Question 12.27: The evaporator and condenser temperatures of 20 tonnes capac...

Refer to Fig. 37. Following the procedure as given in the previous example plot the points 1, 2, 3 and 4 on p-h chart for freon-22. The following values are obtained :
h_{2} = 615 kJ/kg
h_{3} = 664 kJ/kg
h_{4}   =    h_{1} = 446 kJ/kg
v_{2} = 0.14 m³/kg.

(i) Refrigerating effect per kg = h_{2}   –    h_{1} = 615 – 446 = 169 kJ/kg.

(ii) Mass of refrigerant to be circulated per minute,

m  =  \frac{20  ×   14000}{169  ×    60}   = 27.6 kg/min.

(iii) Theoretical piston displacement

= Specific volume at suction × Mass of refrigerant used/min
= 0.14 × 27.6 = 3.864 m³/min.

(iv) Theoretical power

= m ×  (h_{3}   –    h_{2})   =    \frac{27.6}{60}    (664 – 615) = 22.54 kJ/s

= 22.54 kW.

(v)                                                    C.O.P. =  \frac{h_{2}   –    h_{1}}{h_{3}   –    h_{2}}   =  \frac{615   –    446}{664   –    615}   =  3.45.

(vi) Heat removed through the condenser

= m (h_{3}   –    h_{4}) = 27.6 (664 – 446) = 6016.8 kJ/min.

(vii) Theoretical displacement per minute per cylinder

=  \frac{Total   displacement/ min.}{Number   of    cylinders}   =  \frac{3.864}{6}   = 0.644 m³/min

Let diameter of the cylinder = d
Then, stroke length, l = d

Now,                                    \frac{π}{4}   d²  ×    l    =    \frac{0.644}{950} 

or                                            \frac{π}{4}   d²  ×    d   =  \frac{0.644}{950} 

i.e.,                                   d = 0.0952 m or 95.2 mm.

and                                       l = 95.2 mm.