Pure Substances
Substances of fixed chemical composition are known as pure substances.
For Example: Water, Helium, Nitrogen, Oxygen etc.Substances exist in any one of the three phases namely solid, liquid and gas.
For example: H2O may exist in the form ice (solid), Water (Liquid) or Steam (Gaseous). In all these phases it will have the same chemical composition.
A Mixture of two or more phases of a pure substance should also be regarded as pure substance. If Water and Steam Co-exist in a container, the chemical composition of both the Vapour and liquid phases will be identical. Hence this heterogeneous system is also a pure substance.
Phase Transformation
Consider a unit mass of ice heated steadily at a constant pressure of 1 atm. Let the initial temperature be =30o C. Due to heating, temperature increases up to 0o C (Figure 1). At 0o C ice starts melting. Until entire mass of ice becomes water, temperature is remaining constant. Heat added during this phase change is known as latent heat of fusion.
Further heating increases the temperature of water. This continues until 100oC. At 100oC Evaporation of water into steam is taking place. Temperature once again remains constant at 100o C until complete conversion of water into steam occurs. Heat added during this phase change is known as latent heat of evaporation. Temperature of steam continues to increase afterwards.
p -T Diagram of a Pure Substance
Instead of 1atm. pressure, if water is heated at 5 bar, evaporation will be taking place at 15 1.86oC. In the similar manner, each pressure has its own saturation temperature for a given substance.In a p-T diagram the locus of saturation temperatures against the corresponding pressures forms a curve known as vaporization curve. It separates liquid and vapour phases is p-T diagram.
Similarly solid & liquid phases are separated by fusion curve in p-T diagram.
Below a limiting value of pressure known as Triple point, direct conversion of solid into vapour is taking place. This is known as sublimation. Sublimation curve separate solid and vapour phases in p-T diagram. Sublimation curve, vaporization curve and fusion curve are represented on a p-T Coordinates in Figure Sublimation and vaporization curves are having positives slopes for all substances. Fusion curve for most of the substances is having positive slope but for water it is negative. From p-T diagram it can be inferred that the given substance exists in liquid phase when the temperature is below the saturation temperature corresponding to the given pressure and in vapour phase if the given temperature is greater than the saturation temperature. When the given temperature is equal to the saturation temperature it may be liquid, vapor (or) a mixture of both.
T-v Diagram of a Pure Substance
For simplicity let us consider only the liquid and vapour phases, which are commonly encountered in most of the engineering applications. Let a system of unit mass of water be heated at constant pressure. 1-2-3-4 in Figure Shows the T-v Variations at constant pressure.
From 1 to 2, heat addition increases the temperature with a very small increase in volume. State of water between 1 to 2 is known as sub cooled liquid or compressed liquid because for a given pressure it is at a temperature lower than the saturation temperature (or) for a given temperature it is at a pressure higher than saturation pressure. The state of water at 2 is known saturated liquid. Temperature at this state is equal to the saturation temperature. Any further addition of heat causes evaporation of water.
From 2-3 evaporation is taking place. During this phase change, temperature remains constant and increase in volume is high. At state 3, entire mass is in the form of vapour known dry saturated vapour.
From 3 to 4, heating causes increase in both temperature and volume. State of steam in this region is called super heated state.
As mentioned earlier, at higher pressure evaporation occurs at higher temperature and at lower pressure evaporation occurs at lower temperature. Latent heat of evaporation decreases with increase in pressure. For a particular pressure it becomes zero so that the change from liquid to vapour phase occurs suddenly without a distinct intermediate state. This pressure is known as critical pressure. This state on a property diagram is known as critical point. By connecting the saturated liquid state at different pressures a line called saturated liquid line is obtained. In the same way, by connecting the saturated vapour states, saturated vapour line is obtained. It can be observed that the saturated liquid and vapour line meet at critical point. Figure shows all these lines and various regions on a T-v diagram.
The region between saturated liquid line and saturated vapour line is known as wet region, consisting of both liquid and vapour. The percentage of composition or quality of this wet steam is expressed in terms of dryness fraction which is defined as the ratio of mass of vapour to the mass of the mixture. Specific volume of wet steam is expressed as
v = xvg + (1 - x)vf
= vf + x(vg - vf)
= vf + xvfg
Where vf - specific volume of the saturate liquid @ the given Pressure or Temperature
vg - specific volume of sat. vapour @ the given Pressure or Temperature
x - dryness fraction.
Since vf<<vg
v = vf + xvg
In the compressed liquid region, specific volume may be regarded as a function of temperature alone since the liquid is incompressible.
v = vf at the given temperature.
In the superheated region, v is function of both temperature and pressure.
T-s Diagram for a Pure Substance
Similar to T-v diagram, T-s diagram can also be drawn for a pure substance. Figure shows various regions on a T-s diagram. The salient features of this diagram are:- Temperature is taken on Y-axis and entropy is taken on X-axis
- There are three distinct regions : to the left of the saturated liquid line is the liquid region, between saturated liquid and saturated vapour line is wet region, and to the right of saturated vapour line is superheated region
- Constant pressure lines coincide with the constant temperature lines in the wet region. These lines becomes curved in the superheated region
- Slope of the saturated liquid line is less compared to that in T-v diagram.
Entropy of a fluid at saturated liquid state s sf @ the given p or T
For saturated vapour state
s = sg @ the given p, T
For Wet state
s = sf + x sfg
Where sf and sfg are functions of p or T.
For superheated state
s = s(p, t)
For sub cooled liquid
s = sf - cpl ln
Where sf = sat. Liquid entropy @ the given pressure
cpl = Liquid specific heat at the given temperature
Ts = Sat. temp. Corresponding to the given pressure
T = Given Temperature.
H-s Diagram for a Pure Substance
Within the wet region both isobars and isotherms are the same, but beyond saturated vapour line they deviate. Also it can be noted that the constant pressure lines diverge from each other towards the super heated vapour region. In the super heated vapour region, slope of isotherms become almost zero. The slope of constant pressure curves at any point is a measure of temperature, by noting that.
P-v Diagram of a Pure Substance
Figure shows the pv diagram of a pure substance. The saturated liquid and saturated-vapour curves meet at the critical point. The region to the left of the saturated-liquid line is compressed liquid, and the region to the right of the saturated-vapour line is superheated vapour. In between the two lines is the two-phase liquid-vapour region. Several isotherms are shown in the figure. The critical isotherm has an inflection point and a zero slope at the critical point. Isotherms below the critical point experience two discontinuities in slope as they cross the saturated-liquid and saturated-vapour lines. In between these two lines, the slope of the isotherms is zero, and a state in this region can be entirely saturated liquid, entirely saturated vapour, or a combination of the two.
Extending p-v Diagram for a Pure Substance to Solid Phase
Figure shows various regions of pure substances on a p-v coordinates. Volume continuously increases from solid to super heated vapour region. But for water volume decreases on melting and afterwards increases as shown Figure.
P-V-T SURFACE
P-V-T behavior of a pure substance can be expressed in a single three dimensional p-v-t surface as shown in the Figure 7.9(a). For water as its volume decreases on melting unlike other substances its p-v-t surface will be different from that of others as given in Figure.
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