Second Law of Thermodynamics in Terms of Entropy

If a body or engine is taken from one curve to another curve at approximately the same temperature in such a way that dQ of heat is exchanged. This is the second law of thermodynamics in the form of entropy.

Change in entropy ds = dQ/dT

dQ = T ds

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Availability and Irreversibility in Thermodynamics

Availability and immutability can be defined as follows

Availability in Thermodynamics 

When a system absorbs heat and gives the maximum possible work, it operates in a state of a reversible process, after which it reaches equilibrium with the environment. If the work done by the system is maximum then it is called the availability of the system.

Now if a system is in equilibrium with the environment, all final states of the system and the environment are at temperature and pressure, then the force maintains zero velocity and the minimum required potential energy.

Reversible Work = Ψ1 - Ψ2

Ψ = Potential state - final state with corresponding area

= h [h - ToS - v²/2g + g/gc z] - [ h0 - To So + g/gc z²]....(i)

Ψ1 - Ψ2 = h1 - h2 to (S1 - S2) + v1² - v2²/2gc + ( z1 -z²)g/2g .....(ii)

Availability can of course be known as an initial state because it is a property of the entity. Therefore, availability is a property of thermodynamics both at the entrance and exit of the system. And availability should be a reversible function between the two states.

At equilibrium

Reversible Work = Ψ1 - Ψ2 

Availability formula 

h1 - h2 -To (S1 - S2) + v1² - v2²/2gc + ( z1 -z²)g/2g

Where

h1 = Entropy of inlet per unit.

h2 = Entropy of outlet per unit.

z1 = Elevation inlet

z2 = Elevation outlet 

Irreversibility in Thermodynamics 

Reversible work for steady state flow process

W = (h1 - h2) -To (S1 - S2) + v1² - v2²/2gc + g/2g( z1 -z²) .......(i)

Reversible work for the flow process

W = (h1 - h2) -To (S1 - S2) + v1² - v2²/2gc + g/2g( z1 -z²) .......(ii)

Equations (i) and (ii) get reversible work which is maximum work and the heat difference is with the environment only. Apart from this, all real work except products and all real processes are organized for definite Irreversible. All real work is reversible. is less than or equal to work.

W actual = W reversible

Irreversible can be defined by this process.

I = Wr - Wac

Numerical Problem Thermodynamics

Q. The change in specific heat Cp of a substance with temperature T is expressed by the following equation Cp = a + bT + CT² set up an expression for the entropy change?

Solve: Transfer heat when dT changes in the temperature of the substance at temperature T. dQ = Cp dT Change of entropy of a substance

dS = dQ/T = (a + bT + CT²/T) dT

or∫dS = ∫(a + bT + CT²/T)dT

S = a + bT + CT²/2