# Kelvin Planck Statement

## Introduction

In thermodynamics, we study various law to understand the mechanism and output of a system that takes energy from a source or reservoir then perform work and give output. To describe the complete activities in a very simple and right manner there are main 3 laws of thermodynamics. In which the 2nd law of thermodynamics is quite important. The second law of thermodynamics has two-part or we can say two statements; Kelvin-Plank's statement and Clausius's statement. Our focus in this article is Kelvin-Plank's statement.

In simple words, the Kelvin-Plank statement expresses that no human can build an engine that will provide you 100% efficiency, which means to say if we give an amount of input from source to engine then it cannot convert the all input into output, some will be changed in unwanted noise, heat-loss, etc.

## What is Thermodynamics?

Thermodynamics, if we break this word into two parts we can easily predict that the topic will be based on thermo means heat and dynamics mean motion. So, the discussion will be based on the motion of heat or motion due to heat.

Thermodynamics is a branch of science in which we study the relationship between heat and work. Here, we also learn how one form of energy converts into mechanical work and also make a significant visualization of the concept of heat and temperature.

This branch of physics provides us with an idea to know this cycle of conversion of heat into work and work into heat. To know about such conversion between two types of energy in any bulk system, we also use some terms such as pressure, temperature, mass, volume, etc.

## First Law of Thermodynamics

To find out the relationship between heat and mechanical work, scientists gave many laws of thermodynamics. Here we are going to explain the first law of thermodynamics.

According to the first law of thermodynamics, if we give an unknown amount of heat energy to the system which is working or can perform work then the total amount of that energy will be the sum of the change in the internal energy of that system and the amount of external work done by the system on the surrounding.

suppose that we provide an amount of $\mathrm{\Delta Q}$ energy to a system. We notice that the change in their internal energy is $\mathrm{\Delta U}$ and also an external work done by the system that is $\mathrm{\Delta W}$. Then the expression for given energy according to the first law of thermodynamics is

$\mathrm{\Delta Q=\Delta U+\Delta W}$

To simplify the above equation we know that

$\mathrm{work= force \times distance}$

Here, force is the product of pressure and area.

Thus,

$\mathrm{W= p \times A \times x}$

$\mathrm{W= p \times v}$

$\mathrm{\Delta W= p\Delta V}$

using this equation,

$\mathrm{\Delta Q=\Delta U+p\Delta V}$

## The second law of thermodynamics

As thermodynamics has lots of variable quantities so the explanation provided by the First law of thermodynamics is somewhat inconsistent to give a significant reason on some points. This caused the evolution of the Second law of thermodynamics. The Second law of thermodynamics can be stated in two terms.

• Kelvin-Plank Statement: This is a combination of results and theories provided by two scientists Lord Kelvin and Planks. This statement is also known as the heat engine statement.

According to this statement, it is impossible to build an engine that will provide you with 100% efficiency. There is no engine available and will not be available that can change the whole input for work without using energy for any other effect like noise, etc.

Thus, if a working engine takes heat from a source then it cannot convert complete heat for work and remove some amount for the sink.

• Clausius Statement: This is somewhat similar to the concept of potential or level of water. According to this statement, nobody can transfer heat from lower temperatures to higher temperatures. This law applies to our refrigerators. We have to use an external source of energy to cool down any object.

## Kelvin-Plank Statement Equivalence

In the second law of thermodynamics, there are two statements, both statements are equivalence to each other. This equivalence states that violation of one statement also results in violation of the second statement and vice-versa. We can show this relationship using the below diagram.

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Fig:1 Violation of Clausius statement using a heat engine

In the above figure, we have the Clausius violator that makes a falsy action and sends the heat $\mathrm{Q_1}$ from a cold reservoir to heat $\mathrm{Q_2}$ hot reservoir. Here, $\mathrm{Q_1}$ and $\mathrm{Q_2}$ both are equal. Thus, in reality, it is impossible so the system is violating the Clausius statement.

Here, we can see that another system also works in parallel to Clausius violator. This heat engine takes input from the reservoir which is at $\mathrm{T_2}$. The heat gained by the heat engine is equal to the heat sent by Clausius Violator. So, we can remove the reservoir at $\mathrm{T_2}$.

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Fig:2 Violation of Clausius statement using a reversible heat engine

Thus heat engine can take direct heat from the Clausius violator which means that a heat engine is working with a single reservoir. It is impossible. If a heat engine works with a single reservoir, it violates the Kelvin-Plank Statement.

## Consequences of Kelvin-Plank Statement

The second law of thermodynamics is quite important and has the following consequences.

• According to Kelvin Plank's statement, the efficiency of a heat engine can not be unity. This is an ideal condition that is impossible to achieve in practice.

• Also, we find from this law that the coefficient of performance of a refrigerator can not be infinite. This statement defines that we cannot operate the process of refrigeration without any external work.

## Conclusion

In conclusion, this article provides you with a deep and simplest form of explanation of thermodynamics and its laws. Here, we learn that 100% efficiency is never possible in real life.

## FAQs

Q1. What do you mean by Thermal Equilibrium?

Ans. We can say that body A and body B are in thermal equilibrium if the temperature of both bodies is the same.

Q2. What do you mean by Isobaric?

Ans. A system can be defined as isobaric if the total pressure of the system remains constant.

Q3. What are the state variables?

Ans. The microscopic entities which are used by us to determine and measure the equilibrium state of thermodynamics are called state variables.

Q4. what do you mean by cyclic process?

Ans. The process can be defined as cyclic if it occurs after a cycle of steps. We can also say that the process starts from a state and after some changes, it again returns to the initial state.

Q5. What is the standard unit of work?

Ans. Joule.