123 - Exam 1 - Fall 2010 - solutions

123 - Exam 1 - Fall 2010 - solutions - SE) , _«r’|‘”...

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Unformatted text preview: SE) , _«r’|‘” I 1'" . \. | J! (15 pts) Problem 1: Multiple choice conceptual questions. Fill in your answers on the bubble sheet. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. You have two balloons, one filled with air and one filled with helium. If you put both balloons into a tub of liquid nitrogen, which one will end up with the largest volume? a. the air balloon 13k. (>3 MMQ f 4Ame A the helium balloon c. they will end up with the same volume “Oxi‘r \o‘LuQISKH Qfl/xcfihflqsa A pool is filled half with water and half with a light oil (density 600 kg/mg). The oil floats on the water. When a diver comes up from the bottom of the pool, from the water into the oil, she will experience a buoyant force in the oil that is the buoyant force she felt in the water. a. greater than . . C13) less than N dQWSAT “Q (Shut) c. the same as /— be I) For the next three problems, consider the cyclic process described by the figure. For A to B: is Won gas positive, negative, or zero? a. Positive g . (Q Negatlve EXQma95 '— (lo-wk 45>WU: “‘2 42 R J 0 Zero d For B to C: is heat added or taken away from the gas? a. Added No wfi,kl $0 AECKV "': Taken away ' ' \, \ ,. , <0. Neither (Qadded : Afr ‘ + h [\{UQ$ “K S “\6‘ ‘R M Q 01? L (Jag!) For C to A: does the internal energy increase, decrease, or stay the same? 3. Increase __ ‘ - V , ‘ . (ED Decrease /’8 WC 0‘1" ’5 c1313 (vutuai‘zr’i {xx/r"- MU) c. Stays the same (AEim = 0) The figure shows a circular piece of steel with a gap. When the steel is heated, the width of the gap: a. decreases @ increases [5 Q‘fiod'l‘) :(Q 5.. Q"\. (Cur c. stays the same V f {ML ski—Q- d How many degrees of freedom is a CH4 molecule likely to have at room temperature? (That is a molecule that has a carbon atom at the middle of a tetrahedron, with 4 hydrogen atoms sticking out from the carbon in four different directions along the points of the tetrahedron.) ' f. g (1) g_ 2 '5 4r ()vl.s\. 0 NM») 6 2 7 u.n‘\‘ei’§\. W‘ Qua d 3 i. 8 e 4 j. 9 Bernoulli's Law is a statement of: conservation of energy k conservation of (regular) momentum conservation of angular momentum conservation of mass/volume probability none of the above at) c. d. e. f. The first law of thermodynamics is a statement of: "A conservation of energy b. conservation of (regular) momentum c conservation of angular momentum (1. conservation of mass/volume e probability f none of the above Thermo Exam 1 — pg 2 1.10. The second law of thermodynamics is a statement of: a. conservation of energy b. conservation of (regular) momentum 0. conservation of angular momentum d. conservation of mass/volume @ probability f. none of the above 1.11. As an airplane flies horizontally at a constant elevation, the pressure above a wing is the pressure below the wing. a. larger than 63 smaller than Tim... dig/menu Q‘ssf'é'h-"kfi 84m?- i‘u’l‘U 11? 1‘ c. the same as 1.12. A plastic cube and a metal cube of the same size and shape are put into water. The plastic cube floats; the metal cube sinks. On which cube is the bouyant force the largest? a. plastic @ metal 15 ~ Void“, Salami.ng 09 0. same buoyant force 0.14 0.12 1.13. This normalized histrogram was created from 50 students in *2 a physics class. If you pick a student at random, what are the g 010 / chances he/she will be between 61 and 67 inches tall? 3 “N a. 0 ~ 10% ( a 0-08 . 10 — 20°/ . E i) 20 ~ 30%: A” ‘1 1’ was ' 1°43 “W E 0-06 d. 30 ~ 40% , a 5 e. 40 _ 50% Di ,0 is m& - E 0,04 .7 fly 4 i i f. 50 40% “* 002 g. 60 — 70% ' h. 70—80% 000 i h" _7 7, 7 ‘ i. 80 — 90% ' 60 61 a; 67 68 69 7o 71 72 73 74 75 7e 77 78 .1. 90 — 100% Height (inches) 1.14. As I'm taking data in my lab, I typically average data for 1 second per point. Suppose I decide to average the data for 2 seconds per point instead. How much better is my signal-to-noise ratio likely to be? a. the same J2 times better 0. 2 times better (1. 4 times better e. 8 times better 1.15. First, heat is added to a gas while keeping its volume constant, increasing its temperature to 2.5x the original value. Next, the gas is compressed to 40% of its original value while keeping the temperature constant. Which of the following diagrams best represents the two processes on a standard P—V diagram? 21) ) c) d) e) g) b D Thermo Exam 1 — pg 3 A M (10 pts) Problem 2. (a) You have a 1.003 cm diameter steel ball which you desire to pass through a 1.000 cm inner diameter aluminum ring. Both are at 50° C. If you heat up only the ring, how hot does it need to get (°C)? (b) A typical 100 W incandescent light bulb has a tungsten filament which is at a temperature of 3000 K. Typically, of the 100 W that goes into the bulb, 97.4 W of heat is conducted or convected away, and only 2.6 W is radiated as light (and most of that is invisible infrared light—now you see why incandescent lights are so inefficient). If you assume the emissivity of the filament to be 0.4, what is the filament's surface area? sets ,7 C!“ (M VH3] I ‘ p / sag AW) mud) P 'ZW/ $m\i\4\4¢wT§ z\ m 2 , Q, N a!» W s A! ~ Wee—WWW. i Q 63-” ( (M)<S«tfl} (o 3 wflkqjkgbumK)“ Thermo Exam 1 — pg 4 22/3451: 243/13“ (10 pts) Problem 3. A heat pump pumps heat fiom outside your house (10°C) to inside your house (20°C). It pumps heat into your house at a rate of 2000 J per cycle. , ,4. a What is the theoretical limit for the heat pump's coefficient of performance? 3 ‘4 (vi S ‘3’“ i w Caf _: 9i , 9,21.-. lwi (QM"®L§ I _ Tk I @L + : wk jg“ (b) The actual COP is 3.5. How much work per cycle is required to operate the heat pump? MM: :— 917$?)th CM 3-5 w— ") 6+3 (c) How much heat per cycle is removed from the great outdoors? Thermo Exam 1 — pg 5 (12 pts) Problem 4. You add 200 g of copper at 150°C to 300 g of water at 30°C. The water is in a nifty foam container which completely insulates the water and copper from any outside heat and doesn't absorb any heat itself. What is the final temperature of the water/copper mixture? / W Z“ 5:1) WSOQC/ 3011/ V T1) 1 7 L69 (bsl 1:3 (MK '3; wakrri @C ink“ 1 chw/QN my”? Newer; Thermo Exam 1 — pg 6 PM 6 c 57; (20 pts) Problem 5. An engine using 0.2 moles of ‘monatomic ’deal gas is driven by this cycle: starting from state A (150 kPa, 350 K), the gas is compressed isothermally until it rea he‘s*state B at 400 kPa. Then, the gas is heated at constant volume until it reaches state C. Finally, the gas is expanded adiabatically back to the original state. P C 3 V (m ) T (K) T 350 350 B A V %’ (11/; (a) Find the unknown P’s and T’s for all three states. (Hint: it’s probably easiest to find them in the order listed.) state A volume: A flit/4 92 m. 1) ( "gr/Min S PvrMZ‘T ‘D VA, ‘0 ‘\\§b_'“3 WK Av \/,,: ‘3. 9dd"lb'$m MW a W61 3! 37W” it.) «r lg LloD- is”) 13% w...“ . w “M: lgm-maw' Vrg bluish/i“) lmq : \fq abn 1mm" tom‘s... . K . . state C temperature: (Hint: figure out/use the adiabatic relation between T and V to connect states A and C. Warning: be careful! If you get this part wrong, you will likely miss three of the next five questions.) CL C \\ M_Mu__n ‘_ , v .v A > d l > ecu-Eff >344 To” state C pressure: (Hint: after you get this answer, it’s probably worth taking a minute or two and using it to double-check your answer to the state C temperature. If you did things right then, your answer here should satisfy the normal adiabatic relation between P and V that connects states A and C.) J «V “m mp .9 2 SEC : @ ZWJJSE' 3‘ w><¢71059 K v" [WISV-N’gmg Thermo Exam 1 — pg 7 Problem 5, cont. 8 {7K (b) Find the heat added to the gas during each of the three legs. ALB i5°+<whflmmq '\ 1332/4 T mm -+ (ysgmg (32 WWW my! a j “"13mech 3 m “Q,va :szotxgsi E/Wm)C5$m) 5W ( egg—sag?) B-C ‘1 F” (c) What is the efficiency of an engine using this cycle? Hint: Use the heats you just found in part (b) to identify Qh and QC. CW ; Em $1.; to 3" mi ca ~ can *1 2W8! 3 13ml n iiiflfl/ Lotte ’5 a QR ’ gflflefl" “Mm-m Thermo Exam 1 - pg 8 (11 pts) Problem 6. (a) Use the ideal gas law to figure out the density of air at 400K at 1 atm. (The average molar mass of air 6W3 molecules is 0.029 kg/mol.) WV :1 “Wu—T N ’ «(a m __ ‘0 24 NW i: i firt- MW for) O’Z‘i Warm) T r“ 5-" ~ ‘ .1, , , 1, =3 _ fl \ C (.3 :39! ""({,w‘ my; Li :30 L" {I .x. WWWWW'W‘Wj (b) In Lab 1, you used a contraption like this to measure the density of an unknown liquid. h2 Suppose after pressurizing the bottle you measure h = 75 cm and the gauge pressure to be 1.5 psi 4, (0(3) (n__ot the absolute pressure P). What was the density of the liquid? Vmufiéwe lrvu- r.“ “2:. p “()(QSSWF‘ alga 2 ‘00 JV m L\ h gauge pump bottle Thermo Exam 1 — pg 9 “Sr (11 pts) Problem (a) A 3 kg block of metal is suspended from a scale and immersed in water as in the A figure. The dimensions of the block are 12 cm x 10 cm x 8 cm. What will be the reading of the spring 5W? scale? (Le. what will be the tension in the string holding up the block?) (b) What gauge pressure (not absolute pressure) must a pump generate to get a jet of water to leave its nozzle with a speed of 10 m/s QpU at a height of 3 m above the pump? Assume that the area of the nozzle is very small compared to that of the pipe near the pump. V/II".‘;M~”0 Y5\. «Qu\ \“ "x we“- / ——-\> ,K - L) L 3‘ A J? l Thermo Exam 1 — pg l/fIO , ’l ‘8 (AK ’ /§ (11 pts) Problem‘fiC Heat is added to 4 moles of a diatomic ideal gas at 300K, while keeping its volume constant as shown in the 9 (’l 5 diagram. This causes the temperature to increase to 900K. (a) What is the change in entropy of the gas? a“? Cmer “4de? ~, (3) c; “(QM (3"? P B A g A. a? Ci; (w 4-” it‘ll,” elf a y (1ch IT A : 0 CV 3km way—YO V (b) If the heat came in from a reservoir kept at 950K, what was the change in entropy of the universe? Hint 1: It's the sum of ASgas (0 (1H and Asmmr. .. and it had better end up positive! Hint 2: Finding Asmemir is a constant temperature problem. My Ag =‘ 3:. gmgaqwq A \ ” A M? T g ngflyerdk1§Q<. e (Q My, [C32 kg ncvfl 26mm'§_S<-75I:{‘.t)(<avnez-) __ m T _ g Q -— LI?€?C.03“ \Awiaqfifll 9.;QQ (new zil— vlr mews-5 r , Ktow/(5,0 7 4 My — w» » 3“ Ag quL a 526W; 4” AgmrxNQ-UQ [3 33“"; at: pQéQfxlfi-tf —_ 0H1? 5/!K ~ Saw; I/L Thermo Exam 1 — pg 1/0 [\ (4 pts; no partial credit) Extra Credit 1. If you flip 40 coins, what is the probability of getting exactly 12 heads? I Dl‘fi W47$4° $61} 0 head; ‘ _ . 4 J I -_ ‘. Vasca‘s mama . 11”“ r “5" ’WJ ’ (“3 I \ y)’q,\l$ éx) 3th Zb’\)\«fl\‘l 21E ‘ .yu ('3 l 2/ \ 39%"? \%?l k”, eh” r ED l O, _ iii—WWW at opal/l»an lime) I \10 2 W‘s-j. C ‘7' 298.17.! ~ ‘ ; r3. 1" 245 {\QWN—f’ (Sam/:3 was. are) 4! 7t 'l‘oJ—aicii va§§l‘l7|\l’}\\‘-J : 24o V‘Ox g Syb‘zwlfi"3 (Ii—Mi ~ —» MW 9,! m 1% (4 pts; no partial credit) Extra Credit 2. Suppose an atom has only three available energy levels, which are at these energies: state 1 = 0 eV; state 2 = 0.2 eV; state 3 = 0.5 eV. (The conversion between eV and joules is found on page 1 of the exam.) If the temperature is 1000 K, what is the probability twat the azmris in the 10 est energy state? ~20J r. O , fggav 8r \ (O iofioggfif -Zi x a Y 1w 13,26110 U \ imam Gav ; O .8 \ I l wflnmum.,,wr '1‘“ ‘ {2‘ ‘3‘ Q N 9 f; a— are! at a on Titan] am"..sz 6“?“ a. l Thermo Exam 1 — pg 12 ...
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123 - Exam 1 - Fall 2010 - solutions - SE) , _«r’|‘”...

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