VAPOUR POWER CYCLES 589

dharm

\M-therm\Th12-3.pm5

Mercury cycle :

hl = 355.98 kJ/kg

sl = 0.5397 = sm = sf + xm sfg

or 0.5397 = 0.0808 + xm = (0.6925 – 0.0808)

∴ xm =

(.. )

(.. )

0 5397 0 0808

0 6925 0 0808

−

− = 0.75

hm = hf + xm hfg = 29.98 + 0.75 × (329.85 – 29.98)

= 254.88 kJ/kg

Work obtained from mercury turbine

(WT )Hg = hl – hm = 355.98 – 254.88 = 101.1 kJ/kg

Pump work in mercury cycle,

(WP )Hg = hfk – hfn = 76.5 × 10–6 × (4.5 – 0.04) × 100 = 0.0341 kJ/kg

∴ Wnet = 101.1 – 0.0341 ~ 101.1 kJ/kg

Q 1 = hl – hfk = 355.98 – 29.98 = 326 kJ/kg (Q hhfnk~− f)

∴ ηHg cycle ==

W

Q

net

1

101.1

326

= 0.31 or 31%.

Steam cycle :

At 15 bar : h 1 = 2789.9 kJ/kg, s 1 = 6.4406 kJ/kg

At 0.04 bar : hf = 121.5 kJ/kg, hfg = 2432.9 kJ/kg,

sf = 0.432 kJ/kg K, sfg 2 = 8.052 kJ/kg K, vf = 0.0001 kJ/kg K

Now, s 1 = s 2

6.4406 = sf + x 2 sfg = 0.423 + x 2 × 8.052

∴ x 2 =

6 4406 0 423

8 052

..

.

−

= 0.747

h 2 = hf 2 + x 2 hfg = 121.5 + 0.747 × 2432.9 = 1938.8 kJ/kg

Work obtained from steam turbine,

(WT)steam = h 1 – h 2 = 2789.9 – 1938.8 = 851.1 kJ/kg

Pump work in steam cycle,

(W (^) P)steam = hf 4 – hf 3 = 0.001 (15 – 0.04) × 100 = 1.496 kJ/kg ~ 1.5 kJ/kg
or hf 4 = hf 3 + 1.5 = 121.5 + 1.5 = 123 kJ/kg
Q 1 = h 1 – hf 4 = 2789.9 – 123 = 2666.9 kJ/kg
(Wnet)steam = 851.1 – 1.5 = 849.6 kJ/kg
∴ηsteam cycle =
W
Q
net
1

849.6
2666.6
= 0.318 or 31.8%.
(i) Overall efficiency of the binary cycle :
Overall efficiency of the binary cycle
= ηHgcycle + ηsteam cycle – ηHgcycle × ηsteam cycle