Page 452 - Advanced thermodynamics for engineers

442 CHAPTER 18 LIQUEFACTION OF GASES

In this case b 5 ¼ 0 because point 5 (the liquid point at 1 bar) was chosen as the datum for properties,
hence
^
w net ¼ h 1 T 0 s 1 0 ¼ 12097 290 111:63 ¼ 20275kJ=kmol liquid

20275
¼ ¼ 701:6kJ=kg liquid
28:9

4. work required per liquid yield

The compression process is an isothermal one, and hence the work done is
v 2 p 2 p 2
w ¼ p 1 v 1 ln ¼ p 1 v 1 ln ¼ <T 1 ln (18.39)
v 1 p 1 p 1
Substituting the values gives
p 2 200
w ¼ <T 1 ln ¼ 8:3143 290 ln ¼ 12775kJ=kmol gas
p 1 1
12775 442
¼ ¼ 442kJ=kg gas ¼ ¼ 4987kJ=kg liquid
28:9 0:08863

5. rational efficiency
The rational efficiency of the plant is defined as

^
w net 701
h ¼ ¼ ¼ 0:1406 (18.40)
R
w 4987
Hence, the plant is only 14.1% as efficient as it could be if all the energy transfers were
reversible. It is instructive to examine where the irreversibilities occur.
18.2.4.1 The heat exchanger
The irreversibility of the heat exchanger is

I HE ¼ð1 yÞðb 7 b 6 Þ ðb 2 b 3 Þ
¼ 0:91137 f 20275 ð 15518Þg f 7561 ð 5776Þg
¼ 2550kJ=kmol gas

This is equivalent to 20.0% of the work required to compress the gas.

18.2.4.2 The throttle to achieve liquefaction
The irreversibility of the throttle is

I throttle ¼ b 4 b 3 ¼ 0:91137 ð 15518Þ ð 5776Þ¼ 8366kJ=kmol gas
This is equivalent to 65.5% of the work used to compress the gas.