Kelvin Planck 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 into 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 to be added soon)
So, Kelvin Planck statement talks of an ideal heat engine that extracts heat and transform 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 the 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 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
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 statement states that practically we cannot construct PMMSK.
You can view its image below:
(Image to be added 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 into our minds.
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 statement is related to the heat engine, so what is a heat engine?
A heat engine comprises three fundamental parts:
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).
W = Q1 - Q2
Now, let’s calculate the thermal efficiency of the engine
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.