TITLE.PM5

AVAILABILITY AND IRREVERSIBILITY 323

DHARM
M-therm\Th6-2.PM5

Change in entropy of oxygen

= RO 2 loge

v

v

2

1

= 259.6 loge 19.874

1.168

F

HG

I

KJ = 735.7 J/K

Change in entropy of hydrogen

= RH 2 loge vv^2

1

= 4157 loge

19.874

18 706.

F

HG

I

KJ

= 251.78 J/K

Net change in entropy,

∆S = 735.7 + 251.78 = 987.48 J/K

Loss in availability

= T 0 ∆S = 290 × 987.48 J =

290 98748

103

×.

kJ = 286.36 kJ

i.e., Loss in availability = 286.36 kJ. (Ans.)

+Example 6.11. Calculate the decrease in available energy when 20 kg of water at 90°C
mixes with 30 kg of water at 30°C, the pressure being taken as constant and the temperature of
the surroundings being 10°C.
Take cp of water as 4.18 kJ/kg K.
Solution. Temperature of surrounding, T 0 = 10 + 273 = 283 K
Specific heat of water, cp = 4.18 kJ/kg K
The available energy of a system of mass m, specific heat cp, and at temperature T, is given
by,

Available energy, A.E. = mcp 1 0

0

z FHG −TTIKJ

T

T

dT

Now, available energy of 20 kg of water at 90°C,

(A.E.)20 kg = 20 × 4.18^1

283

10 273)

90 273)

FH − IK

+

+

z( T

(

dT

= 83.6 363 283^283

363

283

()lo−−gFHG IKJ

L

N

M

O

Q

e P

= 83.6 (80 – 70.45) = 798.38 kJ

Available energy of 30 kg of water at 30°C,

(A.E.)30 kg = 30 × 4.18^1

283

10 273)

30 273)

FH − IK

+

+

z( T

(

dT

= 30 × 4.18 ()log303 283^283

303

283

−− FHG IKJ

L

N

M

O

Q

e P

= 125.4 (20 – 19.32) = 85.27 kJ

Total available energy,

(A.E.)total = (A.E.)20 kg + (A.E.)30 kg

= 798.38 + 85.27 = 883.65 kJ

If t°C is the final temperature after mixing, then

20 × 4.18 × (90 – t) = 30 × 4.18 (t – 30)