Heat Pump

What is a Heat Pump?

A heat pump refers to a heat engine that works in a reverse direction and often gets used to transfer heat energy from a cold space to a warm space. The heat pump definition states that a heat pump absorbs heat from a cold body and then releases it into a hot body. The students asking what is a heat pump and how its efficiency depends on external factors should check out this article.  

Heat Pump- How it Works? 

A heat pump refers to a cyclically working energy-consuming device whose main aim is to heat a body through external work. By the expense of mechanical energy supplied to the heat pump by an external agent, it transfers thermal energy from a cold system to a hot system. As a result, the cold body becomes colder. Generally, the surrounding atmosphere is a hot system for the heat pump. 

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The above diagram shows QH amount of heat is supplied and when work is done, QL amount of heat is rejected. 

The heat pump used in heating mode follows the basic refrigeration-type cycle that works in a reverse direction. To define a heat pump, it can be said that the device takes heat from the cooler air and transfers it to a hot body. 

Heat Pump- What is the Coefficient of Performance (COP)?

The efficiency of a heat pump generally depends on:

• Coefficient of performance heat pump

• Seasonal Coefficient of performance (SCOP)

• Seasonal Performance Factor (SPF)

It’s the coefficient of performance heat pump, denoted by K that defines its performance. It is given by the formula:

K = QL/ W

where QL represents the heat extracted from the cold system

• W represents work need to transfer it to the cold system

•  K represents heat extracted by work done 

From the First Law of Thermodynamics for the cyclic process, change in internal energy is zero, that is, 

ΔU = 0 .

ΔQ = ΔW

Now, W = QH - QL

So, COP of heat pump formula, K = QL/ QH - QL

If a heat pump has a higher value of K, then it means it will be more efficient. Moreover, if the heat pump has a high coefficient of performance then it will consume less energy and will be more cost-effective. The efficiency of a heat pump often gets affected by factors like control system, auxiliary equipment, technology, and more. 

Common Terms Used in Heat Pump

• Heat Source: Also refers to a hot reservoir, it is a thermal reservoir used in working of a heat engine to supply heat at high temperature.

• Heat Sink: It is a thermal reservoir used to receive the remaining heat at low temperature in a heat engine.

• Heat Engine: Its main objective is to change heat into work. 

Heat source supplies an amount of heat, say, Q1 to the working body of the device. It will convert some heat into work, say, W, and the remaining heat, say, Q2 will get rejected to the sink. 

So, the amount of work done will be equal to:

W = Q2 – Q1

The thermal efficiency of a heat engine is denoted by η and is given by:

η = W/ Q1

η = Q1 – Q2 / Q1 = 1- Q2 / Q1

Refrigerator 

A refrigerator is a cyclically working energy-consuming device. Its main functioning is to refrigerate a body through external work. It receives heat from a low to a high-temperature system or surrounding environment. 

Coefficient of Performance:

COP of Carnot heat pump formula is given by:

COP = TH/ TH - TL

Second Law of Thermodynamics for Heat Pump

There are multiple statements given for the second law of thermodynamics. The main point stated was that no spontaneous process will yield in reverse direction on its own. 

Kelvin- Planck Statement 

A heat pump cannot convert all the heat received from a single source into work. It means some amount of heat remains that is rejected to the second thermal reservoir. Hence, the presence of a second reservoir or sink is essential for COP of heat pump and refrigerator.

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The above diagram shows total work done by the heat engine is equal to the amount of heat supplied (Q1) subtracted by the amount of heat rejected (Q2), that is, W = Q1 – Q2.

Moreover, the output of the work is always less than the energy supplied, so thermal efficiency, η cannot be equal to 1 or η<1.

Clausius Statement

It is impossible for a heat pump to transfer heat from low to a high-temperature system without the help of an external source. It means external work is desired as input; so, the heat pump cannot be equal to infinity. 

Moreover, both these statements are said to be equivalent, that is, if Kelvin- Planck's statement violates, then Clausius's statement also violates, and vice-versa.