Announcements 19 Nov 2009

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Lorraine Kelly
5 years ago
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1 Announceents 19 Nov No class on Tuesday (Fiday instuction). Exa 4 stats today! a. Exa ends Tues Nov 4 (late fee afte 3 p) b. Coves Chaptes 9-1, HW 15-0 (but cuulative) c. Anticipated aveage tie: hous d. Anticipated aveage scoe: 75-80% e. No pobles whee you tun in wok f. ook ove the fist page of exa on class website g. No outside calculatos (you can check one out if you like) h. Things to study, oughly in ode of ipotance: i. HW pobles ii. Conceptual stuff, especially: 1. Clicke quizzes. Waup questions 3. Deos 4. Questions fo old exas iii. Pobles fo old exas iv. Woked pobles fo class v. Textbook pobles Suay of Chapte 1 W on/by gas = aea unde cuve in P-V diaga (watch the signs!) U depends only on T; often it s stictly popotional 3/ nrt fo onatoic, 5/ nrt fo diatoic at ~300K P-V diagas: to gaph changes to state; visualize isotheal contous to undestand changes in tepeatue and hence U 1 st aw: U = Q added + W on syste Fou specific changes constant pessue: W = P V constant volue: W = 0 isotheal: U = 0, W = nrtln(v /V 1 ) adiabatic: Q = 0 Fo fuel Heat Engines: tansfo heat to wok buned exhausted nd aw: but not all of the heat! Q h = W net + Q c efficiency = W net /Q h Canot Theoe: often not even ost of the heat! ax eff. = e c = 1 T c /T h Song: (4 inutes) 1 Fist page of the Exa yellow = stuff specifically fo this exa Constants: g = 9.8 /s but you ay use 10 /s in nealy all cases G = N /kg kb = J/K NA = R = kb NA = J/ol K σ = W/ K 4 Mass of Sun = kg Mass of Eath = kg Convesion factos 1 inch =.54 c 1 3 = 1000 Othe equations b ± b 4ac x = a Suface aea of sphee = 4π 3 Volue of sphee = ( 4 3) π vi + v f vave = v = vo + at 1 x = xo + vot + at v f = vo + a x w = g, PEg = gy F = -kx, PEs = ½ kx f = µ k N (o f µ sn ) P = F// v = Fvcosθ F t = p Elastic: (v1 - v)bef = (v - v1)afte ac length: s = θ v = ω atan = α ac = v / GM GM Fg =, PE g = Ipt ass = R Isphee = (/5) R Ihoop = R Radius of Eath = Radius of Eath s obit = Density of wate: 1000 kg/ 3 Density of ai: 1.9 kg/ 3 inea exp. coeff. of coppe: / C inea exp. coeff. of steel: / C Specific heat of wate: 4186 J/kg C Specific heat of ice: 090 J/kg C Specific heat of stea: 010 J/kg C Specific heat of aluinu: 900 J/kg C 1 at = Pa = 14.7 psi 9 T F = TC Idisk = (1/) R Iod (cente) = (1/1) Iod (end) = (1/3) = p = p = p sinθ P = P 0 + ρgh VFR = A1v1 = Av 1 1 P1 + ρ v1 + ρgy1 = P + ρv + ρgy = α 0 T V = βv0 T; β = 3α 1 3 KEave = v ave = k BT Q = c T; Q = Q T T = ka 1 T 4 P = eσ AT Won gas = aea unde P-V cuve = P V (constant pessue) = nrt ln ( V V 1) (isotheal) = U (adiabatic) 3 3 U = NkBT = nrt (onatoic) 5 5 U = NkBT = nrt (diatoic, 300K) atent heat of elting (wate): J/kg atent heat of boiling (wate): J/kg Theal conduct. of aluinu: 38 J/s C vai = 343 /s at 0 C sin(30 ) = 0.5 cos(30 ) tan(30 ) π 3.14 T = T K C Qh = Wnet + Qc Wnet Qc e = = 1 Qadded Qh eax Tc = 1 Th ω = k, T = ω = g, T = π π T v =, µ = µ k g I β = 10 log I0 = 10-1 W/ I 0 v ± v0 f ' = f v ± v S v f n = n n = 1,,3,... v f n = n n = 1,3,5,... 4 Exa 4 - Review of ipotant concepts 1. Pessue & Buoyancy in Static Fluids F a. Definition of pessue, foce/aea: P = A b. Definition of density: ρ = V c. Static liquids: i. Pessue inceases with depth, P = P 0 + ρgh ii. Pessue in static fluid is the sae at sae h d. Achiedes Pinciple: F B = weight of displaced fluid = displaced fluid g = ρ fluid V object g. Fluid dynaics: Pessue in Moving Fluids a. Viscosity b. Gaden hose equation, VFR = A 1 v 1 = A v i. Why/when tue c. Benoulli effect: otion of fluid causes P to decease i. wings: cobination of ai deflection and Benoulli 1 1 d. Benoulli eqn: P1 + ρ v1 + ρgy1 = P + ρv + ρgy 3 Colton - ectue 4 - pg 1

2 3. Tepeatue effects a. Theal expansion: i. = α o T ii. V = βvo T (β = 3α, fo solids) b. Ideal gas law: PV = nrt, PV = NkBT 1 3 c. Kinetic Theoy Equation : tansl. KEave = vave = kbt i. Use to get aveage speed o aveage KE d. Intenal enegy both ae given on exa U = NkBT = nrt (onatoic) 5 5. U = NkBT = nrt (diatoic, ~300K) 4. Heat a. Caloiety: Q gained by 1 = Q lost by (Bluepint eqn) i. Q = c T; Q = both ae given on exa ii. Colton ethod: Make sue each te is positive heat 4 b. Radiation: P = = eσ AT tie i. Descibes heat eitted and heat absobed heat T T1 c. Conduction: P = = ka tie d. Convection: qualitative only 5. Theodynaics a. P-V diagas i. Isotheal contous to visualize tepeatue changes ii. Wok done on/by a gas: aea unde cuve on P-V 1. Positive vs. negative b. Fist aw: U = Q added + W on syste c. Five special state changes: i. constant P ii. constant V: W=0 iii. isotheal (constant T): U=0 iv. adiabatic: Q=0 v. cycle: U=0 This is what I give you on the exa fo those changes: W on gas = aea unde P-V cuve = P V (constant pessue) = nrt ln ( V V 1 ) (isotheal) = U (adiabatic) d. Engines: geneal pictue i. Q h = W net + Q c Wnet Qh Qc e = = ii. Efficiency: Qadded Q h Tc e 1. Canot Theoe: ax =1 T h iii. Second aw: Two vesions, qualitative eason Colton - ectue 4 - pg Colton - ectue 4 - pg 3 HW 15-. Piston 1 in the figue has a diaete of 0.58 in.; piston has a diaete of 1.5 in. In the absence of fiction, deteine the foce F necessay to suppot the 500-lb weight. HW Oil (ρ = 700 kg/ 3 ) is poued into the ight a of a U- tube and fos a colun = 3 c high. (a) What is h? (b) Ai is blown acoss the left a while the ight a is shielded; the left side gets sucked up until the two sides ae at the sae height. What is v? (ρ ai = 1.3 kg/ 3 ). Answe: 1.5 lbs Answes: 0.9 c, 11.6 /s Colton - ectue 4 - pg 4 Colton - ectue 4 - pg 5

3 HW An undegound gasoline tank at 54 F can hold 930 gallons of gasoline. If the dive of a tanke tuck fills the undegound tank on a day when the tepeatue is 90 F, how any gallons, accoding to his easue on the tuck, can he pou in? Assue that the tepeatue of the gasoline cools to 54 F upon enteing the tank. Use the coefficient of volue expansion fo gasoline given in the textbook, β = / C HW A 45.1-g block of ice is cooled to 78.3 C. It is added to 567 g of wate in an 85-g coppe caloiete at a tepeatue of 5.3 C. Deteine the final tepeatue. Reebe that the ice ust fist wa to 0 C, elt, and then continue waing as wate. The specific heat of ice is 090 J/kg C. Answe: 948 gallons Answe C Colton - ectue 4 - pg 6 Colton - ectue 4 - pg 7 HW What ass of stea that is initially at 11.6 C is needed to wa 340 g of wate and its 86-g aluinu containe fo.5 C to 48.5 C? HW A Styofoa box has a suface aea of 0.83 and a wall thickness of.09 c. The tepeatue of the inne suface is 4.8 C, and that outside is 5.5 C. If it takes 9.79 hous fo 5.54 kg of ice to elt in the containe, deteine the theal conductivity of the Styofoa. Answe: 17.4 g Answe: W/ C Colton - ectue 4 - pg 8 Colton - ectue 4 - pg 9

4 HW Calculate the tepeatue at which a tungsten filaent that has an eissivity of 0.5 and a suface aea of will adiate enegy at the ate of 36 W in a oo whee the tepeatue is C. HW A saple of heliu behaves as an ideal gas as it is heated at constant pessue fo 73 K to 369 K. If 34 J of wok is done by the gas duing this pocess, what is the ass of heliu pesent? Answe: 900 C Answe: g Colton - ectue 4 - pg 10 Colton - ectue 4 - pg 11 HW 19-5 (b). Calculate the wok done on the gas as the gas expands along path IF. P i = 3.05 at and P f = 1.07 at. HW oles of a onatoic ideal gas have a volue of , and ae initially at 354 K. (a) Heat is caefully eoved fo the gas as it is copessed to , causing the tepeatue to eain constant. How uch wok was done on the gas in the pocess? (b) Now the gas is expanded again to its oiginal volue, but so quickly that no heat has tie to ente the gas. This cools the gas to 3 K. How uch wok was done by the gas in this pocess? Answe: -417 J Answes: 4550 J, 3640 J Colton - ectue 4 - pg 1 Colton - ectue 4 - pg 13

5 HW 0-6. A nuclea powe plant has an electical powe output of 1000 MW and opeates with an efficiency of 33%. If the excess enegy is caied away fo the plant by a ive with a ass flow ate of 1.9E6 kg/s, what is the ise in tepeatue of the flowing wate? Answe: 0.6 C Colton - ectue 4 - pg 14

Tidal forces. m r. m 1 m 2. x r 2. r 1

Tidal forces. m r. m 1 m 2. x r 2. r 1 Tidal foces Befoe we look at fee waves on the eath, let s fist exaine one class of otion that is diectly foced: astonoic tides. Hee we will biefly conside soe of the tidal geneating foces fo -body systes.