Thermodynamics and Heat Engine4 (3+1)

LESSON - 18 PURE SUBSTANCES, CHANGE OF PHASE DURING CONSTANT PRESSURE PROCESS AND T-V DIAGRAM

 18.1. PURE SUBSTANCE

A pure substance is a substance which is:

(a) homogeneous in composition,

(b) homogeneous in chemical aggregation,

(c) invariable in chemical aggregation.

The illustrations of the definition of a pure substance is given in Fig. 18.1.

Fig. 18.1. Example of the definition of a pure substance

Refer Fig. 18.1:

• Ratio of H₂ and O are same in Fig. (i) and Fig. (ii) thus satisfies condition (a) i.e.  homogeneous in composition. Fig. (iii) does not satisfy this condition.

• H₂O every where in the system in Fig. 18(i) thus satisfies condition (b) i.e.  homogeneous in chemical aggregation. Fig. 18(ii) and Fig. 18(iii) do not satisfy this condition.

• Ratio of H₂O does not vary with time in Fig. 18(i), thus satisfies condition (c) i.e.  invariable in chemical aggregation.

The above statements conclude that substance (steam and water) in Fig. 18(i) satisfy all three conditions, thus it is a pure substance. Substances in Fig.18(ii) and Fig. 18(iii) are not pure substances as they do not fulfill all the three conditions altogether. 

Similarly, a mixture of steam, liquid water, snow, and ice is also a pure substance.

The other illustrations of the definition of a pure substance are given in Fig. 18.2 below.

 

Fig. 18.2. Other examples of the definition of a pure substance

A mixture of two or more phases of a substance is not necessarily a pure substance as it is in the case of mixture of two phases of liquid water and vapor steam. This can be seen in the above example Fig. 18.2, a mixture of liquid air and gaseous air is not pure substance since ratio of O₂ and N₂ of liquid air and gaseous air is different, and thus the mixture is not homogeneous in composition. 

18.2. PHASE CHANGE PROCESSES OF PURE SUBSTANCE AT CONSTANT PRESSURE

Pure substance  water:

Consider 1 kg of ice (solid) at −10°C contained in a cylinder, say under 1 atmospheric pressure as shown in Fig 18.3 (a). This state of ice is shown by state ‘A’ on T-Q and T-V diagrams in Fig. 18.4 and 18.5, respectively. Now let heat be supplied to the cylinder continuously and slowly. During heating, the pressure inside the cylinder is kept constant at 1 atmospheric pressure.  During heating at constant pressure, various processes along with change of states are observed and plotted on T-Q and T-V diagrams in Fig. 18.4 and 18.5, respectively.  

At the beginning of heating, the temperature of ice rises from -10°C and approaches to 0°C as shown in Fig. 18.3 (b). The warming process is represented by process ‘AB’ in Fig. 18.4 and 18.5. At state ‘B’, the temperature is 0°C.

Fig. 18.3. Formation of Steam.

On further heating, the ice starts melting (a change of phase takes place from solid to liquid state) but the temperature remains constant at 0°C. The two phases (i.e. mixture of ice (solid) and water (liquid)) exist in equilibrium as shown in Fig 18.3 (b-c). This process is shown by process ‘BC’ in Fig. 18.4 and 18.5. At point ‘C’ all the ice has melted and there is only one phase i.e. water (liquid) as shown in Fig. 18.3 (c). The quantity of heat required to transform ice into water (process BC) at constant temperature (i.e. 0°C) is called latent heat of fusion or enthalpy of fusion. The latent heat at 1 atmospheric pressure is numerically equal to 335 kJ/kg. There is a decrease in volume during this melting process, as shown in Fig. 18.5.

With further addition of heat the temperature of water rises till temperature of vaporization (i.e. boiling) is reached as shown in Fig. 18.3 (d). This process is represented by CD in Fig. 18.4 and 18.5. The point ‘D’ corresponds to the boiling (vaporization or saturation) temperature which is 100°C at 1 atmospheric pressure. This boiling temperature is a function of pressure. The state of water at point ‘D’ is called the saturated liquid state because any further addition of heat causes vaporization to start. The heat required to raise water temperature from 0°C to 100°C (Process ‘CD’) is called the sensible heat. During this process, from 0°C to 4°C, the volume slightly decreases but after that from 4°C to 100°C it increases as shown in Fig. 18.5.

When more heat is added, the liquid water starts evaporating and once again another change of phase (from liquid to vapor state) occurs at constant 100°C temperature at the same pressure. This process is called vaporization and is represented by ‘DE’ in Fig. 18.4. In this process there exists a two phase mixture of water (liquid) and steam (vapor) as shown in Fig. 18.3 (d-e) and the resulting mixture of water and steam is called the wet steam. There is a considerable increase in volume during the vaporizing process as shown in Fig. 18.5. The rate of evaporation depends upon the rate of heat supply. At point ‘E’ all the water has vaporized and the state of steam at this point is called dry and saturated steam (vapor) as shown in Fig. 18.3(e) and its corresponding temperature (100°C) is called saturation temperature. The heat required to vaporize liquid to vapor state during Process ‘DE’ at constant temperature is called the latent heat of vaporization. The numerical value of latent heat or vaporization for water at 1 atmospheric pressure is equal to 2256.9 kJ/kg.

With further addition of heat to the saturated steam, the temperature of the steam rises from 100°C as shown in Fig. 18.3 (f) and is represented by process ‘EF’ in Fig. 18.4. There will be also an increase in volume as shown in Fig. 18.5. This process ‘EF’ is called the superheating of steam and the resulting steam is called the superheated steam (vapor).

Now, if  heat is rejected from the cylinder continuously and slowly all the above processes will be reversed. That is, saturated vapor at state ‘E’ will start liquefying (condensing)  at constant 100°C temperature till the state ‘D’ is reached. This process ‘ED’ is then called liquefaction/condensation process.  Similarly Process ‘CB’ will be solidification process.

Fig. 18.4. T-Q. Diagram for Phase change from Ice into steam.	Fig. 18.5. T-V. Diagram for Phase change from Ice into steam.

Pure substance (normal substance) other than water:

For normal substance, the behavior in T-Q diagram is the same as that of water as shown in Fig. 18.4.  However, at low temperature, the behavior on T-v diagram is different from water, as show in Fig. 18.5. It can be seen from the process ‘BC’ in T-v diagram that water contracts while other pure substances (normal substance) expand during melting.

18.2.1. Saturation Temperature and Saturation Pressure

It probably came as no surprise to you that water started to boil at 100°C as seen in Fig 18.3 (d-e). Strictly speaking, the statement “water boils at 100°C” is incorrect. The correct statement is “water boils at 100°C at 1 atmospheric pressure.” The only reason water started boiling at 100°C was because we held the pressure constant at 1 atmosphere (about 1 bar). If the pressure inside the cylinder were raised to 5 bar by adding weights on top of the piston, then water would start boiling at 151.8°C. That is, the temperature at which water starts boiling depends on the pressure; therefore, if the pressure is fixed, so is the boiling temperature. At a given pressure, the temperature at which a pure substance changes phase is called the saturation temperature, T_sat. Likewise, at a given temperature, the pressure at which a pure substance changes phase is called the saturation pressure, P_sat. At a pressure of 1 atmosphere (101.325 kPa), T_sat is 99.97°C. Conversely, at a temperature of 99.97°C, P_sat is 1 atmosphere (101.325 kPa).

18.2.2. Vapor pressure of liquids and solids

When a liquid or solid is in equilibrium with its vapor at a given temperature, the vapor exerts a pressure that depends only on the temperature and is called vapor pressure of liquid or solid. In general, higher the temperature, greater is the vapor pressure. The temperature at which the vapor pressure equals 1 atmosphere (760 mm of Hg) is known as the normal boiling point.

18.2.3. Heat input (change in enthalpy) during formation of superheated steam from ice at -10°c

Refer Fig. 18.4. Since the heating process is at constant pressure, the heat input may be regarded as the change in enthalpy. The enthalpy changes during various processes as follows:-

 (a) The change in enthalpy from -10°C to 0°C as represented by process AB

              (∆h)_AB = C x ∆t

                         where C = specific heat of ice = 2.09 kJ/kg K   ;    ∆t = temperature difference

     or      (∆h)_AB  = 2.09 (0 + 10) = 20.9 kJ/kg

(b) The change in enthalpy during melting of ice at 0°C represented by process BC is given by

         (∆h)_BC  = Latent heat of fusion = 335 kJ/kg

(c) The change in enthalpy during heating of water up to boiling temperature i.e. saturation temperature (100°C) is represented by process CD and is known as the sensible heat and is given by

         (∆h)_CD = C x ∆t  = 4.18 x (I00 - 0) = 418 kJ/kg.

(d) The change in enthalpy during vaporization process at 100°C is represented by DE and is given by

        (∆h)_DE = Latent heat of vaporization =2256.9 kJ/kg.

(e) The change in enthalpy during heating of saturated steam to superheated state up to 200 °C is represented by EF and is given by

      (∆h)_EF  = C_p x  ∆t = C_p (t_sup - t_s)

              Where C_p = Sp. heat of superheated steam = 1.967 kJ/kg K

                          ∆t = temperature difference = 200 - 100 = 100°C

        (∆h)_EF  = 1.967 x l00 = 196. 7 kJ/kg

In order to determine the properties of steam, water at 0°C is arbitrarily assigned as datum for enthalpy and assigned the value of zero enthalpy. This suggests that enthalpy of a substance may be negative in magnitude if the substance goes below 0°C. The negative sign does not mean that the substance does not contain any energy but simply indicates the direction of heat flow with respect to the datum temperature.

18.3. T-V DIAGRAM FOR A PURE SUBSTANCE In the above study (Fig. 18.5), it is to be noted that the formation of steam from water (process C-F) is at 1 atmosphere (about 1 bar) pressure. The formation of 1 kg of water at 0°C into steam at 1 atmosphere has little practical significance. In practice, the water is pumped into a boiler at high pressure (say 100 to 200 bar) and then it is transformed into saturated or superheated steam with the addition of heat at this high pressure. The formation of superheated steam from compressed water at different pressures below critical point is shown in Fig. 18.6. At different constant pressures below critical point the nature of the various processes for water to steam formation is the same but the saturation temperature of steam differ. Points B, F, J and points C, G, K are saturated liquid states and  saturated vapor state, respectively. The saturated liquid states can be connected by a line called the saturated liquid line, and saturated vapor states in the same figure can be connected by another line, called the saturated vapor line. These two lines meet at the critical point, forming a dome as shown in Fig. 18.6.

Fig. 18.6. T-V diagram for phase change from water into steam

 All the compressed liquid states are located in the region to the left of the saturated liquid line, called the compressed liquid region. All the superheated vapor states are located to the right of the saturated vapor line, called the superheated vapor region. In these two regions, the substance exists in a single phase, a liquid or a vapor. All the states that involve both phases in equilibrium are located under the dome between saturated liquid line and saturated vapor line, called the saturated liquid–vapor mixture region, or the wet region. Above critical point there is no longer any distinction between a liquid and a vapor.

18.4. Critical point: It is clear that the critical point is a limiting at which the volume of a liquid is equal to that of an equal mass of vapor, or, in other words, at which the density of liquid equals the density of vapor. If the density of both liquid and vapor are measured as functions of temperature and the results are plotted, the critical temperature can be determined from the point where the two curves meet. Experimental results for propylene are shown in Fig. 18.7.

Fig. 18.7. Liquid- and vapor-density curves of propylene, meeting at the critical point.