What Is the Kelvin Planck Statement and Why Does It Matter?
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:
(Image will be uploaded soon)
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:
(Image will be uploaded soon)
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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FAQs on Kelvin Planck Statement Explained
1. What is the Kelvin-Planck statement of the second law of thermodynamics?
The Kelvin-Planck statement declares that it is impossible to construct an engine that operates in a cycle and produces no other effect than the extraction of heat from a single body (a source) and the complete conversion of that heat into an equivalent amount of work. In simpler terms, no heat engine can be 100% efficient.
2. Can you provide a simple example that illustrates the Kelvin-Planck statement?
Consider a car engine. It burns fuel (absorbs heat from a high-temperature source) to produce mechanical work that moves the car. However, not all the heat energy from the combustion is converted into work. A significant amount of heat is expelled through the exhaust system and dissipated by the radiator into the surrounding air (the cold sink). This rejection of waste heat is necessary, demonstrating that 100% conversion of heat to work is impossible, just as the Kelvin-Planck statement says.
3. What are the essential components of a heat engine as related to the Kelvin-Planck statement?
A heat engine, as described in thermodynamics, must have three essential components for its operation:
- Source: A hot reservoir at a high temperature (T₁) from which the engine absorbs heat (Q₁).
- Working Substance: A substance (like a gas in a cylinder) that undergoes a cyclic process to convert heat into work.
- Sink: A cold reservoir at a lower temperature (T₂) to which the engine must reject a certain amount of waste heat (Q₂).
4. Why is it impossible for a heat engine to have 100% efficiency according to the Kelvin-Planck statement?
A heat engine cannot achieve 100% efficiency because it must operate in a continuous cycle. To return the working substance (e.g., gas in a piston) to its initial state to start a new cycle, it must release some of its heat energy. This heat is rejected to a lower temperature reservoir, known as the sink. Without rejecting this waste heat, the cycle cannot be completed, and the engine would stop after a single expansion. Therefore, some heat input is always 'wasted' and not converted into work, making 100% efficiency physically unattainable.
5. How does the Kelvin-Planck statement relate to the concept of a Perpetual Motion Machine of the Second Kind (PMM2)?
A Perpetual Motion Machine of the Second Kind (PMM2) is a hypothetical device that would absorb heat from a single thermal reservoir and convert it entirely into work. Such a machine would not violate the first law of thermodynamics (conservation of energy), but it would directly violate the Kelvin-Planck statement. The statement essentially forbids the existence of a PMM2 by asserting that a cold sink is always required for a heat engine to operate.
6. What is the key difference between the Kelvin-Planck and the Clausius statements of the second law of thermodynamics?
While both are equivalent expressions of the second law, they focus on different processes. The Kelvin-Planck statement deals with the conversion of heat into work, stating that no heat engine can be perfectly efficient. The Clausius statement deals with the transfer of heat, stating that it is impossible for heat to spontaneously flow from a colder body to a hotter body without external work being done. In essence, Kelvin-Planck addresses limitations on engines, while Clausius addresses limitations on refrigerators or heat pumps.
7. What are some real-world applications that operate based on the principles described by the Kelvin-Planck statement?
The principles underlying the Kelvin-Planck statement are fundamental to any device that converts thermal energy into mechanical work. Key applications include:
- Internal Combustion Engines: Found in cars, trucks, and motorcycles.
- External Combustion Engines: Such as steam engines used in thermal power plants.
- Gas Turbines: Used in jet aircraft and for power generation.
- Power Plants: Including thermal, nuclear, and geothermal plants, all of which use a heat source to run a turbine and generate electricity.
8. If a heat engine cannot convert all heat to work, where does the remaining energy go, and why is this necessary?
The remaining energy is rejected as waste heat to a colder reservoir, commonly called the sink (e.g., the surrounding atmosphere or a body of water). This rejection is not just a byproduct; it is a fundamental necessity for the engine's operation. To work continuously, the engine must complete a cycle, returning its working substance to its original state. This reset is only possible if the substance is cooled down by transferring heat to the sink. Without this step, pressure would not drop, and the cycle could not repeat to produce continuous work.
