RT Z = vactual/videal Ideal gas: Z = 1 Real gases: Z > 1 Z = 1 Z < 1

Real Gases 1 Z T1 T2 T3 T1 < T2 < T3 Ideal Gas P

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

a, b are van der Waals parameters Boyle temperature TB The second virial coefficient B B = b-(a/RT) a, b are van der Waals parameters when B=0 b = a/RT  TB = (a/bR) For carbon dioxide a= 3.59 L2 atm/mol2; b=0.043 L/mol Boyle temperature TB = 3.59 / (0.043 x 0.082) = 1018 K

The reduced equation of state Define: Pr is reduced pressure Vr is the reduced volume Tr 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: - N2, O2, gaseous Air -A mixture of liquid and gaseous water is a pure substance, but a mixture of liquid and gaseous Air is not.

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.

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

T-v diagram for the heating process of water at constant pressure. Saturated liquid 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.

Phase-Change Processes of Pure Substance Saturated temperature, Tsat: At a given pressure, the temperature at which a pure substance changes phase. Saturated pressure, Psat: 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 oC) Solid in equilibrium with vapor and liquid (0 oC) Liquid and vapor in equilibrium ( 0 < T < 100 oC) Saturated Vapor (T = 100 oC) Superheated Vapor (T > 100 oC)

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 : (Pcr= 22.09MPa, Tcr= 374.14C, vcr= 0.003155 m3 /kg)

Copyright © The McGraw-Hill Companies, Inc Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 3-16 T-v diagram of constant-pressure phase-change processes of a pure substance at various pressures (numerical values are for water). 2-2

FIGURE 3-18 T-v diagram of a pure substance. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 3-18 T-v diagram of a pure substance. 2-3

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 & 0.06113 kPa)

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

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

Copyright © The McGraw-Hill Companies, Inc Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 3-27 P-v-T surface of a substance that expands on freezing (like water). 2-9

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

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