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## Lesson 6. Mathematical analysis of vapour compression refrigeration system

*Module 1.Fundamentals of refrigeration*

MATHEMATICAL ANALYSIS OF VAPOUR COMPRESSION REFRIGERATION SYSTEM

**6.1 Introduction**

Refrigeration is a process of removing heat from a space to reduce the temperature below the immediate surrounding temperature. Thus, refrigeration refers the pumping of heat from lower to higher temperature. Heat can flow from higher to lower temperature but reverse heat flow requires input power according to second law of thermodynamics (Fig. 6.1).

Fig. 6.1 Second law of thermodynamics applied to refrigeration system

_{1}lower than T

_{2}(condensing temperature). The performance of refrigeration system as co-efficient of performance is given by

COP = "Refrigeratiing effect" /"Work of Compression"

And

Relative COP = Actual COP/Theoretical COP

Refrigeration cycle is reversed Carnot cycle used in engines.

Carnot COP= T_{1} /(T _{2}- T_{1 })

Carnot cycle is the maximum possible for a refrigeration system operating between two temperatures.

**Example**

A reversed Carnot cycle is used to produce 1500 kJ/S to heat the space. The heat is taken from atmosphere at 10^{ ะพ}C and supplied to conditioned room at 25^{ o}C. Find the kW required to run the system.

**Solution **

**6.2 Vapour Compression Refrigeration System**

In vapour compression refrigeration system, heat is absorbed from the evaporator (Refrigeration effect, R) and work of compression (W) is also added in the system. Heat Q is rejected (Q) at the condenser considering no heat gain or loss any where in the system. Q=R+W.

The operating cycle of the system is represented on P-H, T-Q and P-V diagram in Lesson 4 and 5.