Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mechanical Engineering SSC JE (Technical)

Mechanical Engineering : Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

The document Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Mechanical Engineering SSC JE (Technical).
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ENTROPY

  • Two reversible adiabatic paths cannot intersects each other which violates the Kelvin - Plank's statement.
  • Clausius Theorem

Any reversible path may be substituted by a reversible zigzag path between the same end states, consisting of a reversible adiabatic followed by a reversible isotherm and then by reversible adiabatic such that the heat transferred during the isothermal process is the same as that transfered during the original process.

  • The cyclic integral of  (dQ/T)  for a reversible cycle is equal to zero.

    Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev
  • Entropy: 

The entropy of a system is a thermodynamic property which is a measure of the degree of molecular disorder existing in the system. It describes the randomness or uncertainity of the system, It ios a function of a quantity of heat which shows the possibility of conversion of heat into work. Thus, for maximum entropy, there is minimum availability for conversion into work and for minimum entropy there is a maximum availability for conversion into work.

Characteristics:

  1.  It increases when heat is supplied irrespective of the fact whether temperature changes or not.
  2.  It dectreases when heat is removed whether the temperature changes or not.
  3.  It remains unchanged in all adiabatic reversible processes.
  4.  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.

 Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  •  For reversible adiabatic process

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

=> dS = 0 (∵ dQ = 0)
∴ S = constant

Thus a reversible adiabatic process is an isentropic process.

  •   For reversible isothermal process

At a temperature, To

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

CLAUSIS' INEQUALITY

The Clausius theorem (1855) states that a system (heat engine or heat pump) exchanging heat with external reservoirs and undergoing a cyclic process, is one that ultimately returns a system to its original state,

                                                        ∮                                                              ⁡                                            δ              Q                                      T                              s                u                r                r                                                    ≤        0        ,              {\displaystyle \oint {\frac {\delta Q}{T_{surr}}}\leq 0,}   

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

whereChapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev                    δ        Q              {\displaystyle \delta Q}    is the infinitesimal amount of heat absorbed by the system from the reservoir andChapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev                              T                      s            u            r            r                                {\displaystyle T_{surr}}    is the temperature of the external reservoir (surroundings) at a particular instant in time. 

Remember:-

Equality sign holds good for a reversible process and the inequality sign for an irreversible process.
 Entropy principle:

For an isolated reversible system
Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

For an isolated irreversible system

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

The total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy.
• It is also a statement of second law of thermodynamics.
• Entropy increase of the isolated system is a measure of the extent of irreversibility
of the process under gone by the system.
• When the system is at equilibrium, any conceivable change in entropy would be
zero.
Application of entropy principle
• Transfer of heat through a finite Temperature difference.

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mixing of two fluids

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Final temp (tf) =

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Maximum work obtainable from two finite identical bodies at T1 and T2.

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Final temperature of the two bodies (Tf) = 

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • The final temperature of two bodies initally at T1 & T2, can range from (T1 + T2)/2 with no delivery of work to

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev with maximum delivery of work.

  • Maximum work obtained with finite body & TER

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

T = temp. of body
To = temp. of TER

  •  Adiabatic dissipation of work

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Adiabatic process vs Isentropic process
    • If isentropic process is reversible, it must be adibatic.
    • If isentropic process is adiabatic, it must be reversible.
    • An adiabatic process may not be isentropic because entropy may change due to friction, internal irreversibility etc.
    • If the adiabatic process is reversible, it must be isentropic.
  •  Change in entropy of a system is due to heat transfer and internal irreversibility (entropy generation.)

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

  • Entropy is a point function but entropy generation is a path function.
EquationHolds good for
dQ = dE+ dWReversible, Irreversible, any system
dQ = dU + dWReversible, Irreversible, Closed System.
dQ = dU + pdVReversible, Closed system
dQ = TdSReversible
TdS = dU + PdVReversible, Irreversible, Closed system
TdS = dH – VdpReversible, Irreversible, Closed system
  • Entropy change of a system (solid, liquid ) when its temperature changes from T1 to T2.

Chapter 7 Entropy - Thermodynamics, Mechanical Engineering Mechanical Engineering Notes | EduRev

c : specific heat for solid, liquid

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