Download presentation

Presentation is loading. Please wait.

1
Entropy Physics 202 Professor Lee Carkner Lecture 17

2
PAL #16 Internal Energy 3 moles of gas, temperature raised from 300 to 400 K He gas, isochorically Q = nC V 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 Q = nC P T, CP = C V + R = (5/2) R Q = (3)(5/2)R(100) = 6333 J # 2 for heat, energy in translational and work H2 gas, isochorically Q = nC V T, 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 = nC P T, CP = C V + 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

6
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: S = S f –S i = ∫ (dQ/T)

7
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): S = (1/T) ∫ dQ S = Q/T Like heating something up by 1 degree

8
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: S box = (-Q/T box ) S res = (+Q/T res )

9
Second Law of Thermodynamics (Entropy) S>0 This is also the second law of thermodynamics Entropy always increases Why? The 2nd law is based on statistics

10
State Function Entropy is a property of system Can relate S to Q and W and thus P, T and V S = nRln(V f /V i ) + nC V ln(T f /T i ) Not how the system changes ln 1 = 0, so if V or T do not change, its term drops out

11
Statistical Mechanics We will use statistical mechanics to explore the reason why gas diffuses throughout a container The box contains 4 indistinguishable molecules

12
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

13
Configurations and Microstates Configuration I 1 microstate Probability = (1/16) Configuration II 4 microstates Probability = (4/16)

14
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

15
Multiplicity The multiplicity of a configuration is the number of microstates it has and is represented by: W = N! /(n L ! n R !) n! = n(n-1)(n-2)(n-3) … (1) For large N (N>100) the probability of the equal distribution configurations is enormous

16
Microstate Probabilities

17
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

18
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

19
Arrows of Time Three arrows of time: Thermodynamic Psychological Cosmological Direction of increasing expansion of the universe

20
Entropy and Memory Memory requires energy dissipation as heat Psychological arrow of time is related to the thermodynamic

21
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)

22
Fate of the Universe If the universe has enough mass, its expansion will reverse Cosmological arrow will go backwards Universe seems to be open

23
Heat Death Entropy keeps increasing Stars burn out Can live off of compact objects, but eventually will convert them all to heat

24
Next Time Read: 20.5-20.7 Homework: Ch 20, P: 6, 7, 21, 22

Similar presentations

© 2021 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google