Entropy and Second Law of Thermodynamics

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CHAPTER-20

• Entropy and Second Law of Thermodynamics

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CHAPTER-20 Entropy and Second Law of
Thermodynamics

1. Topics to be covered
2. Reversible processes
3. Entropy
4. The Carnot engine
5. Refrigerators
6. Real engines

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Ch 20-2 Irreversible Process and Entropy

• Irreversible Process One way process
• If the irreversible process proceed in a closed
  system in a reverse way, we will wonder about it.
  A melted piece of ice freezes by itself. Although
  from energy conservation, the process can proceed
  in the reverse path i.e.heat released in in the
  environment in melting ice can be recovered back
  into ice piece to solidify it . Energy
  conservation does not prohibit the process to
  proceed one way or the reverse way.
• Which parameter the one ay direction of the
  process?.
• Entropy set the direction of irreversible process
  and irreversible process proceed through that
  path in which entropy of the system always
  increases
• Entropy Postulate If an irreversible process
  occurs in a closed system, the entropy S of the
  system always increases

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Ch 20-2 Irreversible Process and Entropy

• Change in entropy (The arrow of time)-time
  reversal impossible due to entropy violation
• Entropy definition Two methods
• Using systems temperature and heat loss/gain by
  the system
• By counting the ways in which the atoms or
  molecules of the system can be arranged
• Entropy S state property like P,V,T, S
• Change in entropy ?S?Q/T
• ?SSf-Si?fi ?Q/T

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Ch 20-3 Change in Entropy

• Free Expansion of an ideal gas- Irreversible
  Process
• An ideal gas expands from i to f state in an
  adiabatic process such that no work is done on or
  by the gas and no change in the internal energy
  of the system i.e. TiTf piVipfVf W?Eint0
• ?SSf-Si?fi ?Q/T
• Integral from i to f cannot be solved for an
  irreversible process but can be solved for a
  reversible process.
• Since S is state variable (?Sif)rev (?Sif)irrev
• ?Sirrev ?Srev Sf-Si ?fi ?Q/T (irreversible)
• To find the entropy change for an irreversible
  process in a closed system, replace that process
  with any reversible process that connects that
  connects same initial and final states and
  calculate its change in entropy

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Ch 20-3 Change in Entropy

• Calculation of Entropy in Reversible Process
• In free expansion TiTf, i.e. isothermal process
  then reversible isothermal expansion process can
  be used to calculate change in entropy in free
  expansion. Then
• ?Srev Sf-Si ?fi ?Q/T 1/T?fi?Q (isothermal)
• An ideal gas confined in a insulated cylinder
  fitted with a piston . The cylinder rest on a
  thermal reservoir maintained at temp T.
• Gas is expanded isothermally from I to f state
  and heat is absorbed by the gas from the
  reservoir.?S is positive because ?Q is positive
• ?S Sf-Si ??Q/T

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Ch 20-3,4 Change in Entropy, Second Law of
Thermodynamics

• Entropy as a State function
• ?S Sf-Si ??Q/T but
• ?Eint?Q-W or ?Q ?EintW WpdV ?Eint nCV?T
  
• Then ?S ? ?Q/T ?if (nCVdT/T) ?if (pdV/T)
• nCV ?if (dT/T) ?if (nRdV/V)
• ?S nCV ln(Tf/Ti) nR ln(Vf/Vi)
• Second Law of Thermodynamics
• In a closed system entropy remains constant for
  reversible process but it increases for
  irreversible process.
• Entropy never decreases
• Change in Entropy of a reversible compression of
  an ideal gas in a closed system reservoir gas
• ?Ssys ?Sgas ?Sres -Q/TQ/T0

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Ch 20-5 Entropy in Real World Engines

• A Carnot engine is a device that extracts heat QH
  from a reservoir at temperature TH, does useful
  work W and rejects heat QL to a reservoir at
  temperature TL.
• On a p-V diagram Carnot cycle ( executed by a
  cylinder fitted with a piston and in thermal
  contact with one of two reservoirs at
  temperatures TH and TL.) is bound by two
  isotherms and two adiabatic.

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Ch 20-5 Entropy in Real World Engines

• Heat QH is absorbed at Temperature TH and heat QL
  is rejected at TL.
• Work According to first law of thermodynamics,
  ?Eint?Q-W, ?Eint0
• and W?Q?QH?-?QL?
• Entropy Change ?S
• In Carnot cycle ?S0
• ?S0 QH/TH-QL/TL
• QH/THQL/TL

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Ch 20-5 Entropy in Real World Engines

• Thermal Efficiency of an Engine ?
• ? work we get /energy we pay for
• ? ?W?/ ?QH?
• For a Carnot engine W?QH?-?QL?
• Then Carnot engine efficiency ?C is
• ?C ?QH?-?QL?/?QH?
• ?C1-?QL?/?QH?1- ?TL?/?TH?
• There is no perfect engine i.e. QL0

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Ch 20-6 Entropy in Real World Refrigerators
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Ch 20-6 Entropy in Real World Refrigerators

• A Refrigerator A device that uses work to
  transfer energy QL from a low temperature
  reservoir at temperature TL to a high-temperature
  reservoir at temperature TH
• Coefficient of performance of a refrigerator K
• K what we want /what we pay for
• K?QL?/?W? but W?QH?-?QL?
• K ?QL?/?W??QL?/?QH-?QL?
• K ?QL?/?QH? ?TL?/?TH?-1
• KTL/(TH-TL)
• There is no perfect refrigerator i.e. W0