TITLE.PM5

208 ENGINEERING THERMODYNAMICS

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/M-therm/Th4-6.pm5

Locate the point ‘1’ at an intersection of the 10 bar pressure line and 0.9 dryness fraction
line.

Throttling is a constant enthalpy line so draw a line parallel to X-axis till it cuts the 2 bar
line and locate the point 2. The dryness fraction of steam at point 2 is 0.94.

(The total enthalpy before and after throttling = 2573 kJ/kg)
Hence exit condition of steam = 0.94. (Ans.)
Note. This process occurs during the control of flow of steam supplied to a turbine to take care of the
varying load.

+Example 4.63. Steam initially at a pressure of 15 bar and 0.95 dryness expands
isentropically to 7.5 bar and is then throttled until it is just dry. Determine per kg of steam :
(i)Change in entropy ;
(ii)Change in enthalpy ;
(iii)Change in internal energy.
Using : (a) Steam tables
(b) Mollier chart.
Is the entire process reversible? Justify your statement.
Solution. (a) Using steam tables
Condition 1 : 15 bar, 0.95 dryness
hf 1 = 844.7 kJ/kg ; ts 1 = 198.3°C, sf 1 = 2.3145 kJ/kg K,
sg 1 = 6.4406 kJ/kg K, vg 1 = 0.132 m^3 /kg

h 1 = hxhf 11 + (^1) fg = 844.7 + 0.95 × 1945.2 = 2692.64 kJ/kg
s 1 = sf 1 + x 1 ()ssg 11 − f = 2.3145 + 0.95(6.4406 – 2.3145) = 6.2343 kJ/kg K.
Condition 2 : 7.5 bar
hf 2 = 709.3 kJ/kg, ts 2 = 167.7°C, hfg 2 = 2055.55 kJ/kg, sf 2 = 2.0195 kJ/kg K
sg 2 = 6.6816 kJ/kg K, vg 2 = 0.255 m^3 /kg.
Consider isentropic expansion 1-2 :
(i) Change in entropy = 0
i.e., Entropy at 1 = entropy at 2
∴ s 1 = s 2
6.2343 = sxs sf 222 +− 2 ()g f
= 2.0195 + x 2 (6.6816 – 2.0195)
∴ x 2 =
6.2343 2.0195
6.6816 2.0195
−
−
= 0.9
Now, enthalpy at point 2,
h 2 = hxhf 22 + 2 fg = 709.3 + 0.9 × 2055.55 = 2559.29 kJ/kg.