3 Properties of Pure Substances

BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE - PILANIH YDERABAD C AMPUS

Pure SubstanceWhat is the benefit or importance of learning on properties and behavior of pure substances? Useful in design of equipments/ducts in power producing or absorbing cycles. A pure substance is one that has a homogeneous and invariable chemical composition. It may exist in more than one phase but the chemical composition is the same in all phases. Examples: Water (solid, liquid, and vapor phases) Mixture of liquid water and water vapor Carbon Dioxide (CO2) Nitrogen (N2) Mixtures of gases, such as air, as long as there is no change of phase.ES C112 T H E R M O D YN A M I C S1


A mixture of liquid air and gaseous air, however, is not a pure substance since the composition of liquid air is different from the composition of gaseous air, and thus the mixture is no longer chemically homogeneous. Here the emphasis will be on simple compressible substances. This term designates substances whose surface effects, magnetic effects, and electrical effects are insignificant. But changes in volume, such as those associated with the expansion of a gas in a cylinder, are very important.

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Vapor Liquid Solid Phase Equilibrium in a Pure SubstanceConsider 1 kg of water in the piston/cylinder arrangement as a system. The piston and weight maintain a pressure of 0.1 MPa in the cylinder and that the initial temperature is 200C.

Change from liquid to vapor phase for a pure substance at constant pressureES C112 T H E R M O D YN A M I C S3


The temperature at which vaporization takes place at a given pressure is called saturation temperature. This pressure is called the saturation pressure for the given temperature. Thus, for water at 99.60C the saturation is 0.1 MPa, and for water at 0.1 MPa the saturation temperature is 99.60C. There is a definite relation between saturation pressure and saturation temperature for a pure substance. A typical curve is called vapor-pressure curve.

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If a substance exists as liquid at the saturation temperature and pressure, it is called saturated liquid. If the temperature of the liquid is lower than the saturation temperature, it is called either a sub-cooled liquid or a compressed liquid. When a substance exists as part liquid and part vapor at the saturation temperature, its quality (x) is defined as the ratio of the mass of vapor to the total mass. If a substance exists as vapor at the saturation temperature, it is called saturated vapor. When the vapor is at a temperature greater than the saturation temperature, it is said to exist as superheated vapor

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Temperature Volume diagram for water showing liquid and vapor phasesES C112 T H E R M O D YN A M I C S9


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T100oC

g - f = fg d c

e

Process a: Ice at 20 oC to ice at 0 oC (no phase change) Process b: Ice at 0 oC to water at 0 oC (phase change) Process c: Water at 0 oC to water at 100 oC (no phase change)

0 oC -20 oC

b a

Process d: Water at 100 oC to steam at 100 oC (phase change)

f

g

NOTE: Pressure is constant

Pressure volume diagram of a substance, which expands on freezingES C112 T H E R M O D YN A M I C S11


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Pressure Temperature diagrams for pure substancesES C112 T H E R M O D YN A M I C S13


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Triple Point Data

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Triple Point DataSubstance Helium-4 (l-point) Hydrogen Deuterium Neon Oxygen Nitrogen Ammonia Sulfur dioxide Carbon dioxide Water Temperature K 2.17 13.84 18.63 24.57 54.36 63.18 195.40 197.68 216.55 273.16 Pressure 105 Pa 0.0507 0.0704 0.171 0.432 0.00152 0.125 0.0607 0.00167 5.17 0.00610

From Young, University Physics, 8th Ed., Table 16-3ES C112 T H E R M O D YN A M I C S16


Suppose the cylinder contains 1 kg of ice at -200C, 100 kPa and being heated at constant pressure. The temperature increases until it reaches 00C, at which point the ice melts and temperature remains constant. In this state the ice is called a saturated solid. If the initial pressure of the ice at -200C is 0.26 kPa, heat transfer to the ice results in an increase in temperature to -100C. At this point, the ice passes directly from the solid phase to the vapor phase in the process is known as sublimation. Finally, consider an initial pressure of the ice of 0.6113 kPa and a temperature of -200C. Through heat transfer let the temperature increases until it reaches 0.010C. At this point, further heat transfer cause some of the ice to become vapor and some to become liquid. Therefore at this point it is possible to have the three phases in equilibrium. This point is called as triple point, which is defined as the state in which all three phases are in equilibrium.ES C112 T H E R M O D YN A M I C S17


Water Phase DiagramES C112 T H E R M O D YN A M I C S18


Critical PointIt is defined as the point at which the saturated liquid and saturated vapor states are identical (co-exiting). At pressures above the critical pressure, there is otherwise no distinct process exists.

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Instead, the specific volume of the substance continually increases, and all times there is only one phase present. Eventually, it resembles a vapor, but we can never tell when the change has occurred. Above the critical state, there is no line separates the compressed liquid region and the superheated vapor region. However, it is customary to refer the substance as superheated vapor at temperatures above the critical temperature and as compressed liquid at temperatures below the critical temperatures.

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Specific VolumeThe specific volume of a two-phase liquid-vapor mixture can be determined by using the saturation tables and the definition of quality (x).

x

mg m f + mg

where subscripts f and g are used to designate a property of a saturated liquid and saturated vapor respectively.ES C112 T H E R M O D YN A M I C S21


V = Vliq + Vvap

V Vliq + Vvap Vliq Vvap = = = + m m m m

=

mliqliq m

+

mvap vap m

mliq mvap = m liq + m vap

= (1 x) f + x g = f + x( g f ) = f + x fgwhere

fg = g f

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During a vaporization process, a substance exists as part liquid and vapor. That is, it is a mixture of saturated liquid and saturated vapor. The properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor. During vaporization process, only the amount of saturated liquid changes, not its properties. The same can be said about a saturated vapor. The amount of mass for each phase is usually not known. Therefore, it is often more convenient to imagine that the two phases are mixed very well, forming a homogenous appearance. Then the properties of this mixture will simply be the average properties of the saturated liquid-vapor mixture under consideration.ES C112 T H E R M O D YN A M I C S23


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Thermodynamic SurfacesThe equilibrium states of any simple, compressible substance can be represented as a surface in a rectangular, three-dimensional space.

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Substance that expands on freezingES C112 T H E R M O D YN A M I C S

Substance that contracts on freezing26


Equation of State Any equation that relates the temperature, pressure, and specific volume of a substance is called the equation of state. The simplest and best-known equation of state for substances in a gas phase is the ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected region.

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Ideal Gas EquationThe combination of Boyles and Charles laws for gases at low pressure result in the equation of state for the ideal gas as

where R is the constant of proportionality and is called the gas constant and takes on a different value for each gas. If a gas obeys this relation, it is called an ideal gas. We often write this equation as

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P = absolute pressure in MPa, or kPa = molar specific volume in m3/kmol T = absolute temperature in K = 8.3145 kJ/(kmolK)ES C112 T H E R M O D YN A M I C S29


Is Water Vapor an Ideal Gas?At pressures below 10 kPa, water can be treated as an ideal gas, regardless of its temperature. But at higher pressures, the ideal-gas assumption yields unacceptable errors, particularly in the vicinity of the critical point and the saturated vapor line. Percentage of error

([

table

ideal / table ] 100)

involved in assuming steam to be an ideal gas, and the region where steam can be treated as an ideal gas with less than 1 percent error are shown in the T-v diagram for water.

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T - v Diagram for WaterES C112 T H E R M O D YN A M I C S31


T - v Diagram for WaterES C112 T H E R M O D YN A M I C S32


Compressibility FactorTo understand the above criteria and to determine how much the ideal gas equation of state deviates from the actual gas behavior, we introduce the compressibility factor Z as follows. or

actual It can also be expressed as Z = idealFor an ideal gas Z = 1, and the deviation of Z from unity measures the deviation of the actual P-V-T relation from the ideal gas equation of state.

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Compressibility Chart for NitrogenES C112 T H E R M O D YN A M I C S34


The compressibility factor is expressed as a function of the reduced pressure and the reduced temperature. The Z factor is approximately the same for all gases at the same reduced temperature and reduced pressure, which are defined as

P T TR = and PR = Tcr Pcr where Pcr and Tcr are the critical pressure and temperature, respectively. This is known as the principle of corresponding states.

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Compressibility Chart based on Data for a Large Number of GasesES C112 T H E R M O D YN A M I C S36


Lee-Kesler Simple Fluid Compressibility FactorES C112 T H E R M O D YN A M I C S37


These charts show the conditions for which Z = 1 and the gas behaves as an ideal gas: At very low pressure (PR 2), ideal gas behavior can be assumed with good accuracy (except PR >> 1). The deviation of gas from ideal-gas behavior is greatest in the vicinity of the critical point. Note: When PR is small, we must make sure that the state is not in the compressed liquid region for the given temperature. A compressed liquid state is certainly not an ideal gas state.

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Numerical Problems

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Q Determine whether water at each of the following states is a compressed liquid, superheated vapor, or a mixture of saturated liquid and vapor. a) 10 MPa, 0.003 m3/kg b) 1 MPa, 1900C c) 2000C, 0.1 m3/kg d) 10 kPa, 100C

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Q Calculate the specific volume of saturated steam at 2000C, if the quality of steam is 70%. Q Calculate the specific volume of saturated steam at 2000C, if the 1 m3 closed vessel contains 1:9 volumetric ratio of liquid and vapor. Determine the mass of vapor and liquid Find quality Compute the % vapor present by volume and also by mass, what is the difference?

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Q For water at 100 kPa with a quality of 10% find the volume fraction of vapor. This is a two-phase state at a given pressure: Table B.1.2: vf = 0.001043 m3/kg, vg = 1.6940 m3/kg From the definition of quality, we get the masses from total mass, m, as mf = (1 x)*m, mg = x*m The volumes are Vf = mf*vf = (1 x)*m*vf, Vg = mg*vg = x*m*vg So the volume fraction of vapor is Fraction = Vg/V = Vg/(Vg + Vf) = x*m*vg/(x*m*vg + (1 x)*m*vf) = 0.1 1.6940.1 1.694 + 0.9 0.001043 = 0.16940.17034 = 0.9945 Notice that the liquid volume is only about 0.5% of the total.

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Q A glass jar is filled with saturated water at 500 kPa of quality 25%, and a tight lid is put on. Now it is cooled to -10oC. What is the mass fraction of solid at this temperature?

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V Constant volume 1 = 2 = m from steam table for P sat = 500 kPa Tsat = 151.8o C

1 = 0.001093 + 0.25 * 0.3738 = 0.094543From table B 1.5, Tsat = - 10 C Psat = 0.2601 kPao

2 = 0.0010891 + x2 466.756 = 1 = 0.094543 x2 = 0.002 mass fraction vapor xsolid = 1 - x2 = 0.9998 or 99.98%

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3 Properties of Pure Substances