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2nd Law
• about Spontaneity and Efficiency
• Spontaneity  Rate
• Depends on U?
• Bouncing ball coming to rest
• Dispersal of energy
• Entropy, S dS = dqrev/T A measure of disorder !!
• 2nd law statement: Suniv = SSys + Ssurr > 0 for any spontaneous process
• State function, extensive property, a strictly macroscopic concept
Example 1: Heat transfer from a hot to cold body
We know it is an irreversible process,  S > 0
2 identical metal blocks, one at 100 ̊C and other 0 ̊C brought in thermal contact, isolated from surroundings
Final temp., Tf = 50 ̊C
We can calculate q, but it is qirreversible
Take a moment
Infinitesimal reversible heat transfer (dqrev) between system and surroundings at infinitesimally different temp. apart,
Entropy change for the system, dSSys = dqrev/T, and for surroundings, dSsurr = dqrev/T
 dSUniv = 0 for a reversible process
= 0.024*c > 0
So, did I just trick you ?
Tc TH
q
Ssurr for finite changes?
For the surroundings, V    heat transfer at const. volume  qSurr = USurr (path independent)
Also, CV    TSurr remains constant  Ssurr = qSurr/Tsurr
E.g, For an adiabatic process, ∵ qsys = qsurr= 0  Ssurr = 0 and Ssys = ?
Infinite number of heat baths between the hot and cold blocks, each at infinitesimally higher temperature, dT
 Reversible heat transfer between adjacent bodies, dqrev = c dT
Entropy Calculation
• Determine the initial and final states
• Devise a reversible path or a combination of reversible paths that takes you from the initial to the final state.
• Evaluate dqrev and dS
Example 2: Free adiabatic expansion of an ideal gas: Vi  2Vi
Free expansion is an irreversible process,  S > 0
• (pi, Ti, Vi)  (pf, Tf, 2Vi)
gas vacuum
Example 3: Now imagine mixing of 2 different ideal gases
(same pi, Vi and Ti), each occupying one half of the chamber, separated
by a removable massless barrier
Show that Smixing = 2*nRln2 (Assignment)
Example 4: Irreversible adiabatic expansion of an ideal gas
gas A gas B

TH
TC
P
W
qc
qH

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CH1201-TD-2nd Law.pptx

  • 1. 2nd Law • about Spontaneity and Efficiency • Spontaneity  Rate • Depends on U? • Bouncing ball coming to rest • Dispersal of energy • Entropy, S dS = dqrev/T A measure of disorder !! • 2nd law statement: Suniv = SSys + Ssurr > 0 for any spontaneous process • State function, extensive property, a strictly macroscopic concept Example 1: Heat transfer from a hot to cold body We know it is an irreversible process,  S > 0 2 identical metal blocks, one at 100 ̊C and other 0 ̊C brought in thermal contact, isolated from surroundings Final temp., Tf = 50 ̊C We can calculate q, but it is qirreversible Take a moment Infinitesimal reversible heat transfer (dqrev) between system and surroundings at infinitesimally different temp. apart, Entropy change for the system, dSSys = dqrev/T, and for surroundings, dSsurr = dqrev/T  dSUniv = 0 for a reversible process
  • 2. = 0.024*c > 0 So, did I just trick you ? Tc TH q Ssurr for finite changes? For the surroundings, V    heat transfer at const. volume  qSurr = USurr (path independent) Also, CV    TSurr remains constant  Ssurr = qSurr/Tsurr E.g, For an adiabatic process, ∵ qsys = qsurr= 0  Ssurr = 0 and Ssys = ? Infinite number of heat baths between the hot and cold blocks, each at infinitesimally higher temperature, dT  Reversible heat transfer between adjacent bodies, dqrev = c dT
  • 3. Entropy Calculation • Determine the initial and final states • Devise a reversible path or a combination of reversible paths that takes you from the initial to the final state. • Evaluate dqrev and dS Example 2: Free adiabatic expansion of an ideal gas: Vi  2Vi Free expansion is an irreversible process,  S > 0 • (pi, Ti, Vi)  (pf, Tf, 2Vi) gas vacuum
  • 4. Example 3: Now imagine mixing of 2 different ideal gases (same pi, Vi and Ti), each occupying one half of the chamber, separated by a removable massless barrier Show that Smixing = 2*nRln2 (Assignment) Example 4: Irreversible adiabatic expansion of an ideal gas gas A gas B
  • 5.
  • 6.
  • 7.