Physics 73 Recit Answer Key

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  Name: Student Number:Recit 01Physics 73 TWHFALumantas 17 August 2016 Section: Recit Teacher: ^#; fo' 3a, Instructions. Answer the following problems completely. Write your complete and tractable solutions on the space provided and box your final answers. You may discuss with your classmates. You are also allowed to ask your recit instmctor. However, you are not allowed to open any notes, books, orelectronic devices. Problem 1. Thermal Expansion[5pts] You are making pesto for you pasta and have a cylindrical measuring cup of 1O.O cm high made of ordinary glass [p :2.7 x 1O-s(Co)-1] ttrat is filted with olive oil [c :2.27 x 1g-+16'o;-r]to a treiitrt of 3.Ofrelow the top of the cup. Initially, the cup and oil are at22.OoC.You get a phone call and forget aboutthe olive oil which you leave on the hot stove. Thecup and the oil heat up slowly and have a common temperature. At what temperature will theolive oil start to spill out of the cup? olofTabe+[etcmpena{rere...Pl'o $reoliueoilo}q'thospit} Vo1 , p t bo *Be ,,Xl'X,it ood uolurnq cxyaosioo oDQ+f^uc$l vat r da be tie ,f,r',ItrJ onol (.tn'or | '0 'ltrc ot(,oe oit sta/k t slitt trhtvt V rp (Ir) - Vorirrroil (T.) ,%r * prV.s a'[ = Vo. + f Vo, 61 of 1* orf tt u oh'.e oi I 8o, Vo1 f P, Url AI = Vo, + td,bVo. Ai AT= Vr1 -U0,, (te Vo. - P, Sr) Problem 2. Temperature Scales (A) you put a bottle of soft drink in a refrigerator and leave it until its temperature has dropped iO.Of. What is its temperature change in (a) C [2pts] and (b) F ? [3pts] (o) lo' o 0' =b Tz = vcr-vr- rTr =&B) {Tr .XItorhr- p,t ) or a[,= s4T,l32 oV, = u/rucr) se Lb ) oc, -- [ 'F, - b') 5 o 9rU /s =[ 9t /5 o F= (lo) Gn.Uor' p, Va 1 L = G3''1 C Porit - O1  Recit 01Physics 73 TWHFALumantas 17 August 2AL6@) Another temperature scale having an absolute zero is the Rankine temperature scale. The freezing point and boiling point of water correspond to 491.67 R aod 671.67\ respectively. Give &e conversion from Fahrenheil to Rankine (i.e., F to R). [5pts] 7rce;i1 y oiot 4 gt. 07 l? gaoF [ iliy yt. Jiy. Ld orthlry f+ I lnrjf 6T. al \ o 2t2 F t60 tg0 farki e {crnntq f So, Problem 3. Melting Ice [Spts] Suppose you have some ice kept at 0 C. You want to bring 450 [mL] of lukewarm Iiquid waterfrom 27 C to OoC at atmospheric pressure. How many grams of ice should you put in the water? (c : 419O1/kg'K,Lf = 3.34x10s J/kg, Lv=2.256xL061/kg) Q;,, .t Qwow , O rnice Lt 1 lttwCw AT = O rhr.e : - Iwcw Df = - 4Eo^L (ts/^L)Awo tr)(- ttb) Lr i.n xros 11* o( Problem 4. Calorimetry [spts] A 30-g silver teaspoon at room temperature (20 C) is placed into 200 g of hot tea (100 C). No heat escapes the spoon-tea system. You may assume that the specific heat of tea is the same as that of water. The specific heat of silver is 0.0564 cal/9.R. What is the equilibrium temperature of the system? [10pts] cc= Q.ostclca'L (1tt}'tl)(+Z) = 235'97?b Tf. \ tc^t /\tvg I Q silver * 0rro i O msqATs + mscaAls =o fnsct(1 - zot) + r*cu('rt - roo)'6 Te = loe tfiaCa) + ZO lTtt Cg = J- r€.'R C*r k + r'q-cr) fft lT, . 99.o 'c I  _'' -'- ,tt Parit-ol too(o.d Q r{.r) t eoitu.og%:Y2t:A \ (o'otrt'*or2,.,, q l R= oF-l 4se.coT  Recit 02 Physics 73 TWHFA-x Lumantas 24 August 2016 Name: Student Number: Section: Recit Teacher: Instructions. Answer the following problems completely. Write your complete and tractable solutions on the space provided and box your final answers. You may discuss with your classmates. You are also allowed to ask your recit instructor. You are also allowed to open your notes' Problem 1. Heat Conduction [9 Pts] A hollow cylinder has length L, inner radius, a, outer radius, b, and the temperature at the inner and outer surfaces are Tp and ?6 where Tru ) Tc (The cylinder could represent an insulated hot water pipe. The thermal conductivity of the material of which the cylinder is made is k. (a) Write an expression of the heat current,H, in terms of its thermal conductivity, k,latetal surface area, A,and temperature gradient O'/Or(2 pts) (b) What is the lateral surface area of a cylinder? Substitute this expression in your answer inpart (a). (2pts) (c) Place all expressions with H, r and dr on the left side of the equation and all other expressions,k,dT, etc. on the right side of the equation. Put proper limits of integration for thi radius r and the temperature T and integrate. Write the total heat current through the wallsof the cylinder, H,in terms of k, a,b,Ty and'76? (3pts) (d) Show that the equation for the total heat current reduces to an equation for the linear heat flow when the cylinder wall is very thin' (2pts) Problem 2. A Thermos for Liquid Helium [5 pts] A physicist uses a cylindrical metal can of 0.250 m high and 0.900 m in diameter to store liquid heiium at 4.22 K. The boiling point of helium is at 4.22 K at latm and its latent heat of vaporization is2.09 x 104 I /1rn.Co*pletely surrounding the metal can are walls maintained at the temperature of liquid nitrogen,TT 3K,with vacuum between the can and the surrounding walls. How much helium is lost per hour? The emissivity of the metal can is 0.200. The only heat transfer between the metal canand the surrounding walls is by radiation? H n r- a he r(l*- T,o ) z fi: e-rrh l-2trrz = \\n,r = Ae.d(lq-t.t) = A frJh 1. Ln1L '= o. o83zl b obs th ) (s . G'tx; s)to''1 (r.*t - 't7'3 ,) a - o' (Y31'l W N- o ' 03?11 T/# ngalirG ri1 'ry(rnJ $^{ \^16$ ',, #^0 l-nt'f c,''(d +' -}te +' }al *U 11;; \*ai ,crn bc olrotk), rog tg(.', cavcoa6 i{ il' V r1on'r< rnlv = o'-wT f/S (Ecoo't) *..,,@ Ll2  Recit 02 Physics 73 TWHFA-x Lumantas 24 August 2016Problem 3. Ideal Gas [6 ptslHelium (M : 4.00 g/mol) gas with a volume of 2.50 L, under a pressure of 0.180 atm and at a temperature of 39.0oC is warmed until both pressure and volume are doubled.(a) What is the final temperature? (4pts) (b) How many grams of helium are there? (3pts) (q) ho'n PU = nRT d> I- = ,60 =o crvrFrn\ '\ -./ ?tU, = P* i ?z=2?, i uz, ?u, T, 1x ?r{ = ayw) =P Iz 'i 2- = 4 x (usr ar3 r5 K) L5) fl, IrU, TK -- [o ts6 rK)(a.q)vf 6;n;qv/(, Ds?nG V^4 ) Go\.F i fn-.nM= 4'oo€ * o'0l1tmo\ wo\ : 0. D l?L rnole Problem 4. Counting [5 pts]Compute the number of molecules in 1 mm3 of nitrogen in standard temperature and pressure. (Trtp = 0.000 C, Prtp = 1 [atm] = 101313 [Pa], R = 0.08206 fL'atm/mol'K] - 8.3'L4 []/mol.K], 1 [mL] = 1 [cm3], Na = 6.022 x 1023) Hint: Compute for the number of moles first. \@wAGo)'r'^ '/( rc]'nr /( wo t' ) h = Prl FI .l{ = Os: fl)''s)k jr= tL49 (,- d(rxra-6t*) ., = 4 4oxto-8*,1 fo,oteol LLb \( k) f ;[* ')\ ) r1 Nn = Q o6 x\p Brol )(t .ozlxro e' 9rk :) L-o I tL \) z 7. Gg X Io r ,olec,,,l/l Recit - 02 212
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