Question

An aircraft air conditioner works between the pressure limits of 1 bar and 5 bar. The temperature of the air entering the compressor from the cabin and expansion cylinder are 10oc and 25oC respectively. The expansion and compression follow the pv1.3=constant. Find the following: 1. The theoretical C.O.P of the refrigeration cycle: 2. If the load on the system assuming the actual C.O.P is 50% of the theoretical C.O.P 3. The stroke length and the piston diameter of single acting compressor running at 300 r.p.m and the volumetric efficiency is 85%. (Take L/d = 1.5 : cp = 1.005 kJ/kgK ; cv = 0.71 kJ/kgK )

Answer 1

Here, $T_4= 25 ^0C= 25+273=298 K$ , $T_3=10+273= 283$

1. Theoretical $cop= \frac{T_4}{T_3 -T_4}= \frac{298}{298-283}=19.867$

(2) Practical cop$= \frac{50 \times 19.867 }{100}=9.93$

$\eta_l= \frac{ \pi}{4} d^2l$

$0.85= \frac{ \pi}{4} d^2\times1.5 d$

$d^3=2.267$

d=1.31 m

and length= 1.965 m