Data Loading...
Pure Substances - VTU e-Learning Centre Flipbook PDF
If a substance exists as vapor at the saturation temperature it is called saturated vapor or dry saturated vapor with x=
125 Views
124 Downloads
FLIP PDF 450.29KB
Pure Substances P-T and P-V diagrams Triple point and critical point Sub cooled liquid Saturated liquid, mixture of saturated liquid and vapor Saturated vapor and superheated vapor states of a pure substance with water as example. Enthalpy of change of phase, dryness fraction, T-S and H-S diagrams. Representation of various processes on these diagrams. Steam tables and its use. Throttling Calorimeter, Separating Calorimeter. Throttling and Separating Calorimeter.
Introduction: A pure substance is one that has a homogeneous and in variable chemical composition. It may exist in more than one phase, but the chemical composition is the same in all phases. Thus liquid water, a mixture of liquid water and water vapor, and a mixture of ice and liquid water are all pure substance: every phase has the same chemical composition. On the other and mixture of liquid air and gaseous air is not a pure substance. Because of the composition of the liquid phase is different from that of the vapor phase. Some times a mixture of gases such as air is considered a pure substance as long as there is no change of phase. Strictly speaking this is not true.
Vapor liquid solid phase equilibrium in a pure substance:
Fig 1: Constant pressure change from liquid to vapor phase for a pure substance
Consider a system one kg of water contained in a piston cylinder arrangement as shown in the figure. Suppose that the piston and weight maintain a pressure of 0.1 MPa in the cylinder and that initial temperature be 20 0C. As the heat is transferred to the water the temperature increases appreciably, the specific volume increases slightly under constant pressure. When the temperature 99.6 0C, additional heat transfer results in a change of phase. I.e. some of the liquid becomes vapor. During this process both temperature and pressure remain constant where as sp. Volume increases considerably. When the last drop of liquid has vaporized further transfer of heat results in an increase in both temperature and sp. volume of the vapor. The term saturation temperature designates the temperature at which vaporization takes place at a given pressure. Or the pressure is called saturation pressure corresponding to the saturation temperature. Thus for water 99.6 0C the saturation pressure is 0.1MPa, and for water at 0.1MPa the saturation temperature is 99.60C. Thus there is a definite relation between saturation pressure and saturation temperature.
Pressure
Vapor-pressure curve
Temperature Fig 2: Vapor – Pressure curve of a pure substance If the 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 for the existing pressure it is called either a sub cooled liquid or a compressed liquid. When the substance exists as a part liquid and part vapor at the saturation temperature a dryness fraction comes into picture. It is also called as quality and it is defined as the ratio of mass of vapor to the total mass. It is denoted by the symbol ’x’. Quality has meaning only when the substance is in saturated state. I.e at the saturation pressure and temperature. The quality x is an intensive property.
If a substance exists as vapor at the saturation temperature it is called saturated vapor or dry saturated vapor with x=1. When the vapor is at a temperature greater than the saturation temperature at the saturation pressure, it is said to exist as superheated vapor. After that the temperature increases as heat is added at constant pressure.
Temperature – Volume (T-V) diagram for water:
Fig 3: T-V diagram for water It is clear from the figure that constant pressure lines are ABCD, EFGH, IJKL etc. the peak point of the figure indicated by N is the critical point of water. Thus the critical pressure 22.089 MPa and corresponding critical temperature is 374.14 0C. A constant pressure process at a pressure greater than the critical pressure is represented by curve PQ. Thus water at 40 MPa, 20 0C is heated in a constant pressure process, there will be never be two phases present at the state shown. Instead there will be continuously in density at all the times and there will be only one phase present. The question arises is: when do we have a liquid and when do we have a vapor? The answer is that this is not a valid question at super critical pressures. We simply term the substance as fluid. However rather arbitrarily at temperatures below the critical temperatures we usually refer to it as a compressed liquid and at temperatures above the critical temperatures as superheated vapor. It should be noted that however at pressures above the critical pressures we never have a liquid and vapor phase of pure substance existing in equilibrium.
Table1: Some Critical point data Critical Temperature, 0C Water 374.14 Carbon dioxide 031.05 Oxygen -118.35 Hydrogen -239.85
Critical Pressure, MPa 22.089 07.39 05.08 01.30
Critical Volume, m3/kg 0.003155 0.002143 0.003438 0.032192
Consider another experiment with piston cylinder arrangement. Suppose that the cylinder contains one kg of ice at –200C and one bar. When heat is transferred to the ice the pressure remains constant the specific volume increases slightly and the temperature increases until it reaches 0 0C, at which point the ice melts and temperature remains constant. This state is called saturated solid state. For most substances the specific volume increases during this melting process. But for water specific volume of the liquid is less than the specific volume of the solid. Sublimation: If the initial pressure of the ice at –200C is 0.26 kPa, heat transferred to the ice results in an increase in the temperature to –100C. At this point however the ice passes directly from the solid phase to the vapor phase. This process is known as sublimation. Further heat transfer results in superheating of the vapor Triple Point: Consider the ice at 0.6113 kPa and temperature of –200C. Through heat transfer let the temperature increase until it reaches 0.01C. At this point however further heat transfer may cause some of the ice to become vapor and some to become liquid. At this point it is possible to have three phases in equilibrium. This point is called the triple point. Triple point is defined as the state in which all three phases may be present in equilibrium. The pressure and temperature at the triple point for a number of substance is given in following table. Table 2:Triple Point Data Temperature, 0C Hydrogen -259 Oxygen -219 Nitrogen -210 Carbon Dioxide -56.4 Mercury -39 Water 0.01 Zinc 419 Silver 961 Copper 1083
Pressure, kPa 7.194 0.15 12.53 520.8 0.00000013 0.6113 5.066 0.01 6.000079
Consider a solid state as shown in the figure, when the temperature increases with constant pressure the substance passes directly from solid to vapor phase. Along the constant pressure line EF the substance passes from solid to liquid phase at one temperature and then from liquid to vapor phase at higher temperature.
Constant pressure line CD passes through the triple point and it is only at the triple point the three phases exists together in equilibrium. At a pressure above critical pressure such as GH line there is no sharp distinction between liquid and vapor phases. The triple point temperature and critical temperature vary greatly from substance to substance. For ex: critical temperature of helium is 5.3K. Therefore absolute temperature of helium at ambient conditions is over 50 times greater than the critical temperature. On the other hand water has a critical temperature 374.14 0C (647.29K) and at ambient conditions the temperature of water is less than ½ the critical temperature.
Allotropic transformation It should be pointed out that a pure substance can exist in a number of different solid phases. A transition from one solid phase to another is called an allotropic transformation. This can be well understood by the following figure.
Temperature Fig 4: P-T Diagram for water.
Fig 5: P-T Diagram for iron
Independent properties of a pure substance: One important reason for introducing the concept of pure substance is that the state of a simple compressible pure substance is defined by two independent properties. For ex: if the specific volume and temperature of a super heated steam are specified the state of the steam is determined. To understand the significance of the term independent property, consider the saturate liquid and vapor state of a pure substance. These two states have the same pressure and temperature but they are definitely not the same state. In a saturation state therefore pressure and temperature are not independent properties. Two independent properties such as pressure -specific volume, pressure and quality, temperature-specific volumes are required to specify a saturation state of a pure substance.
Equations of state for the vapor phase of a simple compressible substance: From the experimental observations it has been established that the equation of state under low-density gases is given by PV=RuT. The ideal gas equation of state and compressibility factor equation are good approximations at low-density conditions. Therefore ideal gas equation of state is very convenient to use in thermodynamic calculations. The question comes what is low density? Or what range of density will the ideal gas equation of state hold with accuracy? The analysis gives the pressure temperature deviations from ideal gas behavior. To answer5 the question the concept of compressibility factor Z is introduced and is defined by the relation Z= PV/R uT. For ideal gas Z=1 and the deviation of Z from unity is a measure of the deviation of actual relation from the ideal gas equation of state.
Fig 6: Compressibility of Nitrogen
It shows a skeleton compressibility charge for nitrogen. Three observations can be made from this chart. All the temperature Z 1 as P 0. i.e. as the pressure approaches zero the P-VT behavior closely approaches that predicted by the ideal gas equation of state. Note also that at temperatures of 300K and above i.e. above room temperature the compressibility factor is near unity up to a pressure of 10MPa. This means that the ideal gas equation of state can be used for nitrogen over this range with considerable accuracy. Now suppose we reduce the temperature from 300K but keep the pressure constant at 4MPa, the density will increase and we note a sharp decrease below unity in the value of compressibility factor. Values of Z