Reversibility. Processes in nature are always irreversible: far from equilibrium

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Caren Bridges
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Reversibility Processes in nature are always irreversible: far from equilibrium Reversible process: idealized process infinitely close to thermodynamic equilibrium (quasi-equilibrium) Necessary

1 Reversibility Processes in nature are always irreversible: far from equilibrium Reversible process: idealized process infinitely close to thermodynamic equilibrium (quasi-equilibrium) Necessary conditions for Reversibility. No work must be done by friction, viscous forces, or other dissipative forces that produce heat (no dissipation). 2. eat conduction can only occur isothermally. 3. he process must be quasi-static so that the system is always in an equilibrium state (or infinitesimally close to one).

2 PS question An ideal gas is taken around the cycle shown in this p diagram, from a to b to c and back to a. Process b c is isothermal. hich of the processes in this cycle could be reversible? A. a b B. b c. c a D. two or more of A., B., and. E. none of A., B., or. Natural processes onsider a free expansion: hy is this process irreversible? hy the gas doesn t compress itself to its original volume? (it wouldn t violate the st law) e have missed something e need another principle 2

3 eat engines eat flows from the hot reservoir to the cold reservoir, producing work he process is cyclic ork during a cycle: + e define thermal efficiency as e +

3 3 eat engines eat flows from the hot reservoir to the cold reservoir, producing work he process is cyclic ork during a cycle: + e define thermal efficiency as e + Refrigerators Mechanical work induces a heat flow from the cold reservoir to the hot reservoir he process is cyclic ork during a cycle: + e define the coefficient of performance as K

2 nd Law of hermodynamics It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts all the heat completely into mechanical

4 2 nd Law of hermodynamics It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts all the heat completely into mechanical work, with the system ending in the same state in which it began engine, or Kelvin-Planck statement he second law limits the availability of energy and the ways in which it can be used and converted. e cannot have an engine with 00% efficiency: No perpetuum mobile 2 nd Law of hermodynamics It is impossible for any process to have as its sole result the transfer of heat from a cooler to a hotter reservoir refrigerator, or lausius statement 4

5 Reversible vs. Irreversible processes o increase efficiency, we must avoid irreversible processes: hen an engine absorbs or discards heat, it must be done at the temperature of the reservoirs or, avoiding temperature drops (isothermal) hen an engine performs work at some intermediate temperature, it must avoid heat transfer (irreversible), therefore work at intermediate temperatures must be involve an adiabatic process he arnot cycle (a reversible engine of maximum efficiency) 5

6 6 he arnot cycle a b ab nr ln d c cd nr ln ) / ln( ) / ln( a b d c he arnot cycle ) / ln( ) / ln( a b d c γ γ c b e know that during the adiabatic processes: γ γ d a d c a b / / e arnot

7 he arnot cycle and the 2 nd law No engine can be more efficient than a arnot engine operating between the same two temperatures Entropy! e define the differential increase in entropy ds as: d ds here the heat is added or removed in a reversible process Note: his does not mean that the process has to be reversible for the entropy to change. his formula gives as a method for calculating the entropy change rev As we shall see, entropy is a state function. 7

8 Entropy change for a arnot cycle he entropy change in the hot and cold reservoirs is: S ; S e know that for a arnot cycle: S otal + + ( / ) 0 he entropy change during a reversible cycle is zero: the entropy change from a state to a state 2 is independent of the path: S is a state function Entropy of an ideal gas For an ideal gas: d du + d du + pd d d + nr d his Eq. cannot be integrated unless we know how depends on. his another way of saying that is not a state function. owever, if we divide by : d d d + nr ds If we assume that v remains constant, we can readily integrate it: d 2 S ln + nr ln 2 8

9 Entropy changes for various processes Isothermal expansion (constant): d S nr ln 2 he entropy change of the environment has the same magnitude but opposite sign: In a reversible process, the entropy change of the universe system+environment is zero Entropy changes for various processes Free expansion of an ideal gas: Since entropy is a state function, it only depends on the initial and final state, and the change is the same for all processes, thus: d S nr ln 2 he entropy change of the environment is zero: he entropy of the universe is positive In an irreversible process, the entropy of the universe increases. 9

10 Entropy changes for various processes Isobaric processes (Pconstant): d d S p p ln 2 his expression gives the entropy change of any process between the two temperatures, reversible or irreversible, as long as the pressure remains constant Entropy and the Second Law No processes are possible in which the entropy of the universe decreases 0

11 Entropy and probability onsider a free expansion: hy is this process irreversible? hy the gas doesn t compress itself to its original volume? (it wouldn t violate the st law) e can see that the probability of finding N molecules in the smaller volume is N very small small number!!! N p 2 ln ln p N ln N 2 small nn A ln small Entropy and probability ln ln p N ln N 2 small nn A ln small e can compare this expression to the expression for the entropy change: d S nr ln small S R N A ln p k ln p k: Boltzmann s constant Negative entropy fluctuations correspond to very low probability states. In an irreversible process, the universe moves from a state with low prob. to a state with high prob.

Chapter 5. The Second Law of Thermodynamics (continued)

Chapter 5. The Second Law of Thermodynamics (continued) hapter 5 he Second Law of hermodynamics (continued) Second Law of hermodynamics Alternative statements of the second law, lausius Statement of the Second Law It is impossible for any system to operate