We will review for the exam on Monday. Have questions ready to ask in class.

Transcription

1 Homework #: Graded problems: a,b,c 6 points 0b-e 8 points 6b 3 points 34c 6 points otal 3 points 36 Lec Fri 5sep7 Class average = 3.6/3 = 59.0 % (fair) for HW# Solutions will be posted later today Objectives for Exam are posted Reading for today s lecture: Chapter 3, pp 66-7 We will review for the exam on Monday. Have questions ready to ask in class.

2 NOE... and much more (posted on website)

3 Always rue U = q + w H = U + pv H = U + p V - p V dw w he beginning of your 4 x 6 sheet for Exam. pv pv = p = V V ext p dv ext dv Conditional Adiabatic: q = 0 ; U = w ; Constant V: U = C d U = C v ( - ) if C v constant For ideal gas the above is always true (even if volume changes) For p=p ext = constant and pv work only: H = q = H = Cpd H = C P ( - ) if C P constant For ideal gas the above is always true (even if pressure changes) for p ext constant: w pv = -p ext (V V ) ; if isothermal reversible and ideal gas: V w pv = p = nr V dv ln V V Solids and Liquids (volume changes are very small) Cp Cv and H U v 3

4 w pv V = R ln V = 8.345* 98*0.693 = 77 J S = =q rev / = Rln = 77/98 = 5.76 J/K q rev =+77 S surr = - q/ = Rln = J/K S UNIV = 0 4

5 he 3 rd Law of hermodynamics In 867, Ludwig Boltzmann earned his PhD for research on the kinetic theory of gases. Later, he began to see that entropy could be related to disorder, and he published the famous equation for absolute entropy S = k B lnw where W is the number of quantum microstates (the number of possible arrangements of the positions and velocities of the collection of molecules in the system a truly enormous number while at dynamic equilibrium), and k B = Boltzmann s constant (= R/6x0 3 ) so has units of J K - molecule - his, however, was well ahead of its time, and he died a discouraged man in 906, just as the world of physics was waking up to the idea of atoms and molecules. 5

6 As 0 Kelvin is approached, all systems are in the zero point quantum mechanical energy level. For a perfect crystal in lowest energy level there is only microstate : W= S = k B ln = 0, i.e., he entropy of a perfect crystal at 0 K = 0. (this is one form of the 3 rd Law) his means there is a basis for having absolute values for entropy, (unlike energy) 6

7 Molecular Interpretation of Entropy S = k B ln W (Boltzmann ~900) Reversible isothermal expansion of ideal gas: herefore, qrev = wrev = nr ln V V q rev V S = = nr ln = V W nr ln W becausethe number of microstates is proportional to volume S = nr ln W nr ln W = S S, on a molar basis dividing by the number of molecules gives S = k B ln W k B ln W, on a molecule basis 7

8 able A.5 Appendix Absolute entropies at 98 K For ions in solution the S 0 values are arbitrarily set relative to H + (aq) = 0 (thus, the ion S 0 will not make obvious physical sense) 8

9 Relating q rev to heat capacity S = dq rev = Cd ( done slowly) C d his is heat capacity times the sum of fractional differences in starting at and ending at and that is?? S = C ln 9

10 S C ln over a small enough temperature range that C is effectively constant Phase transitions at the transition temperature (e.g., melting point, boiling point, ) are reversible, so: S S fusion vap = = H H vap boiling fusion mp 0

11 Absolute (hird Law) Entropy at any temperature (this is where the numbers in able A.5 come from) Below is the case in which there are solid phases such as for N S( ) = 0 + tran 0 C P ( solid ) d + H transition trans + mp trans C P ( solid ) d + H fusion mp + bp mp C P ( liquid) d + H vap equil + bp C P ( gas) d

12 Notice how stays constant (vertical lines) at phase transitions vaporization: N (l) ---> N (gas) melting: N (s) ---> N (l) solid ---> solid : N (s) ---> N (s)

13 vaporization: benzene(l) ---> benzene(gas) melting: benzene(s) ---> benzene(l) 3

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15 Business as usual 5

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17 DECREASING molecules INCREASING molecules 7

18 decreasing ions decreasing ions decreasing ions decreasing ions no change in ions INCREASING ions What is the lesson so far? Ions order water! What does methane do to water? Hydrophobic effect Methane orders water 8

19 Pictures of MEHANE Plumes! 7 I Sonar image near Svalbard

20 Methane Clathrates or Methane Hydrates burning ice are found in deep and/or cold coastal ocean sea beds (in the top few hundred meters ). 7H