A sta6s6cal view of entropy
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1 A sta6s6ca view of entropy 20-4 A Sta&s&ca View of Entropy The entropy of a system can be defined in terms of the possibe distribu&ons of its moecues. For iden&ca moecues, each possibe distribu&on of moecues is caed a microstate of the system. A equivaent microstates are grouped into a configura&on of the system. The number of microstates in a configura&on is the mu6picity W of the configura&on. For a system of N moecues that may be distributed between the two haves of a box, the mu&picity is given by Here n 1 is the number of moecues in one haf of the box and n 2 is the number in the other haf. A basic assump&on of sta&s&ca mechanics is that a the microstates are equay probabe John Wiey & Sons, Inc. A rights reserved.
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3 Moecues are 20-4 dis&nguishabe A Sta&s&ca View of Entropy An insuated box contains six gas moecues. Each moecue has the same probabiity of being in the em haf of the box as in the right haf. The arrangement in (a) corresponds to configura&on III in Tabe 20-1 (b) corresponds to configura&on IV John Wiey & Sons, Inc. A rights reserved.
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5 20-4 A Sta&s&ca View of Entropy Probabiity and Entropy The mu&picity W of a configura&on of a system and the entropy S of the system in that configura&on are reated by Botzmann s entropy equa6on: Here k = J/K is the Botzmann constant. When N is very arge (the usua case), we can approximate n N! with S6ring s approxima6on: 2014 John Wiey & Sons, Inc. A rights reserved.
6 Chapter summary 20 Summary Irreversibe (one-way) Process If an irreversibe process occurs in a cosed system, the entropy of the system aways increases. Second Law of Thermodynamics If a process occurs in a cosed system, the entropy of the system increases for irreversibe processes and remains constant for reversibe processes. Eq Entropy Change Entropy change for reversibe process is given by Eq Entropy Change The efficiency ε of any engine Efficiency of Carnot engine Eq Eq & John Wiey & Sons, Inc. A rights reserved.
7 Chapter summary Refrigerator Coefficient of performance Entropy of a from Sta6s6ca Point of refrigerator: View For a system of N moecues: Carnot Refrigerator Eq Eq &16 Botzmann s entropy equa&on: Eq Eq S&ring s approxima&on: Eq John Wiey & Sons, Inc. A rights reserved.
8 Chapter 14 Fuids Copyright 2014 John Wiey & Sons, Inc. A rights reserved.
9 14-1 Fuid Density and Pressure 14-1 Fuid Density and Pressure Learning Objectives Distinguish fuids from soids When mass is uniformy distributed, reate density to mass and voume Appy the reationship between hydrostatic pressure, force, and the surface area over which that force acts John Wiey & Sons, Inc. A rights reserved.
10 14-1 Fuid Density and Pressure 14-1 Fuid Density and Pressure Physics of fuids is the basis of hydrauic engineering A fuid is a substance that can fow, ike water or air, and conform to a container This occurs because fuids cannot sustain a shearing force (tangentia to the fuid surface) They can however appy a force perpendicuar to the fuid surface Some materias (pitch) take a ong time to conform to a container, but are sti fuids The essentia identifier is that fuids do not have a crystaine structure 2014 John Wiey & Sons, Inc. A rights reserved.
11 14-1 Fuid Density and Pressure 14-1 Fuid Density and Pressure The density, ρ, is defined as: Eq. (14-1) In theory the density at a point is the imit for an infinitesima voume, but we assume a fuid sampe is arge reative to atomic dimensions and has uniform density. Then Eq. (14-2) Density is a scaar quantity Units kg/m John Wiey & Sons, Inc. A rights reserved.
12 14-1 Fuid Density and Pressure 14-1 Fuid Density and Pressure The pressure, force acting on an area, is defined as: Eq. (14-3) We coud take the imit of this for infinitesima area, but if the force is uniform over a fat area A we write Eq. (14-4) We can measure pressure with a sensor 2014 John Wiey & Sons, Inc. A rights reserved. Figure 14-1
13 14-1 Fuid Density and Pressure 14-1 Fuid Density and Pressure We find by experiment that for a fuid at rest, pressure has the same vaue at a point regardess of sensor orientation Therefore static pressure is scaar, even though force is not Ony the magnitude of the force is invoved Units: the pasca (1 Pa = 1 N/m 2 ) the atmosphere (atm) the torr (1 torr = 1 mm Hg) the pound per square inch (psi) 2014 John Wiey & Sons, Inc. A rights reserved.
14 14-2 Fuids at Rest 14-2 Fuids at Rest Learning Objectives Appy the reationship between the hydrostatic pressure, fuid density, and the height above or beow a reference eve Distinguish between tota pressure (absoute pressure) and gauge pressure John Wiey & Sons, Inc. A rights reserved.
15 14-2 Fuids at Rest 14-2 Fuids at Rest Hydrostatic pressures are those caused by fuids at rest (air in the atmosphere, water in a tank) 2014 John Wiey & Sons, Inc. A rights reserved. Figure 14-2
16 14-2 Fuids at Rest 14-2 Fuids at Rest Write the baance of forces: Eq. (14-5) Rewrite: forces with pressures, mass with density Eq. (14-7) For a depth h beow the surface in a iquid this becomes: Eq. (14-8) 2014 John Wiey & Sons, Inc. A rights reserved.
17 14-2 Fuids at Rest 14-2 Fuids at Rest The pressure in 14-8 is the absoute pressure Consists of p 0, the pressure due to the atmosphere, and the additiona pressure from the fuid The difference between absoute pressure and atmospheric pressure is caed the gauge pressure because we use a gauge to measure this pressure difference The equation can be turned around to cacuate the atmospheric pressure at a given height above ground: 2014 John Wiey & Sons, Inc. A rights reserved.
18 14-2 Fuids at Rest 14-2 Fuids at Rest Answer: A the pressures wi be the same. A that matters is the distance h, from the surface to the ocation of interest, and h is the same in a cases John Wiey & Sons, Inc. A rights reserved.
19 14-3 Measuring Pressure 14-3 Measuring Pressure Learning Objectives Describe how a barometer can measure atmospheric pressure Describe how an opentube manometer can measure the gauge pressure of a gas John Wiey & Sons, Inc. A rights reserved.
20 14-3 Measuring Pressure 14-3 Measuring Pressure Figure 14-5 shows mercury barometers The height difference between the air-mercury interface and the mercury eve is h: Eq. (14-9) Figure John Wiey & Sons, Inc. A rights reserved.
21 14-3 Measuring Pressure 14-3 Measuring Pressure Ony the height matters, not the cross-sectiona area Height of mercury coumn is numericay equa to torr pressure ony if: o Barometer is at a pace where g has its standard vaue o Temperature of mercury is 0 C 2014 John Wiey & Sons, Inc. A rights reserved.
22 14-3 Measuring Pressure 14-3 Measuring Pressure Figure 14-6 shows an open-tube manometer The height difference between the two interfaces, h, is reated to the gauge pressure: Eq. (14-10) Fig The gauge pressure can be positive or negative, depending on whether the pressure being measured is 2014 John Wiey & Sons, Inc. A rights reserved. greater or ess than atmospheric pressure
23 11-4 Pasca's Principe 11-4 Pasca's Principe Learning Objectives Identify Pasca's principe For a hydrauic ift, appy the reationship between the input area and dispacement and the output area and dispacement John Wiey & Sons, Inc. A rights reserved.
24 14-4 Pasca's Principe 11-4 Pasca's Principe Pasca's principe governs the transmission of pressure through an incompressibe fuid: Consider a cyinder of fuid (Figure 14-7) Increase p ext, and p at any point must change Eq. (14-12) Independent of h Figure John Wiey & Sons, Inc. A rights reserved.
25 14-4 Pasca's Principe 11-4 Pasca's Principe Describes the basis for a hydrauic ever Input and output forces reated by: Eq. (14-13) The distances of movement are reated by: Eq. (14-14) Figure John Wiey & Sons, Inc. A rights reserved.
26 14-4 Pasca's Principe 11-4 Pasca's Principe So the work done on the input piston equas the work output Eq. (14-15) The advantage of the hydrauic ever is that: 2014 John Wiey & Sons, Inc. A rights reserved.
27 14-5 Archimedes' Principe 14-5 Archimedes' Principe Learning Objectives Describe Archimedes' principe Appy the reationship between the buoyant force on a body and the mass of the fuid dispaced by the body For a foating body, reate the buoyant force to the gravitationa force For a foating body, reate the gravitationa force to the mass of the fuid dispaced by the body Distinguish between apparent weight and actua weight Cacuate the apparent weight of a body that is fuy or partiay submerged John Wiey & Sons, Inc. A rights reserved.
28 14-5 Archimedes' Principe 14-5 Archimedes' Principe The buoyant force is the net upward force on a submerged object by the fuid in which it is submerged This force opposes the weight of the object It comes from the increase in pressure with depth Figure John Wiey & Sons, Inc. A rights reserved.
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