Question

. Air enters the compressor of an ideal gas refrigeration cycle at 7oC and 40 kPa and the turbine at 37oC and 170 kPa. The mass flow rate of air through the cycle is 0.3 kg/sec. Assuming variable specific heats for air, determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Also, draw the T-s diagram of the gas refrigeration cycle.

Answer 1

Given Data

At compressor inlet

At turbine inlet

Solution

The ideal gas refrigeration cycle is a reverse Brayton cycle where the cooling effect is obtaining air through a turbine and then passing the air through a heat exchanger similar to the evaporator in vapor compression cycle. In ideal gas refrigeration cycle, the gas does not change its phase.

The Ts diagram of the ideal gas cycle is shown below

Assuming the turbine and compressor are isentropic.

We need to find the properties of air at four different points in the gas refrigeration cycle from the properties of air table.

At point 1,   and ,

At point 3, and  ,

For point 2, since and the process 1-2 is isentropic, therefore,

And for and  ,

similarly at point 4, and the process 3-4 is isentropic, therefore,

And for and  ,

( These values are approximate, refer to reliable air property table)

(a) The rate of refrigeration is the refrigerating effect ,.

  

(b) The net power input,

The compressor work

The turbine work

The net work input

(c) The COP is

(d) TS diagram of Gas refrigeration cycle