Entropy Notes for SSC JE & Other AE JE Exams

Introduction of Entropy

The word 'entropy' was first used by Clausius, taken from the Greek word `tropee’ meaning `transformation’.Entropy is a thermodynamic property that measures the degree of randomization or disorder at the microscopic level.

A macroscopic feature that is associated with entropy production is a loss of ability to do useful work and sometimes it is said that there is a decrease in the availability of energy. The notion that entropy can be produced, but never destroyed, is the second law of thermodynamics.

The Clausius Inequality

The first law is just a balance of energy. The second law states an inequality ie an irreversible process is less efficient than a reversible process. One of such important inequalities is that of the Clausius inequality in Thermodynamics according to which the cyclic integral of δQ / T is always less than or equal to zero. It is valid for all cycles, be it reversible or irreversible.

Temperature-Entropy Plot

The infinitesimal change in entropy dS due to reversible heat transfer dQ at temperature T is

Now dQ_rev, = TdS

Thus, area under the T -S plot on S axis will give the heat transfer in a reversible process.

Fig.: Area under a reversible path on the T-s plot

The Increase of Entropy Principle

Consider a cycle that is made up of two processes:

Process 1-2, which is an arbitrary process (reversible or irreversible),

and Process 2-1, which is internally reversible in nature, as shown in the Figure below,

Fig.: Combination of reversible & irreversible process

where the equality is for the reversible process and inequality for the irreversible process.

Note that the entropy generation S_gen is always a positive quantity or zero. Its value depends on the process, and thus it is not a property of the system.

For an isolated system, 

dQ = 0 since no energy interaction occurs between the system and the surrounding.

Therefore, for an isolated system

dS_iso ≥ 0

For a reversible process,

 dS_iso = 0

implies, S = constant

 For an irreversible process

dS_iso > 0

Entropy change of the system:

Entropy charge of the system is summation entropy change due to internal irreversibility and entropy change due to external interaction

T-dS EQUATION

The relation between entropy, temperature, volume and pressure are:

........(1)

........(2)

Equations (1) & (2) are applicable for both reversible processes as well as the irreversible process because they contain all properties.

Applications of Entropy Principle

For every irreversible process, there is an increase of entropy of the universe, and this entropy increase determines the extent of the irreversibility of the process. The higher the entropy increase of the universe; the higher will be the irreversibility of the process.

Some of the applications of the entropy principle are illustrated in the following.

(A) Heat transfer through a Finite Temperature Difference.

(B) Two fluids mixing with each other.

(C) Maximum Work that can be obtained from Two Finite Bodies at Temperatures T₁ and T₂ interacting in a reversible manner.

The sources of energy can be divided into two groups i.e., high-grade energy (mechanical work, electrical energy, water power, wind power) and low-grade energy (heat or thermal energy, heat derived from nuclear fission or combustion of fossil fuels). That part of the low-grade energy which is available for, conversion is referred to as available energy, while the part which is not available is known as unavailable energy.

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