[Physics Class Notes] on Kelvin Planck Statement Pdf for Exam [2024]

Kelvin Planck’s statement is an ideal case of the second law of thermodynamics.

Kelvin Planck statement: We cannot construct any device like the heat engine that operates on a cycle, absorbs the heat energy, and completely transforms this energy into an equal amount of work. Some of the heat gets released into the atmosphere. Practically no device bears 100% thermal efficiency.

The below diagram shows the practical working of an engine:

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So, Kelvin Planck’s statement talks of an ideal heat engine that extracts heat and transforms it into work by forbidding/violating the second law of thermodynamics.

Kelvin Statement Planck Statement

The first law of thermodynamics needed the law of nature that could decide whether a given process permitted by the first law shall take place or not; therefore, the second law of thermodynamics can be stated in many ways, out of which we will study is the Kelvin Planck statement of the second law of thermodynamics.

Kelvin Statement of Second Law of Thermodynamics

Kelvin Planck second law of thermodynamics states that practically a reservoir never gives a positive net amount of work from the heat extracted from a thermal reservoir.

So, basically, you cannot have a heat engine that operates between the two temperature levels and it has no heat rejection.

It is not possible to achieve a continuous supply of work from a body by cooling it to the temperature below the coldest of its surroundings.

We know that the heat engine absorbs heat from the source (higher temperature) and transforms it into useful work, releasing some amount of heat into the sink (surroundings). It means that the sink is essential for the continuous supply of work by converting heat into equivalent work.

Let’s suppose if the source and the sink are at equal temperatures; in this case, the thermal efficiency of the heat engine becomes zero. Also, we cannot obtain any work at the time when the engine cools down below the temperature of the sink.

Therefore, the form of this law implies that no heat engine can convert the whole amount of heat extracted from the source into the equivalent work. It simply means that the entire heat cannot transform into work though the reverse is possible, we can convert the whole amount of work into heat energy.

Thus we cannot construct a perfect 100% thermally efficient engine in real-life.

Planck Statement

The Planck statement is very simple to understand. It states that we cannot construct a heat engine that runs in a cycle, extracts heat from the reservoir, and performs an equal amount of work; this is impossible.

So, Kelvin Planck statement consists of the word ‘impossible’ and though these laws cannot be proved; however, they are accepted universally like Planck statement has a huge role in a wide variety of the following applications

Chemical reactions
Thermoelectricity
Electric cells
The study of solutions
Change of states

Kelvin Planck Statement Example

A Russian-German Chemist and Philosopher named Friedrich Wilhelm Ostwald introduced a theoretical concept of ‘Perpetual Motion Machine of the Second Kind, abbreviated as PMMSK or PMM2.

PMMSK was a device that could perform work solely by absorbing heat from the body. Such a device completely follows the first law of thermodynamics. However, Kelvin Planck’s statement states that practically we cannot construct PMMSK.

You can view its image below:

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Ideal Engine: Carnot’s Engine

If we talk of a 100% thermally efficient engine, then the work of a French engineer and Physicist named Nicolas Leonard Sadi Carnot comes to mind.

Carnot advanced the study of the second law of thermodynamics by framing Carnot’s rule that satisfies all the limitations on the maximum efficiency the heat engine can achieve.

Since we know that Kelvin Planck’s statement is related to the heat engine, what is a heat engine?

Heat Engine

A heat engine comprises three fundamental parts:

Source
Working substance
Sink

If Q₁ is the amount of heat absorbed by the working substance from the source at TK, and

Q2 is the amount of heat rejected to the sink at TK.

W is the total amount of external work done by the working substance

Therefore, the net amount of heat absorbed is given as:

dQ = Q₁ – Q₂

(Since Q₁ is at a higher temperature and Q₂ at lower, so Q₁ > Q₂).

Here, we are considering an ideal case of an engine, i.e., Carnot’s Engine, so the net amount of heat absorbed by the system equals the external work done by the system.

So, applying the first law of thermodynamics:

dQ = dU + dW

Here, dQ = dW (the working substance returns to its initial state, so change in its internal energy, i.e., dU = 0).

Or,

W = Q₁ – Q₂

Now, let’s calculate the thermal efficiency of the engine

Thermal Efficiency

The thermal efficiency is denoted by the symbol (pronounced as ‘eta’), and written in the following manner:

= Net work done per cycle (W) / the total amount of heat absorbed by the working substance in a cycle (Q₁)

η = (Q₁ – Q₂) /Q₁

For a 100% thermally efficient engine, η is unity.

However, practically, some amount of heat always gets rejected to the sink, i.e., Q₂ ≠ 0, so, in this case, η is always less than 1.

Applications of Kelvin Planck’s Statement and other Laws of Thermodynamics

The list of the applications of thermodynamics is endless and if you want to mention the individual applications, these can be infinite. Thermodynamics involves the study of the infinite universe itself and it, therefore, has infinite applications. Following are some of the uses of laws of the thermodynamics (including the real-life use of Planck’s statement):

All the various types of vehicles involved in our daily lives such as cars, motorcycles, trucks, ships, aeroplanes, and many other types work on the foundation of the second law of thermodynamics and the demonstrated Carnot Cycle/ Carnot engine. These vehicles may be using any fuel type or engines such as petrol engine or diesel engine, but the same law remains applicable across all of them.
Home appliances and devices such as refrigerators, deep freezers, industrial refrigeration systems, all types of air-conditioning systems, heat pumps, etc., function on the rules of the second law of thermodynamics.
In all air and gas compressor types, blowers, fans, etc. The engine runs on the basic laws of thermodynamic/ thermodynamic cycles.
Of all the known applications, the important area of thermodynamics is concerned with the concept of heat transfer, which simply means the transfer of heat between two media. Three modes of heat transfer are known: conduction, convection, and radiation. This concept of heat transfer finds applicability in a wide range of devices such as heat exchangers, evaporators, condensers, radiators, coolers, heaters, etc.
Thermodynamics also concludes studies in many diverse types of power plants like thermal power plants, nuclear power plants, hydroelectric power plants, power plants (most of which are based on renewable energy sources like solar energy, wind energy, geothermal energy, the energy of tides & oceanic waves, etc.)
With the rising levels of pollution and global warming, most economies have invested a major chunk of their monetary and human resource in renewable energy. This renewable energy forms a key subject area of thermodynamics as it involves studying the feasibility of using different types of renewable energy sources for domestic and commercial purposes.
When an individual sweats in a crowded room: In a crowded room, most people will be sweating (especially when there is a lack of ventilation). This is due to the body’s natural mechanism to start cooling down by heat transfer from the body to the moisture molecules, which cause cooling due to latent heat of vaporization. Sweat evaporates adding heat to the room. This only happens due to the existence of the first and second laws of thermodynamics, working in sync for producing the effect. One must remember that heat is only transferred and not lost while attaining equilibrium with maximum entropy.
Melting of an ice cube: The ice cubes in a drink also liquify by means of absorption of heat from the drink, thereby making the drink cooler. If we forget to drink it for some reason, after an interval, it regains lost heat from the room temperature by absorbing the atmospheric heat. All this happens as per the laws of thermodynamics.

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