#### Refrigerators, Physics tutorial

Refrigerator:

This is a device that uses work to transfer energy from a low temperature reservoir to a high temperature reservoir as is continuously repeats a set series of thermodynamic processes. Refrigerator operates in a direction opposite to that of the heat engine. The system that undergoes this reverse cycle of heat engine is called refrigerant. Air conditioners, heat pumps are also example of refrigerators. Carnot engine is capable of being reversed and when it is reversed it is called a Carnot refrigerator. Just like Carnot engine, Carnot refrigerator is an ideal refrigerator. The Stirling cycle is also capable of being reversed and is the most useful type of refrigerator. This reversed cycle is called Stirling refrigeration cycle.

For refrigeration process work is done on working body (i.e. on refrigerant) and this work is supplied by the electric motor or by other means. Work supplied is utilized to remove heat QC from cold reservoir and deposit heat QH into hot reservoir. These processes are reversed of one in heat engine.

Interior of the refrigerator (i.e. space inside where we put things such as food, fruits and drinks) is cold reservoir, while exterior is hot reservoir. The outside surfaces (usually sides and back) of most refrigerators are warm to touch while they are operating. Reason for this is as they are the hot reservoir.

Energy conservation holds also for refrigeration process (i.e. QH =W + QC ). Equation QC/QH = TC/TH also holds for ideal refrigerators.

Heat Pumps: Heat pumps work on same principle as refrigerator. Only difference is that for heat pumps, cold reservoir is outside while hot reservoir is inside of house. Another name for heat pump is electric heating system. Electric heating system is usually utilized to warm house during winter or cold weather.

Air conditioners: For air conditioners, cold reservoir is inside of the house while hot reservoir is the outside of the house. Refrigerators, air conditioners, and heat pumps are similar devices and their principles of operation are similar.

Coefficient of Performance of Refrigerators:

The term similar to efficiency of heat engine utilized to determine performance of the refrigerator is coefficient of performance ω. Coefficient of performance is expressed as ratio of heat extracted from cold reservoir QC to work done W on refrigerant

ω = Heat extracted from cold reservoir/work done on refrigerant

Therefore ω = QC/W = QC/(QH - QC)

Coefficient of Performance of Heat Pumps:

Coefficient of performance of heat pumps w is stated as ratio of heat delivered to house QH to work done W needed to deliver it.

ω = Heat delivered/work done on required

Therefore ω = QH/W

Two examples of refrigeration cycles (that is Carnot-cycle refrigeration and Stirling-cycle refrigeration) are discussed here.

Carnot Refrigerator:

Carnot refrigeration is the reversed of Carnot cycle. Carnot-cycle refrigerator is identical to Carnot-cycle engine except that heat absorbing end of machine now becomes cold region, whereas heat rejecting end of machine becomes hot region. PV diagram of Carnot-cycle refrigerator is given below.

Description of the Processes in Carnot-Cycle Refrigerator:

Processes in Carnot-cycle refrigerator shown above are explained below.

Process gf is an isothermal expansion. During this process, heat QC is absorbed from the cold reservoir at temperature TC and the working substance undergoes isothermal expansion from volume Vg to Vf .

Process fe is an adiabatic compression i.e no heat is added as the working substance compresses from volume Vf to Ve. Temperature increases during the process from TC to TH.

Process ed is an isothermal compression. During this process, heat QH is ejected to the hot reservoir at temperature TH.

Process dg is an adiabatic expansion i.e. no heat is transferred as the working substance expands from volume Vd to Vg. Temperatures decreases during the process from TH to Tc.

Coefficient of Performance of Carnot-Cycle Refrigerator:

The purpose of any refrigerator is to extract as much heat as possible from a cold reservoir with the expenditure of as little work as possible. The output is the heat extracted from the cold reservoir and the input is work.

Coefficient of performance ω is

ω = QC/W = QC/(QH - QC)

For a Carnot cycle, it has be established that

QH/TH = QC/TC

Then

ω = TC/(TH- TC)

ω may be considerably larger than unity.

Ideal Stirling-Cycle Refrigerator:

The ideal Stirling-cycle refrigerator is the reverse of the ideal Stirling-cycle engine. Cycle comprises of two isochoric processes and two isothermal processes. PV diagram of ideal Stirling-cycle refrigerator is given below.

Explanation of Processes in Ideal Stirling-Cycle Refrigerator:

Processes in ideal Stirling-cycle refrigerator are explained below.

Process ed is the isothermal expansion during which heat QC is absorbed from cold reservoir at temperatureTC .

Process dg is the isochoric process. Temperature of working substance increases from TH to TC and pressure also increases from Pd to Pg.

Process gf is the isothermal compression during which heat QH is ejected to hot reservoir at temperature TH.

Process fe is the isochoric process. Temperature of working substance decreases from TC to TH and pressure also decreases from Pf to Pe.

Coefficient of Performance an Ideal Stirling-Cycle Engine:

Coefficient of performance of refrigerator ω is

ω = QC/W

From Stirling engine, expression for work W has been obtained to be:

W = nRlnVg/Ve(TH - TC)

And heat QC as

QC = nRTClnVg/Ve

Hence

ω = nRTClnVg/Ve/(nRlnVg/Ve(TH - TC)) = TC/(TH - TC)

This is the coefficient of performance for ideal Stirling-cycle refrigerator and is equal to that of Carnot-cycle refrigerator. But the efficiency of the real Stirling-cycle refrigerator (i.e. the practical Stirling-cycle refrigerator) is always less than that of Carnot-cycle refrigerator operating between the same temperatures TC and TH.

Clausius Statement of Second Law:

No process is possible whose sole results is transfer of heat from the cooler body to hotter body.

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