2nd Law of Thermodynamics

1
2nd Law of Thermodynamics

• 1st Law energy is conserved
• But is that enough ?
• Object drops converting KE to heat but never see
  the opposite
• H2 and O2 react to form H2O when ignited at room
  temperature but not the reverse
• 1st Law would permit the reverse but 2nd Law does
  not.

2
Irreversibility

• A flywheel is spinning in a fluid in an isolated
  box.
• Eventually flywheel (and gas) slow down and stop
  the fluid is now hotter.
• KE flywheel has been converted to Ufluid
• Organized motion has become random
• Reverse does not happen by itself

3
Entropy

• Mechanical energy organized generally more
  useful than heat random i.e., its more
  valuable form of energy (e.g., flywheel can drive
  a generator directly).
• Entropy (S) is a measure of the
  disorder/randomness of a system.
• Systems naturally tend towards disorder.

4
Properties of the Entropy

• Entropy increases with increases disorder,
  reduced useful energy.
• Entropy can only be created not destroyed. (2nd
  Law)
• Production Ps ?S
• Isolated system Ps ?S

5
Isolated System

• Can imagine 3 types of processes
• Ps lt 0 impossible (2nd Law)
• Ps 0 reversible process energy flow between
  thermal, mechanical, etc reversible.
• Ps gt 0 irreversible to reverse need S to
  decrease - not in isolated system

6
Non-Isolated System

• Two types of reversible flow possible
• Internally reversible, system always proceeds
  through equilibrium states with no entropy
  production
• Totally reversible no entropy production in both
  system and surroundings
• Reversible processes are idealizations.

7
Entropy Transfer

• Rigid walled cylinder containing H2O
• At t1 mostly ice, at t2 mostly liquid
• Liquid more random S2 gt S1
• Where does the entropy come from ?
• Process is reversible overall Ps for water
  0 how is entropy reduced during freezing ?

8
Entropy Transfer

• Heat transfer can lead to entropy transfer.
• As T increases in colder system, its randomness
  increases and vice versa.
• Work represents organized energy
• Work does not transfer entropy unless it is
  done irreversibly.

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2nd Law for Closed System

• Two approaches for developing mathematical
  formulation
• Postulate existence of entropy and relate to
  temperature Reynolds Perkins, Engineering
  Thermodynamics, McGraw Hill
• Observe behavior of devices (cycles) and develop
  the concept of temperature Black and Hartley,
  Thermodynamics, HarperCollins

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Deriving the 2nd Law (2nd approach)

• Postulate existence of S, describing microscopic
  disorder or amount of useful energy of a
  system.
• Systems A B enclosed by
• rigid walls in contact heat
• transfer ( ) only
• Combined system C is isolated

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Equilibrium at Maximum Entropy

• Total energy, Uc, fixed
• SC,final - SC,initial Ps 0
• Let A B not be in equilibrium
• SC SA(UA,VA) SB(UB,VB)
• Also UC UA UB ?UC (1-?)UC
• where ? is the fraction of UC located in A
• SC increases until equilibrium is reached

U2 UB UC UA
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T.D. Definition of Temperature

• SC SA SB, SS(U,V, ), V constant
• 0 (equilibrium i.e., TA TB) when

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T.D. Definition of Temperature

• From above let
• Show that above definition consistent with old
  idea that U increases with T

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T.D. Definition of Temperature

• If TB gt TA then
• 2nd Law says dSc gt 0, therefore d? gt 0
  
• Energy from B to A
• If is a maximum
• then

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Some fancy math.

16
Does this agree with Traditional Idea of
Temperature ?