Concepts of entropy
- 1. Concepts of Entropy & Third law of Thermodynamics
- 2. CLAUSIUS INEQUALITY • The Clausius theorem states that a thermodynamic system (e.g. heat engine or heat pump) exchanging heat with external reservoirs and undergoing a thermodynamic cycle, • where is the infinitesimal amount of heat absorbed by the system from the reservoir and is the temperature of the external reservoir (surroundings) at a particular instant in time. The closed integral is carried out along a thermodynamic process path from the initial/final state to the same initial/final state. In principal, the closed integral can start and end at an arbitrary point along the path. • If there are multiple reservoirs with different temperatures then Clausius inequality reads:
- 3. • In the special case of a reversible process, the equality holds.The reversible case is used to introduce the state function known as entropy. This is because in a cyclic process the variation of a state function is zero. In other words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir. Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around. • The generalized "inequality of Clausius“ for an infinitesimal change in entropy S applies not only to cyclic processes, but to any process that occurs in a closed system.
- 4. Concept of Entropy • “Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work. The increase in entropy is small when heat is added at a high temperature and is greater when heat addition is made at a lower temperature. Thus for maximum entropy, there is minimum availability for conversion into work and for minimum entropy there is maximum availability for conversion into work.”
- 5. Entropy Change During Thermodynamic Process • Let m Kg of gas at a pressure P1, volume V1 , absolute temperature T1 and entropy S1, be heated by any thermodynamic process. • Its final pressure, volume, temperature and entropy are P2 , V2 , T2 and S2 respectively.
- 6. Law Of Conservation Of Energy • δ Q = dU + W, Where, • δQ = small change in heat • dU = small change in internal energy • δW = small change of work done • dT = small change in temperature • dv = small change in volume • δQ = mC dT + pdv
- 7. Dividing the equation by T
- 10. Entropy Change For Pure Substances • Consider (M) Kg of ice is heated continuously at constant atmospheric pressure.
- 11. • T₁ = initial temperature of ice • T₂ = melting temperature of ice = 0C = 273 K • T = boiling temperature of water =100C • Tᵤ = superheated steam temperature Cᵨᵢ = specific heat of ice • Cᵨᵥᵥ = specific heat of water • Cᵨ = specific heat of steam
- 12. Process 1-2 Sensible Heating Of Ice • Temperature of ice increase from T to ₁ T . Change of entropy during 1-2
- 13. Process 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
- 14. Process 3-4 Sensible Heating Of Water • Water from T is heated to water at T ₂ . • Change of entropy during process
- 15. Process 4-5 Boiling Of Water • On 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.
- 16. Process 5-6 Sensible Heating Of Steam • Temperature of steam increases from Ts to Tsup
- 17. T ds Equations • The differential form of the conservation of energy equation for a closed stationary system (a fixed mass) containing a simple compressible substance can be expressed for an internally reversible process as
- 18. • This equation is known as the first T ds, or Gibbs, equation. Notice that the only type of work interaction a simple compressible system may involve as it undergoes an internally reversible process is the boundary work. The second T ds equation is obtained by eliminating du from Eq. 7–23 by using the definition of enthalpy (h u Pv): • These T ds relations are developed with an internally reversible process in mind since the entropy change between two states must be evaluated along a reversible path. However, the results obtained are valid for both reversible and irreversible processes since entropy is a property and the change in a property between two states is independent of the type of process the system undergoes.
- 19. • Explicit relations for differential changes in entropy are obtained by solving for ds in Eqs:-
- 20. Third law of Thermodynamics • The third law of thermodynamics is stated as follow : ‘‘The entropy of all perfect crystalline solids is zero at absolute zero temperature’’. • The third law of thermodynamics, often referred to as Nernst Law, provides the basis for the calculation of absolute entropies of substances.
- 21. • According to this law, if the entropy is zero at T = 0, the absolute entropy sab. of a substance at any temperature T and pressure p is expressed by the expression.
- 22. • Thus by putting s = 0 at T = 0, one may integrate zero kelvin and standard state of 278.15 K and 1 atm., and find the entropy difference. Further, it can be shown that the entropy of a crystalline substance at T = 0 is not a function of pressure, viz. • However, at temperatures above absolute zero, the entropy is a function of pressure also. The absolute entropy of a substance at 1 atm pressure can be calculated using eqn; for pressures different from 1 atm, necessary corrections have to be applied.
- 23. Application • Provides an absolute reference point for the determination of entropy. • Explaining the behaviour of solids at very low temperature. • Measurement of action of chemical forces of the reacting substances. • Analysing the chemical and phase equilibrium.