Dear Katyal

The second law of thermodynamics known as a non-reversible law, that means at any movement of the system boundary there is an entropy generation this called the entropy generation due to the work. As well as the heat transfer to the system causes two types of entropy, the first one is the entropy generation and the second is the entropy transport.

The entropy generation due to work and heat always greater than zero. While the entropy transport due to the heat transfer can be negative or positive depending on the direction of heat flow. Thus, the heat flow to the system produced useful work and part of the heat is lost as entropy generation and entropy transport.

Dear Amit Katyal:

Regards, Personally I'm always fascinated with the Second Law and its implications.

You are 100 % correct on your statements mentioned above.

The way you described it, as: "all of the heat added to a system cannot be used to do useful work" ... "so all of the heat added to a system cannot be used to do useful work?" is historically the way Lord Kelvin (Sir William Thomson) used to state it, trying to give it a more engineering approach to its implications. It is known as the Kelvin Statement of the 2nd Law.

As for the Entropy,

Entropy always has to increases in a closed system, the source of Entropy are the irreversibilities of the System and the process. So in any transformation between the different types of energies, entropy must be generated, this is why sometimes the 2nd Law it is also stated in a mathematical form as:

dS_system >= 0 (remember, for Closed systems)

So the concepts of Thermodynamic Entropy and the Second Law are two of which always coexist together, and you can get useful insights with one or the other.

Regards !

The Kelvin-Planck statement states that it is impossible to build a machine that has a 100% yield. There will always be waste heat, which in most cases amounts to more than half of the heat absorbed. This is an echo that affects all types of thermal plants that generate electricity, refrigeration machine, internal combustion engine, or any thermal machine of this nature.

All answer are well explain one more thing I would like to add ,It is impossible to develop a reversible system it means all available systems in universe are Irreversible. So change in entropy of system will be always greater than zero. If there is more irreversibility means more entropy less irreversibility means less entropy. Irreversibility of system will depends on internal and external thermodynamic conditions. So it is impossible to convert 100% of heat energy in to mechanical energy or exergy. Heat is a low grade energy i.e losses takes place during the conversion. Kelvin Plank Statement is "it is impossible to developed a heat engine that work on thermodynamic cycle and single reservoir" Or you can say It is impossible to developed a heat engine having 100% efficiency.it means certain part of heat energy get loosed during conversion.

Thanks for the answers.

Can we combine first and second law of thermodynamics as

dQ=dW + dU +TdS

Dear Amit Katyal, Thank you for initiating this interesting thread :

The First Law of Thermodynamics is basically the Law of Conservation of energy for closed systems, it is written (in its differential form) as:

dU = deltaQ + deltaW

The First Law describes Energy changes of the system, not the Energy itself. The equation above means that in a closed thermodynamic system there are two ways to increase or decrese the energy of the system; by doing (extracting) Work on (from) the system and/or by adding (removing) Heat to (from) the system.

Two important things to point out from the above equation:

1. dU is an exact differential, since U, the Internal Energy, is a state function (meaning that its variation just depend on the initial and final states of the system). On the other hand, deltaQ and deltaW are inexact differentials, since they are path-dependent quantities (its changes intrinsically depend on the process).

2. In the way I wrote the First Law, Q and W are positive when they are added to the system.

By contrast to the First Law, The Second Law is not a conservation Law.

The second Law describes the impossibilities of reversible processes in day-to-day systems. Another way to say this is: It accounts for the irreversibilities of a system or a process.

Often it is written in a mathtematical form as:

dS_closed system >= 0

This equation litterally means that the Entropy of a closed system can at best kept unchanged. But this is an ideal scenario, this is why the Entropy in the above formula is in its differential form. Because, for the change in Entropy of a process to be = 0, the change should have to be infinitely small (in time for example), and proccesses in nature are does n't happen with an infinitely small rate of change.

The First Law and Second Law are two principles which are independent on each other. Each of it which describes the evolution of the system in different aspects, and involves different quantities.

So, algebraically, they cannot be combined in a single equation

Best Regards ! :)

But second law states that heat cannot be converted 100% to work. As per first law heat is used in doing work and raising the internal energy. Internal energy can be negative if it is transferred to surrounding making perpetual motion machine of first kind possible. Concept of entropy was introduced to make perpetual motion machine of second kind impossible even when perpetual motion machine of first kind was possible. Also dQ =TdS.

Is it not correct?

Dear Amit Katyal :

I guess you are right in those statements, just one thing,

deltaQ = TdS is not the form of the Second Law, is the definition of Thermodynamic Entropy. these are two different things.

Regards !

If dQ=TdS is not applicable for second law then what is the relationship between dQ and dS for second law? DeltaQ=TdS for reversible systems. For irreversible systems DeltaQ

Dear Amit Katyal:

deltaQ=TdS is not named as a Law of Thermodynamics, is just the definition of the Thermodynamic Entropy, is the way, historically, Clausius defined this property. Is a mathematical definition, more commonly written as: dS=deltaQ/T .

If you got to review any book on Thermodynamics in Mechanical Engineering at undergraduate level, you will find this expression for the definition of Entropy,

Of course there is a relation between Heat, Entropy, and the Second Law of Thermodynamics, this is Clausius Inequality :

Closed integral(deltaQ/Tsurroundings)

BTW, regarding to Clausius Inequality:

DELTA(S) in the expression DELTA(S)= Closed integral(deltaQ/T) is the change in Entropy of the system, which is the only magnitude we can calculate, in opposition with the absolute Entropy.

Is not possible to know the absolute Entropy of a System's state, since just the change in Entropy can be known for macroscopic processes, except for one case, and I suppose approximately, for a few "finely tunned" systems:

In the absolute zero is possible to calculate the absolute Entropy of a system (a state which is physically impossible to get to, this time mainly due to the limitations of Quantum Mechanics)

But, I guess you can approximate some systems which its Total Energy is close to its Energy of its Ground State. Maybe systems such as: Bose-Einstein Condensates or some Superfluids, as He3+ and He4+ . Maybe these systems do can be studied attempting to calculate its Entropy value instead of just changes on it.

So, is worth so say that DELTA(S) in the above eq. represents the change in Entropy of a Macroscopic non-reversible process.

Regards !