Entropy of Vapours in 3 Phases: Water, Evaporation and Superheated Steam | Thermodynamics

Liquids are heated and evaporated at constant pressure. The vapours are also superheated at constant pressure in superheaters. For this reason the entropy of vapours can be calculated from the formula for the change of entropy at constant pressure.

We consider the entropy of vapour in three phases of formation.

In the following topic the entropy of steam and the same principles can be applied to any vapour are discussed:

(1) Entropy of Water:

Let us consider unit mass of water which will be raised to unit mass of steam at constant pressure. The temperature of water is raised from 0°C to saturation temperature corresponding to the pressure of steam generation.

Heat supplied = d_q = _cfdT for a small increase in temperature. Though the specific heat c_f for water varies with temperature, for normal temperatures its average value may be taken as 4.188 kJ/kg-K.

The process of heating water, from freezing point upto saturation temperature, at constant pressure is shown by the curve d – b points .

(2) Entropy of Evaporation:

After the water has reached its saturation temperature, any further addition of heat does not raise the temperature of water but changes its state. During the change of state, the temperature remains constant. The process of evaporation is represented by a horizontal line on temperature entropy diagram.

The amount of heat supplied during evaporation will be xh_fg if the steam is wet at the end of heat supply and will be h_fg if the steam is dry and saturated at the end of heat supply, This heat supply takes place at constant temperature T_sat. For wet steam the change in entropy will be xh_fg / T_sat where x is the dryness fraction of steam.

The evaporation process on temperature entropy diagram (fig. 3-8) is represented by horizontal line be. There is all water at b and all dry saturated steam at c. The heat supplied during the evaporation process is represented by the rectangle bcfg.

(3) Entropy of Superheated Steam:

After complete evaporation of water, any further addition of heat will raise the temperature of steam above the saturation temperature. This heat supply takes place at constant pressure i.e., the pressure of steam generation. Let T_sup be the absolute temperature of the steam at the end of constant pressure heat supply. Let C_p be the mean specific heat of superheated steam for the given range.

Heat received by one kg of steam during a small rise in temperature during superheating = C_pdT.

The superheating of steam at constant pressure is represented on the temperature- entropy diagram by a curve cd. The area cdefc of the temperature-entropy diagram represents the superheat of the steam.

In fig. 3-8, we have,

area abgoa = h_f = sensible heat,

area bcfgb = h_fg = latent heat or enthalpy of vaporization,

area cdefc = C_p (t_sup – t_sat) = superheat, and

area abcdeoa = H = total enthalpy.

From the equations derived in this article we can calculate the entropy of wet steam, dry steam and superheated steam. The values obtained by these equations are approximate.

Example:

Calculate the entropy of 1 kg of steam reckoned above 0°C and at a pressure of 10 bar when

(a) The steam is wet and of dryness fraction 0.8,

(b) The steam is dry and saturated, and

(c) The steam is superheated, the temperature of the steam being 200°C. Assume the specific heat of superheated steam to be 2.3 kJ/kg-K.