Thermodynamics Second Law Entropy

Transcription

1 Thermodynamcs Second Law Entropy Lana Sherdan De Anza College May 8, 2018

2 Last tme the Boltzmann dstrbuton (dstrbuton of energes) the Maxwell-Boltzmann dstrbuton (dstrbuton of speeds) the Second Law of thermodynamcs

3 Overvew entropy (macroscopc perspectve) entropy (mcroscopc perspectve) (?)

4 Reversble and Irreversble Processes Reversble process a process that takes a system from an ntal state to a fnal state f through a seres of equlbrum states, such that we can take the same system back agan from f to along the same path n a PV dagram. Irreversble process any process that s not reversble. In real lfe, all processes are rreversble, but some are close to beng reversble. We use reversble processes as an dealzaton.

5 20-3 CHANGE IN ENTROPY Irreversble Process Example not obey a conservaton law. lways remans constant. For always ncreases. Because of alled the arrow of tme. For rn kernel wth the forward e backward drecton of tme o the exploded popcorn red process would result n an System Stopcock closed Vacuum 537 ange n entropy of a system: ergy the system gans or loses toms or molecules that make roach n the next secton and Insulaton (a) Intal state Irreversble process Stopcock open by lookng agan at a process ree expanson of an deal gas. state, confned by a closed d contaner. If we open the, eventually reachng the fnal rreversble process;all the of the contaner. ws the pressure and volume (b) Fnal state f

6 s nd Irreversble Process Example of re, e a the old a py ay the cts on Ths process has well-defned ntal and fnal equlbrum states, but durng the expanson of the gas s not n equlbrum. Pressure Volume Fg A p-v dagram showng the It cannot be plotted on a PV dagram. Also, no work s done on the gas ntal thsstate process. and the fnal state f of the free f

7 Fgure 20.7 Gas n a cylnder. (a) The gas s n contact wth an energy reservor. The walls of the base n contact wth the reservor s conductng. (b) The gas expands slowly to a larger volume. (c) T A Reversble Counterpart Allow gas to expand very slowly through equlbrum states at 20.5 The Frst Law constant temperature. The gas s ntally at temperature T. The hand reduces ts downward force, allowng the pston to move up slowly. The energy reservor keeps the gas at temperature T. Th n te T co by m w ab Energy reservor at T a Energy reservor at T b c

8 A Reversble Counterpart 606 Chapter 20 The Frst Law of Thermo We can plot ths sothermal expanson: P P f P Isotherm PV = constant The curve s a hyperbola. f Isothermal Ex Suppose an deal Ths process s d hyperbola (see A stant ndcates th Let s calculate The work done on process s quas-st V V f V Fgure 20.9 The PV dagram Negatve work s done Because T s con for an on sothermal gas, expanson heat s transferred of n, and the nternal energy and deal thegas temperature from an ntal reman state constant. to a n and R: fnal state.

9 Comparng the Processes In both of these processes the gas expands nto a regon t was not n prevously. The energy of the system spreads out. Ths corresponds to a change of state, but t s not captured by the nternal energy of the gas system, whch does not change n ether process.

10 Comparng the Processes In both of these processes the gas expands nto a regon t was not n prevously. The energy of the system spreads out. Ths corresponds to a change of state, but t s not captured by the nternal energy of the gas system, whch does not change n ether process. Somethng does change n these processes and we call t entropy.

11 State Varables State varables of a thermodynamcs system are varables that are determned f the system s n thermodynamc equlbrum and you know the system s state. Examples: pressure, volume, nternal energy, temperature. Also, entropy.

12 State Varables State varables of a thermodynamcs system are varables that are determned f the system s n thermodynamc equlbrum and you know the system s state. Examples: pressure, volume, nternal energy, temperature. Also, entropy. Each varable on t s own s not enough to determne the state of the system. (Many systems n dfferent states mght have the same volume.) Once the current state s known, we do know all of these varables values. How the system arrved at ts current state, does not affect these values. Heat and work are not state varables.

13 Entropy Sad Carnot dscovered that the most effcent possble engne must be reversble (more on ths to come). Rudolph Clausus nterpreted ths as beng due to the behavor of a new quantty (entropy). The change n entropy movng between two states and f s: S = f dq r T where dq r s an nfntesmal heat transfer when the system follows a reversble path. (T can be a functon of Q!)

14 Entropy Example # 42 An ce tray contans 500 g of lqud water at 0 degrees C. Calculate the change n entropy of the water as t freezes slowly and completely at 0 degrees C.

15 Entropy When a reversble path s followed: S r = f dq T Can we fnd the entropy change for an rreversble process?

16 Entropy When a reversble path s followed: S r = f dq T Can we fnd the entropy change for an rreversble process? Yes! Snce entropy s a state varable, we can consder the entropy change n any reversble process wth the same ntal and fnal states. Then: S rr = f dq r T The entropy change n that process wll gve us the entropy dfference between those two states, regardless of the process.

17 Entropy Change Consder an ntal state and fnal state f. We can fnd the entropy change movng between those two states (for any process, reversble or rreversble), by fndng the entropy change along an arbtrary reversble path. Frst law, de nt = dw + dq r Rearrangng, we can fnd an expresson for dq r, usng E nt = nc V T : dq r = nc V dt +P dv To fnd entropy, we multply by 1/T and ntegrate: S = f dq f r T = nc f V T dt + P T dv

18 Entropy Change S = f Fnally, replace P T = nr V dq f r T = (deal gas): nc f V T dt + P T dv S = f The entropy dfference s: dq f r T = nc V T f dt + nr ( ) ( ) Tf Vf S = nc v ln + nr ln T V 1 V dv

19 Queston Quck Quz True or False: The entropy change n any adabatc process must be zero because Q = 0. (A) True (B) False 1 Serway & Jewett, page 673.

20 Queston Quck Quz True or False: The entropy change n any adabatc process must be zero because Q = 0. (A) True (B) False 1 Serway & Jewett, page 673.

21 Example (Macroscopc Entropy Analyss) What s the entropy change durng an adabatc free expanson of an solated gas of n moles gong from volume V to volume V f? (Note: such a process s not reversble.)

22 Example (Macroscopc Entropy Analyss) What s the entropy change durng an adabatc free expanson of an solated gas of n moles gong from volume V to volume V f? (Note: such a process s not reversble.) In an adabatc free expanson Q = 0, and snce ts solated, W = 0, and therefore E nt = 0 and T f = T. ( ) ( ) Tf Vf S = nc v ln + nr ln T V

23 Example (Macroscopc Entropy Analyss) What s the entropy change durng an adabatc free expanson of an solated gas of n moles gong from volume V to volume V f? (Note: such a process s not reversble.) In an adabatc free expanson Q = 0, and snce ts solated, W = 0, and therefore E nt = 0 and T f = T. usng ln 1 = 0 becomes ( ) ( ) Tf Vf S = nc v ln + nr ln T V ( ) Vf S = nr ln V

24 Example Exercse for you: What s the entropy change the same n moles of gas (a datomc gas around room temperatures) n an constant volume process, wth temperature gong T to T f? What s the entropy change when the pressure s constant and the volume goes V to V f?

25 Queston Quck Quz An deal gas s taken from an ntal temperature T to a hgher fnal temperature T f along two dfferent reversble paths. Path A s at constant pressure, and path B s at constant volume. What s the relaton between the entropy changes of the gas for these paths? (A) S A > S B (B) S A = S B (C) S A < S B 1 Serway & Jewett, page 673.

26 Queston Quck Quz An deal gas s taken from an ntal temperature T to a hgher fnal temperature T f along two dfferent reversble paths. Path A s at constant pressure, and path B s at constant volume. What s the relaton between the entropy changes of the gas for these paths? (A) S A > S B (B) S A = S B (C) S A < S B 1 Serway & Jewett, page 673.

27 Clausus Equalty Clausus found that the entropy change around any reversble cycle (closed path) s zero. Ths s called the Clausus Equalty: S = dqr T = 0 And moreover that snce real engnes can never qute conform to ths deal, for all engnes the Clausus Inequalty holds: dqr S = T 0

28 Entropy n an solated system Ths gves us another way to state the second law: 2nd Law In an solated system, entropy does not decrease. ds dt 0 In a non-solated system (ether closed or open) entropy can decrease, but only by ncreasng the entropy of the envronment at least as much.

29 Summary entropy as a thermodynamc varable (macroscopc perspectve) entropy (mcroscopc perspectve) (?) Homework Serway & Jewett: Ch 22, onward from page 679. CQs: 9; OQs: 9, 11; Probs: 43, 45, 47, 53 (entropy problems)