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Temperature-Enthalpy Graph During Formation of Steam

The water at A is having temperature of 0°C. The different stages are as follows:

 

(a) Induction stage : AB shows the heating of water upto boiling temperature. The heat required to raise the temperature of water (1 kg mass) from 0°C to boiling point (B) is known as sensible heat of water. It is denoted as hf” Sensible heat  = mass of water x specific heat x rise in temperature

= 1 x 4.2 t s + 273- 273] = 4.2 l 5

where specific heat of water is taken as 4.2 KJ / kg.

 

(b) Warming stage: BC shows the chage of state from liquid to steam. The heat absorbed during this stage is FG, known as latent heat of vaporisation (h18).

 

(c) Evaporation stage: CD shows the superheating process. The heat absorbed during this stage is GI I, known as heat of superheat. Line AH represents the total heat required to go upto superheated point D.

 

11.4.1 Effect of Change of Pressure

If we increase the pressure to P1 (bar), the boiling temperature also increases. TI1e point *B1 represents the boiling temperature or saturating temperature at P1 bar. The point C1 is the point on dry saturated steam. Line C1D1 shows constant pressure process in which the steam is superheated (after C1 point). In a similar manner a family of curves may be drawn for different pressures. The line A- B-B1- B2 is called saturated liquid line which forms boundary line between water and steam. Similarly C2- CcC-A1 is called dry saturated steam line which forms boundary line between wet and superheated steam. As the pressure increases the latent heat of vaporisation decreases (saturation temperature increases). It becomes zero at E where liquid and dry steam lines meet. This point E is called critical point. For steam, critical temperature is 374.15°C and critical pressure is 221.2 bar.

 

Total heat (enthalpy) of dry saturated steam (point C) is Jz8 = h1 + h/g”

where  hg = enthalpy of 1 kg of dry saturated steam

h f = sensible heat of 1kg of water

h fg = enthalpy of vaporisation of 1 kg of dry saturated steam = Latent heat of

steam.

The enthalpy of heating of water upto saturation temperature

h f  = c pf (T sat – 273.16)

where              c  pf = 4.18 kj / kg k.

 

(a) Wet steam: If

mg= mass of actual dry steam

m1= mass of water in suspension

m = mass of wet steam

 

(b) Dryness fraction : (x)

x = mg / mg + mf

x is also called the quality of wet steam

for x = 0, it is saturated liquid

for x = 1, it is dry and saturated steam.

0 < x < 1.

 

(c) Internal energy:     h f = u f + P v f

f stands for fluid (water)

u1= hrPv1

for dry steam              u g = hg – P v g

g stands for gas (vapour).

 

(d) sp. enthalpy of wet steam:

h = h1+ xh fg

(e) sp. enthalpy of superheated steam:

h sup = h f+ h fg + C pg U sup – t sat)

c g for steam = 2.1 KJ /kg0k.

t sup – t snt = Degree of superheat.

 

(j) Specific volume: Specific volume of wet steam

v =v1+x(vg -v1)

= x vg + (1 – x) v1

Charles law when       P = C

U sup / T sup = u g / T sat

 

(g) Specific entropy : specific entropy of wet steam

s = s1 + x (Sg – s1)

 

(h) Work done during evaporation

=P(vg -v1)

= Pv g as v1= negligible

 

(i) Work done during evaporation of a wet state

= Px vg.

 

(j) work done by superheated steam

‘Pv sup.

 

(k) specific entropy of steam:

The steam is produced at constant pressure. The entropy is assumed to be zero at 0°C.

Change m· spec1· f·1 c entropy= ds = dQ / T

 

(i) The heat supplied for heating 1 kg of water at constant pressure is given by

D θ = c pf dT

ds = c pf dT / T

 

Integrating

or                                 s f = c pf in T sat / 273

 

(ii) The change in entropy during evaporation is given by

S fg = h fg / T sat

 

(iii) The change in entropy during evaporation is given by

S g = s f + s fg

= c pf in T sat / 273 + h fg / T sat

 

(iv) Entropy during superheating of steam is given by

(v) Entropy of superheated steam is given by

S sup = s g + s gj

= c pf in T sat / 273 + h fg / T sat

where cp g = sp heat of superheated steam

= 2.1 KJ/ kg° K

And                             c pf = 4.18 KJ/ kg0K.