Vapour Properties Mollier Chart Heat Capacities

The objective is to develope the basics understanding of following concepts:
  • Properties of Vapour
  • Enthalpy of Vaporization
  • Degree of Super heat
  • Mollier Chart
  • Heat Capacities

Properties of Vapour

Liquids when heated converted into vapour. The difference physical characteristics of liquids and vapours helps in working of engines, in which phase change took place. When steam condensed to liquid water to create a partial vacuum in a piston cylinder enclosure, and thus the excess atmospheric pressure works over the low pressure and acting on the opposite face of the piston to provide the actuating force that drove the first engine successfully in the early eighteenth century.

Later with the development of the technology atmospheric pressure was replaced by steam pressure on the piston as the driving force for the work. Examples are reciprocating engines and steam turbines working of which depends upon pressurized steam.
Given below is the Temperature Entropy diagram (T-S) Temperature Entropy diagram Above figure is for a pure substance in which temperature is plotted against entropy.

  1. When a sub cooled liquid at state 1, having a constant pressure is heated then it results in increase in entropy, enthalpy and temperature till the liquid reached a saturated state
  2. Further transfer of heat at state 2, failed to increase the temeparture of the system but results in increase of enthalpy and entropy in a boiling or vaporization process. During this process the conversion of saturated liquid at state 2 to a mixture of liquid and vapour, and finally to a saturated vapour takes place at state
  3. The enthalpy difference between the saturation values (vapour and liquid) h3 – h2 is called the heat of vaporization or enthalpy of vaporization. At state 3, if we continued heat addition, resulting in superheating the steam to state.
  4. At state 4 temeparture, enthalpy and entropy further increases. As given in the earlier Chapter tittled Enthalpy Entropy and 2nd law of thermodynamics.
Above equation stood clear with regard to heat addition and entropy increase (heat addition results in increase in system entropy, since dq is in the numerator) and on the other side, if the temperature of the system decreases then because of the cooling effect the entropy decreases.

A measure of proximity of a superheated state (state 4 in the fig) to the saturated vapour line is the degree of superheat. The difference between the superheated temperature(T4) and the saturated vapour temperature (T3), at the same pressure is the degree of superheat of steam at state 4 (T4 – T3).
During the process of phase change from state 2 to state 3, the temperature and pressure give no indication of the relative quantities of liquid and vapour in the system. The quality ‘x’ at a given pressure is defined as the ratio of the mass of the liquid mixture to vapour in a saturation curve at any point. Thus the quality varies i the range from 0 for saturated liquid to 1 for saturated vapour.
Since, extensive properties are directly related to mass, thus they vary with the vapour quality in the mixed region. Example, entropy varies for saturated liquid sl at state 2 to the saturated vapour entropy sv at state 3 in accordance with the following quality equation:  Where, s is the entropy per unit mass
The effect of quality can also be seen on the other extensive properties like enthalpy and volume.
Moisture is the variable which is closely related with the quality, together moisture and quality can be expressed as a percentage.
Moisture fraction M, is defined as the ratio of mass of liquid to total mass of liquid and vapour.
The sum of quality and the moisture fraction of a mixture is one.

Mollier Chart

The one of the purpose of mollier chart is to determine the work done and the power of steam turbine by finding from the chart the values of enthalpy and entropy. Mollier chart comprises of:
  • Constant pressure lines
  • Constant temperature lines
  • Entropy lines are the vertical lines used to read the entropy at the end of the line.
  • Enthalpy lines are horizontal line and used to read the enthalpy at the end of the line.
mollier chart

Specific Heats or Heat Capacities

The specific heat or heat capacities at constant volume and at constant pressure are:  Change in pressure has little influence on volume and internal energy in Solid and Liquids, thus Cv = Cp.

Thermally perfect gas obeys PV = RT and its internal energy, enthalpy and heat capacities are functions of temperature only  A gas is said to be calorically perfect in addition it being thermally perfect, if it also has constant heat capacities i.e at low and moderate pressure and temepartures.


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