CARNOT HEAT ENGINE AND CONCEPT OF ENTROPY IN THERMODYNAMICS

We were discussing the concept of heat engine and heat pump in our previous post. We have also discussed the basics of a reversible and irreversible thermodynamics process with the help of few examples too. We have also seen the concept of Carnot’s theorem and its explanation in our previous posts.

Today we will see here the concept of Carnot engine and introduction of entropy in the field of thermal engineering, first we will see here the Carnot engine and after that we will see the introduction of entropy with the help of this post.

So let us see first Carnot engine

Carnot heat engine is basically defined as one heat engine which works on the fundamental of reversible Carnot cycle. Carnot had provided the concept of an ideal cycle which was termed as Carnot cycle and it was having the following four reversible processes as mentioned below.

Reversible isothermal expansion process of heat addition
Reversible adiabatic expansion process
Reversible isothermal compression process of heat rejection
Reversible adiabatic compression process

Carnot cycle /Carnot heat engine

We have already discussed the complete fundamentals of a Carnot cycle and we have also determined the efficiency of a Carnot cycle in our post “Carnot cycle and its efficiency”. Therefore find here the post Carnot cycle and its efficiency in order to secure the basics of a Carnot cycle.

In simple words we can say that heat engine that will be operated according to the concept of a Carnot cycle will be termed as Carnot engine.

Introduction to entropy

The concept of entropy is quite simple. It is observed that all heat energy supplied to the system will not be equally important or valuable during conversion in to the work energy. Heat energy, which will be supplied at higher temperature to the system, will have more possibilities for conversion in to the work energy. While in other hand heat energy, which will be supplied at lower temperature to the system, will have least possibilities for conversion in to the work energy.

Entropy is basically defined as the function of a heat quantity that indicates the possibility of conversion of that heat quantity in to work energy. Increment in entropy will be small when heat energy will be supplied to the system at higher temperature while in other hand increment in entropy will be higher when heat energy will be supplied to the system at lower temperature.

Therefore,it could be expressed that for the maximum entropy there will be least availability of conversion in to work energy and for minimum entropy there will be much availability of conversion in to work energy.

As we know that for a reversible heat engine or cycle, we will have following equation as mentioned here

Q₁/Q₂ = T₁/T₂

Q₁/T₁ = Q₂/T₂

Q₁/T₁ + (-Q₂) /T₂ = 0

As we know that differential of a point function will be zero and therefore,

Where we have assumed S is one point function here, therefore

dS = dQ/T

If a system which is reversible from state 1 to 2, when heat energy will be supplied to a thermodynamic system by a reversible process, the change in entropy in the thermodynamic system will be expressed as mentioned here.

This is the entropy and entropy is basically dependent on initial and final state of thermodynamic system and it does not depend over the path followed during the process.

We will see another topic i.e. “First law of thermodynamics for closed system undergoing a cycle” in our next post in the category of thermal engineering.

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