Kelvin Planck Statement: Examples, Carnot’s Cycle, Heat Engine

The Kelvin-Planck statement is derived from two different statements given by Lord Kelvin and Planck. The statement is also known as Kelvin’s statement and Planck’s statement.

• Kelvin Planck's statement talks about an ideal heat engine that extracts heat and transforms it into work.
• According to Kelvin-Planck’s statement, no process is possible whose sole result is the transfer of heat from a cooler object to a hotter object.
• Based on Kelvin Planck's second law of thermodynamics, a thermal reservoir can never give a positive net amount of work.

Key Terms: Heat engine, Carnot engine, Kelvin statement, Second law of thermodynamics, First law of thermodynamics, Work, Energy, Efficiency.

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Kelvin-Planck’s Statement

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

• Kelvin Planck's Statement states that we cannot build any device like the heat engine that runs on a cycle, absorbs heat energy, and completely transforms that energy into equal work.
• Some of the heat is released into the atmosphere.
• Practically it is impossible for any device to have 100% thermal efficiency.
• Thus, Kelvin Planck's statement talks about an ideal heat engine that extracts heat and transforms it into work by violating the second law of thermodynamics.

The diagram below shows the practical operation of a heat engine:

.Kelvin Planck’s Statement in Detail 

Kelvin Statement- Planck Statement

Kelvin’s statement stated that:

It is not possible to derive a mechanical effect from any matter by cooling it below the maximum cooling temperature of the surrounding objects.

Planck’s statement states that:

The reversible system remains constant for the total sum of entropies. By combining both these statements the Kelvin-Planck statement was derived.

To decide whether a given process authorized by the first law should take place or not, the first law of thermodynamics needed the law of nature. So, the second law of thermodynamics can be stated in several ways, of which we will study Kelvin-Planck's statement of the second law of thermodynamics.

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Kelvin Statement of Second Law of Thermodynamics

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Kelvin-Planck's Second Law of Thermodynamics states that a reservoir never provides a net amount of positive work from the heat extracted from a heat reservoir. 

• It is impossible to have a heat engine that runs between the two temperature levels and has no heat rejection.
• It is also not possible to get a continuous supply of work from a body by cooling it to the lowest temperature.
• The heat engine absorbs heat from the source (higher temperature) and turns it into useful work by releasing some amount of heat in the sink (surrounding).
• This means that the heat sink is essential for the continuous supply of work by converting heat into equivalent work. 

Suppose that the source and the sink are at the same temperature; in this case,

• The thermal efficiency of the heat engine becomes zero.
• Also, we cannot do any work because the engine cools below the radiator's temperature. 
• Therefore, the form of this law implies that no heat engine can convert the entire amount of heat extracted from the source into equivalent work.
• It just means that not all heat can turn into work although the reverse is possible, we can convert all amounts of work into thermal energy. 
• So, in real life, we cannot build a perfect 100% thermally efficient heat engine.

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Planck’s Statement

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Planck’s statement states that it is impossible to construct a heat engine that runs in a cycle, extracts heat from the reservoir, and performs an equal amount of work.

Planck’s statement has a huge role in various applications: 

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

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Kelvin-Planck Statement Example

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Kelvin Planck's Second Law of Thermodynamics states that practically a reservoir never provides a net amount of positive work from the heat extracted from a heat reservoir. So, it is impossible to operate a heat engine in between.

• A Russian-German chemist and philosopher named Friedrich Wilhelm Ostwald introduced a theoretical concept of a "perpetual motion machine of the second kind, abbreviated as PMMSK or PMM2".
• The PMMSK was a device capable of doing work only by absorbing heat from the body.
• Such a device completely follows the first law of thermodynamics.
• However, Kelvin Planck's statement indicates that it is practically impossible to construct PMMSK.

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Carnot’s Engine

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Any heat engine does not have 100% efficiency. French engineer and physicist named Nicolas Léonard Sadi Carnot introduced a hypothetical, ideal heat engine that has the maximum possible efficiency.

• Carnot has advanced the study of the second law of thermodynamics by stating Carnot's rule which satisfies all the limitations on the maximum efficiency that the heat engine can achieve.
• For maximum efficiency of the heat engine, the process should be reversible.

“A reversible heat engine operating between two temperatures is called Carnot Engine and the sequence of steps constituting one cycle is called the Carnot Cycle.”

Carnot Engine Video Explanation

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Heat Engine

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Any device that transforms heat partly into work or mechanical energy is called a Heat engine.

• A quantity of matter inside the heat engine undergoes expansion or compression by absorbing or releasing heat is called the working substance of the heat engine.
• For example, a mixture of fuel vapour and air in a gasoline or diesel engine or steam in a steam engine is the working substance.
• The working substance undergoes a cyclic process, i.e. a sequence of processes that brings the substance to the same state in which it started.

A heat engine is made up of three basic parts:

• Source
• Working substance
• Sink

If Q₁ is the amount of heat absorbed by the working substance from the source at temperature T₁, and Q₂ is the amount of heat rejected to the heat sink at temperature T₂. If W is the total amount of external work done by the active substance. Then, the net amount of heat absorbed is given by:

 dQ = Q₁ - Q₂

Since Q₁ is at a higher temperature and Q₂ is at a lower temperature, therefore, Q₁ > Q₂.

Here, we consider an ideal case of an engine, i.e. the Carnot engine, so the net amount of heat absorbed by the system is equal to the external work done by the system. 

So, applying the first law of thermodynamics:

dQ = dU + dW 

Here, dQ = dW (the functional substance returns to its initial state, then changes internal energy, i.e. dU = 0).

Or, 

W = Q₁ - Q₂

With this, we can also calculate the thermal efficiency of the engine. 

Thermal Efficiency

Thermal efficiency is indicated by the symbol η and written as: 

Thermal Efficiency = net work done per cycle (W) / the total amount of heat absorbed by the working substance in one cycle (Q₁)

η = (Q₁ - Q₂) /Q₁

For a 100% thermally efficient engine, this is unity. However, a certain amount of heat is always pushed back to the radiator, i.e. Q₂ ≠ 0, so in this case, it is always less than 1.

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Things To Remember

• The Kelvin-Planck statement is derived from two different statements given by Lord Kelvin and Planck. 
• Kelvin Planck's statement gives an overview of an ideal heat engine that extracts heat and transforms it into work.
• Kelvin-Planck's statement is an ideal case of the second law of thermodynamics. 
• Kelvin-Planck's Second Law of Thermodynamics states that a reservoir never provides a net amount of positive work from the heat extracted from a heat reservoir. 
• Carnot gives the statement of a 100% thermally efficient engine.
• Formula to calculate the work done by a heat engine: 

W = Q₁ - Q₂

• The Thermal Efficiency of a heat engine can be calculated by the following formula:

η = (Q₁ - Q₂) /Q₁