Thermodynamics General


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1 Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons, unts, etc. Dmenson Unts (MKS) 1. mass M kg 2. length L m 3. tme T s 4. acceleraton L T 2 m s densty M L 3 kg m force M L T 2 kg m s 2 (N) 7. pressure N M 2 kg m 1 s energy M L 2 T 2 kg m 2 s 2 (J ) a. 1 calore = J 9. specfc energy L 2 T 2 m 2 s 2 (J kg 1 ) 10. power M L 2 T 3 (W) kg m 2 s 3 (W) 11. mole (n) s the amount of a substance wth as many elementary unts as n 12 g of the sotope carbon12 (n = mass / Molecular weght) a. Avogadro's Number: N = x molecules/mole b. One atomc weght of a substance (atomc, onc, molecular) has N partcles. B. Sgn conventon n thermodynamcs. 1. When a system experences a gan n some property the sgn of that change s postve. 2. When a system experences a loss n some property the sgn of that change s negatve. 3. Examples a. If a system gans work (W), heat (Q), or a quantty of matter (n; number of moles) a sgn s assgned to change, e.g., dw, dq, dn C. Systems 1. A system s a part of the physcal unverse confned to a defnte space by the boundary that separates t from the rest of the unverse. a. The surroundngs nclude all matter n the envronment (the rest of the unverse) that may eventually nteract wth the system. 2. Boundares of a system can be open or closed. a. Open system. An open system allows for an exchange of matter and energy wth the surroundngs or envronment (the rest of the unverse). Most systems are open. Open systems usually are very dffcult to study b. Closed system. A close system does not exchange matter wth the 1
2 surroundngs or envronment. A system s sad to be solated f no matter or energy s exchanged wth the surroundngs or envronment D. State parameters and propertes 1. A complete descrpton of a system s gven by ts propertes or physcal varables that descrbe the propertes. When a system changes the magntude of ts propertes change. A stage n the change s descrbed by states of consttuents ncludng V, ρ, p, T, n, µ, magnetc, electrostatc, gravtatonal felds. a. For example, consder a closed system:. Mass and chemcal composton defne the system. V, ρ, p, T, n, µ, magnetc, electrostatc, gravtatonal felds, etc. defne the state of the system 2. A phase of a system s defned as a restrcted porton of a system that s homogeneous wth respect to all of ts propertes. 3. Extensve propertes: a. By defnton, extensve propertes are dependent on the amount of mass n a substance (ncludng the bulk or phase of a system).. Examples of an extensve propertes are the quantty of matter (number of moles), volume, energy, heat, entropy, poston and molar specfc heat. Extensve propertes are addtve 4. Intensve propertes: a. By defnton, ntensve propertes are ndependent of the amount of mass n a substance (ncludng the bulk or phase of a system).. Examples of an ntensve propertes are temperature (T), pressure (p), vscosty (ν), force, and concentraton. Intensve propertes are ndependent of the extent of bulk or phase of a system and therefore are not addtve 5. Combnatons of Intensve and Extensve propertes. The work done by compresson can be wrtten as dw = P dv where P s pressure (ntensve) and V s volume (extensve).. Smlarly, work can be descrbe by dw = f dl where f s force (ntensve) and l s poston (extensve) And fnally, the change n heat content correspondng to a change n temperature (ntensve) experenced by a mole of a system f molar heat capacty C (extensve) s dq = C dt E. Equlbrum of a system 1. Equlbrum and stable equlbrum a. A system that s solated from ts surroundngs s n stable thermodynamc equlbrum when ts ntensve propertes are constant n tme and not senstve to small perturbatons. When small changes are made to the ntensve propertes they return to ther orgnal values.. There are three mportant forms of equlbrum; thermal, mechancal, and chemcal.. Note that ndependence of tme s a necessary but t s not suffcent for equlbrum. 2
3 . "The constancy of propertes wth tme should hold for every porton of the system even f we solate t from the rest of the system and from ts surroundngs" 2. Unstable equlbrum a. A small change n the state of a gven system results n large changes n the system from equlbrum.. The smplest analogy s a rock sttng on top of hll peak, whch s then gven a small push. A rolls off the hll and wll not return spontaneously to the top of the hll. 3. Metastable equlbrum a. A system n metastable equlbrum s stable to small changes, and unstable to large changes. b. Another example s a room feld wth H and O n atomc states. A small catalyst wll spark a volent, spontaneous reacton. 4. More on Equlbrum... a. Departures from 'true' equlbrum may occur n three ways:. mechancal equlbrum. chemcal equlbrum. thermal equlbrum 5. Thermal contact a. Two substances are a sad to be n thermal contact when they can exchange heat n the absence of macroscopc (as opposed to molecular scale) work 6. Zero'th Law of Thermodynamcs a. The Zero'th Law of Thermodynamcs states that f two separate substances A and B are not n contact and each s n thermal equlbrum wth a thrd substance C, then A and B are n thermal equlbrum wth each other.. If TA = TC and TB = TC then TA = TB F. Reversble transformaton 1. A reversble transformaton s one n whch each state (pont) n a system s n equlbrum so that a reversal n the drecton of a small change returns the system to ts orgnal equlbrum state. (A reversble transformaton s one n whch each ntermedate state n a system s n equlbrum so that a reversal n the drecton of a small change returns a system to ts orgnal state.) a. An example of a reversble transformaton s sothermal expanson / compresson. There are no dsspatve effects (turbulence, frcton, electrcal resstance) n a reversble transformaton. b. There are no dsspatve effects n a reversble transformaton.. e.g., turbulence, frcton, electrcal resstance. 2. An rreversble transformaton s always a transformaton accompaned by a dsspatve effect. a. An example s free expanson of a gas nto a vacuum. 3. In an deal reversble transformaton (e.g., sothermal expanson) a contnuous graph can be drawn and unque values of p and V can be assgned. 4. In an rreversble system, no graph can be drawn; no unque values can be assgned to a values descrbng the system. a. For example, n a pston system, the pressure mmedately behnd the pston s less than the average n the medum as a whole because of the tme lag n stress. Thus, as was sad above, no unque value can be assgned as the pressure of the system. 3
4 II. Macroscopc descrpton of an deal gas A. The Gas Laws are concerned wth the mass m of a gas confned to a volume V at pressure P and temperature T. 1. Pressure s defned as the net force of the molecules exerted per unt area. 2. Temperature s a measure of the mean knetc energy of the molecules n the gas 1/2 m v 2 where m s mass and v s velocty. If two gasses have equal temperatures, the one wth more massve molecules wll have, on average, slower movng molecules. At a temperature of absolute zero, v = 0. B. In general the gas laws are qute complcated. However, f the gas s mantaned at very low densty (n addton, temperature s suffcently hgh and pressure s suffcently low) then the gas laws can be smplfed greatly. An deal gas assumes that ntermolecular attractve forces are neglgble. Most gasses at room temperature essentally are deal gasses. C. Boyle's Law: Gven an deal gas system wth a constant temperature and fxed mass, a change n pressure or volume n the system wll result n a changes of pressure and volume such that PV = f(t). D. Charles' Law: Gven an deal gas system wth a constant pressure and fxed mass, the temperature ncrease and the relatve volume ncrease occur n approxmately the same proporton (the approxmaton owes to the coeffcent of expanson of the gas). 1. Charles' also deduced that gven an deal gas system wth a constant volume and fxed mass, the temperature ncrease and the relatve pressure ncrease occur n approxmately the same proporton (the approxmaton owes to the coeffcent of expanson of the gas). E. Gas Law (Equaton of State) 1. Start wth a homogeneous mx of constant composton a. H2 gas.. Mass of 1 kg of H2 used to defne system b. The state of the gas may be specfed by 2 of 3 varables. p, T, V are the state varables. Only two of p, T, V, the state varables, are ndependent. U, S, H (IE, Entropy, Enthalpy) are state functons:.e.; functons of state varables. v. State functons are perfect dfferentals. c. Laboratory experments suggested that p, T, V could be related by 'equaton of state'. 2. The equaton of state for deal behavor of gasses (gasses for whch molecules are ndependent of each other;.e., no attractve forces exst between each other). a. pv = nr T = mr T/M = mrt. n = number of moles = m / M. R = unversal gas constant ( J mol 1 K 1 ). M = molecular weght (kg kmol 1 ) v. R = R/M = specfc gas constant v. m = mass of gas 4
5 3. Defne densty as ρ = m / V a. Equaton of state becomes... pv = mrt p = (m/v) RT = ρrt b. for 1 kg of an deal gas, specfc volume (a) s defned as. ρ = 1/α 4. Defne the number of moles n a gas as n = m / M = mass / (mass/mole) 5. The unversal gas constant R s from Avogadro's hypothess. a. Gasses contanng the same number of molecules occupy the same V at the same p and T b. Ths results n pv = nrt 6. Van der waals equaton descrbes behavor of real gases from sememprcal relatons (p+a V 2 ) (Vb) = RT (for 1 mol) a. a and b are constants for each of the gases 7. Gas Law n terms of ndvdual molecules. a. Boltzmann's Constant  unversal gas constant for molecules 1 1 R 8314 J K kmol 23 1 k = = = 1.381x10 J K 26 1 NA 6.022x10 kmol b. The equaton of state s,. p = no k T. no = number molecules / unt volume. Gas Law appled to molecules. F. Mxtures of gases 1. Partal pressure a. The pressure p of the 'th gas s the pressure t would have f t alone occuped the volume at the same temperature T. 2. Total pressure. (Dalton's Law) For an deal gas, the total pressure s equal to the sum of the pressures exerted by each of ts consttuents consdered separately. p= p 3. The Gas Law for each gas n a mxture s m R pv = nr T = mrt, where M = = n R 4. The Gas Law for the gas as a whole s pv = n R T mr T = a. The total moles number of moles n = n 5. The mean 'specfc gas constant' and mean molecular weght are mr R m and M nm = = n 6. The mole fracton of each consttuent of a gas mxture s N = n n 5
6 G. Atmospherc composton 1. Major consttuents M % V %M R (J/Kg/K) N O Ar CO H a. Mean gas constant for dry ar: Rd = J / kg / K b. Mean M for dry ar: Md = g / mol 6
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