246 ENGINEERING THERMODYNAMICS

dharm
/M-therm/th5-2.pm5

coupled to a Carnot engine which absorbs heat from a source which is maintained at 220°C by
burning liquid fuel of 44500 kJ/kg calorific value and rejects the heat to the atmosphere. Determine :
(i)Power developed by the engine ;
(ii)Fuel consumed per hour.
Take enthalpy of fusion of ice = 334.5 kJ/kg.
Solution. (i) Fig. 5.16 shows the arrangement of the system.
Amount of ice produced per day = 15 tonnes.

(220 + 273)

= 493 K

(25 + 273)

= 298 K

(25 + 273)

= 298 K

(0 + 273)

= 273 K

Heat

engine

Heat

pump

Qe1 Qp1

Qe2 Qp2

W

Fig. 5.16

∴ The amount of heat removed by the heat pump,

Qp 2 15 1000 334 5

24 60

= ××

×

.

= 3484.4 kJ/min

C.O.P. of the heat pump =

Q

W

p 2 273

298 273

=

−

∴ W = Qp 2

298 273

273

× − = 3484 4^25

273

. × = 319.08 kJ/min
This work must be developed by the Carnot engine,

W=319 08

60

.

= 5.3 kJ/s = 5.3 kW

Thus power developed by the engine = 5.3 kW. (Ans.)

(ii) The efficiency of Carnot engine is given by

ηcarnot =

W

Qe 1

= 1 –

298

493

= 0.396

∴ Q

W

e (^1396)
3
396

0. 
   


1. 
   


2. 
   

   = 13.38 kJ/s
   ∴ Qe1(per hour) = 13.38 × 60 × 60 = 48168 kJ
   ∴ Quantity of fuel consumed/hour
   =^48168
   44500
   = 1.082 kg/h. (Ans.)