1 / 24

Entropy

Physics 202 Professor Lee Carkner Lecture 17. Entropy. PAL #16 Internal Energy. 3 moles of gas, temperature raised from 300 to 400 K He gas, isochorically Q = nC V D T, C V = (f/2)R = (3/2) R Q = (3)(3/2)R(100) = 3740 J # 4 for heat, all in translational motion He gas, isobarically

taini
Download Presentation

Entropy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 202 Professor Lee Carkner Lecture 17 Entropy

  2. PAL #16 Internal Energy • 3 moles of gas, temperature raised from 300 to 400 K • He gas, isochorically • Q = nCVDT, CV = (f/2)R = (3/2) R • Q = (3)(3/2)R(100) = 3740 J • # 4 for heat, all in translational motion • He gas, isobarically • Q = nCPDT, CP = CV + R = (5/2) R • Q = (3)(5/2)R(100) = 6333 J • # 2 for heat, energy in translational and work • H2 gas, isochorically • Q = nCVDT, CV = (5/2) R, f = 5 for diatomic • Q = (3)(5/2)R(100) = 6333 J • # 2 for heat, energy into translational and rotational motion • H2 gas, isobarically • Q = nCPDT, CP = CV + R = (7/2) R • Q = (3)(7/2)R(100) = 8725 J • # 1 for heat, energy, into translation, rotation and work

  3. Randomness • Classical thermodynamics is deterministic • Every time! • But the real world is probabilistic • It is possible that you could add heat to a system and the temperature could go down • The universe only seems deterministic because the number of molecules is so large that the chance of an improbable event happening is absurdly low

  4. Reversible • Why? • The smashing plate is an example of an irreversible process, one that only happens in one direction • Examples: • Heat transfer

  5. Entropy • What do irreversible processes have in common? • The degree of randomness of system is called entropy • In any thermodynamic process that proceeds from an initial to a final point, the change in entropy depends on the heat and temperature, specifically: DS = Sf –Si = ∫ (dQ/T)

  6. Isothermal Entropy • In practice, the integral may be hard to compute • Let us consider the simplest case where the process is isothermal (T is constant): DS = (1/T) ∫ dQ DS = Q/T • Like heating something up by 1 degree

  7. Entropy Change • Imagine now a simple idealized system consisting of a box of gas in contact with a heat reservoir • If the system loses heat –Q to the reservoir and the reservoir gains heat +Q from the system isothermally: DSbox = (-Q/Tbox) DSres = (+Q/Tres)

  8. Second Law of Thermodynamics (Entropy) DS>0 • This is also the second law of thermodynamics • Entropy always increases • Why? • The 2nd law is based on statistics

  9. State Function • Entropy is a property of system • Can relate S to Q and W and thus P, T and V DS = nRln(Vf/Vi) + nCVln(Tf/Ti) • Not how the system changes • ln 1 = 0, so if V or T do not change, its term drops out

  10. Statistical Mechanics • We will use statistical mechanics to explore the reason why gas diffuses throughout a container • The box contains 4 indistinguishable molecules

  11. Molecules in a Box • There are 16 ways that the molecules can be distributed in the box • Since the molecules are indistinguishable there are only 5 configurations • If all microstates are equally probable than the configuration with equal distribution is the most probable

  12. Configurations and Microstates Configuration I 1 microstate Probability = (1/16) Configuration II 4 microstates Probability = (4/16)

  13. Probability • There are more microstates for the configurations with roughly equal distributions • Gas diffuses throughout a room because the probability of a configuration where all of the molecules bunch up is low

  14. Multiplicity • The multiplicity of a configuration is the number of microstates it has and is represented by: W = N! /(nL! nR!) n! = n(n-1)(n-2)(n-3) … (1) • For large N (N>100) the probability of the equal distribution configurations is enormous

  15. Microstate Probabilities

  16. Entropy and Multiplicity • The more random configurations are most probable • We can express the entropy with Boltzmann’s entropy equation as: S = k ln W • Sometimes it helps to use the Stirling approximation: ln N! = N (ln N) - N

  17. Irreversibility • Irreversible processes move from a low probability state to a high probability one • All real processes are irreversible, so entropy will always increases • The universe is stochastic

  18. Arrows of Time • Three arrows of time: • Thermodynamic • Psychological • Cosmological • Direction of increasing expansion of the universe

  19. Entropy and Memory • Memory requires energy dissipation as heat • Psychological arrow of time is related to the thermodynamic

  20. Synchronized Arrows • Why do all the arrows go in the same direction? • Can life exist with a backwards arrow of time? • Does life only exist because we have a universe with a forward thermodynamic arrow? (anthropic principle)

  21. Fate of the Universe • If the universe has enough mass, its expansion will reverse • Cosmological arrow will go backwards • Universe seems to be open

  22. Heat Death • Entropy keeps increasing • Stars burn out • Can live off of compact objects, but eventually will convert them all to heat

  23. Next Time • Read: 20.5-20.7 • Homework: Ch 20, P: 6, 7, 21, 22

More Related