Engineering Thermodynamics (2131905)

Guided by :Prof. Nita R. Patel

Prepared By : Name : Shah Preet .P.Enroll. No. : 160410119117Batch : CDept : Mechanical

Topic : Entropy

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TopicTopic Entropy Change During

Thermodynamic Process

Entropy Change For Pure Substances

Third Law Of Thermodynamics (Nernst Law)

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Entropy Change During Entropy Change During Thermodynamic ProcessThermodynamic Process

Let m Kg of gas at a pressure P , volume V , ₁ ₁absolute temperature T and entropy S , be ₁ ₁heated by any thermodynamic process.Its final pressure, volume, temperature and entropy are P , V , T and S respectively.₂ ₂ ₂ ₂

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Law Of Conservation Of EnergyLaw Of Conservation Of Energy

Q = dU + W,δ δ

Where, Q = small change in heatδdU = small change in internal energy W = small change of work doneδdT = small change in temperaturedv = small change in volume

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Q = mC dT + pdvδ ᵥ

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Change Of Entropy Of Different Change Of Entropy Of Different Processes Processes 1. Constant Volume Process2. Constant Pressure Process3. Constant Temperature Process4. Reversible Adiabatic Process5. Irreversible Adiabatic Process6. Polytropic Process

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Heating A Gas At Constant Heating A Gas At Constant Volume ProcessVolume ProcessConsider a m Kg of perfect gas being

heated at a constant volume process. Heat supplied at constant volume

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Heating A Gas At Constant Heating A Gas At Constant Pressure Pressure Consider a m Kg of perfect gas being

heated at a constant Pressure process. Heat supplied at constant Pressure

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Isothermal Process Or Constant Isothermal Process Or Constant Temperature Process Temperature Process Consider a m Kg of perfect gas being

heated at a constant temperature during expansion process.

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Reversible Adiabatic ProcessReversible Adiabatic Process In the adiabatic process, heat is neither supplied to system or

rejected by the system.

This shows that the change of entropy during a reversible adiabatic process is zero, the T-S graph is shown by line 1-2.

The entropy of the gas remains constant during reversible adiabatic expansion or compression of the gas, this process is said to be isentropic process.

It is frictionless adiabatic process.

In this, change in internal energy is equal to the work done by the gas during expansion .

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Irreversible Adiabatic ProcessIrreversible Adiabatic Process

If adiabatic process with internal friction, it is known as irreversible adiabatic process.

If the irreversible adiabatic expansion process takes place between same temperature limits T₁ and T₂ then due to internal friction, the internal energy of the gas at the end of expansion will be more than at point 2 of reversible process.

Suppose, δQ’ heat gain by gas due to internal friction then the increase of entropy will be given by,

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It means that higher entropy at the end of expansion of irreversible process, therefore work done by gas will be less than that of reversible process.

Mathematically,

U₁ - U₂ = W, dS = 0 for reversible adiabatic process

U₁ - U’₂ = W’ dS > 0 for irreversible adiabatic process

Where,

U’₂ = internal energy of gas at the end of irreversible expansion

U₂ = internal energy of gas at the end of reversible expansion

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Polytropic ProcessPolytropic ProcessConsider a m

quantity of perfect gas being expanded by polytropic process.

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Entropy Change For Pure Entropy Change For Pure SubstancesSubstances

Consider (M) Kg of ice is heated continuously at constant atmospheric pressure.

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T₁ = initial temperature of ice T₂ = melting temperature of ice = 0C =

273 KT = boiling temperature of water =100C T = superheated steam temperatureᵤCᵨ = specific heat of ice ᵢCᵨ = specific heat of waterᵥᵥCᵨ = specific heat of steam

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Process 1-2 Sensible Heating Of Ice Process 1-2 Sensible Heating Of Ice Temperature of ice increase from T to ₁

T . Change of entropy during 1-2₂

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Process 2-3 Melting Of IceProcess 2-3 Melting Of Ice On further heating of ice is converted

into water at constant temperature T ₂(0C).

The heat supplied is utilized to change phase called latent heat of fusion of ice (h ).ᵢ

Therefore Q = mhᵢ Change of entropy during process

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Process 3-4 Sensible Heating Of Process 3-4 Sensible Heating Of WaterWaterWater from T is heated to water at T₂ .Change of entropy during process

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Process 4-5 Boiling Of WaterProcess 4-5 Boiling Of WaterOn further heating of water, is

converted into steam at constant temperature T .

The heat supplied is utilized to change phase called latent heat of evaporation.

Change of entropy during process.

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Process 5-6 Sensible Heating Of Process 5-6 Sensible Heating Of SteamSteamTemperature of steam increases from Ts

to Tsup .

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Third Law Of Thermodynamics Third Law Of Thermodynamics (Nernst Law)(Nernst Law)

Entropy is a measure of molecular randomnessAt absolute zero temperature molecules become completely motionless.The entropy of a pure crystalline substance at absolute zero temperature is zero since there is no uncertainly about the state of the molecules at that instant.

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This is third law of thermodynamics which states that

“ The entropy of all perfect crystalline substance (Solid) is zero at absolute zero temperature”. In equilibrium crystalline state, its atoms are arranged in a pattern that represents the maximum degree of order, and if it also at absolute zero temperature there must be a minimum of disordering thermal motion.Mathematically,

The third law of thermodynamics provides an absolute reference point for the determination of entropy. The entropy determined relative to this reference point is called absolute entropy.

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ApplicationApplication

1. Provides an absolute reference point for the determination of entropy.

2. Explaining the behaviour of solids at very low temperature.

3. Measurement of action of chemical forces of the reacting substances.

4. Analysing the chemical and phase equilibrium.

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Thank YouThank You

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