exam 1 - solutions

exam 1 - solutions - EX 0M l §nlo+WE “ Piqu_5ll'3...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EX 0M l §nlo+WE “ Piqu_5ll'3 W\r¢\itf ‘ZQU ‘ Cth (17 pts) Problem 1: Multiple choice conceptual questions. Choose the best answer and fill in the appropriate bubble on your bubble sheet. You may also want to circle the letter of your top choice on this paper. 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. An extremely precise scale is used to measure an iron weight. It is found that in a room with the air sucked out, the mass of the weight is precisely 2.000000 kg. If you add the air back into the room, will the scale reading increase, decrease, or stay the same? r V ,. a. increase ’Tlnq loco‘PW‘ {ch L- £«wx ’i‘A‘L 0W “\QW‘ kill)“ .. the. V; lg “ 3th.} decrease go p f“ V ’r ,L mm. c. stay the same Three cubes of the same size and shape are put in water. They all sink. One is lead, one is steel and one is a dense wood (ironwood). plead > psteel > pimnwood. On which cube is the buoyant force the greatest? . 1 d V _ lax 5:261 :‘J‘fiQ~ fl 5‘0”va buoxjc..;i 0. wood same buoyant force Water flows from a little pipe into a big pipe with no friction or height change. The volume flow rate (m3/s) in the little pipe will be in the big pipe. a. greater than @ the same as 0. less than fl$ Rh: Q} J {wit} LS CflCwngrt Sbl\«i€/ Va» C-m“$“~i'5wl"”' As an airplane flies horizontally at a constant elevation, the pressure above a wing is wing. a. larger than i b. smaller than c." the same as the pressure below the W.) 1,27: ow plumb .0 t.\ I x} . "l Melba (k Marysr Cam.0txr'-»a.«~s.'i' W crawling " “$4,? TAG“ Q40. 53”“: dqujmfmnqu a‘bmo ~\ inflict») NJ “2% A grandfather clock is controlled by a swinging brass pendulum. It keeps perfect time at 20°C. If the temperature drops to 10°C does the clock run fast, slow, or the same? runs fast . » A .- h .—l -. <1 A 5: km» "’72 “*5. "2" b. runs slow 5 ‘1 e r Q V ‘ Kg ) 0. runs the same : ‘. l " \ «midis You have two jars of gas: helium and neon. Both have the same volume, same pressure, same temperature. Which jar contains the greatest number of gas molecules? (The mass of a neon molecule is greater than the mass of a helium molecule.) 9 -- I . . 2 " «f ,, 'L 5' a. met. a. Jarofhehum " [\‘(LW B 'i i’V'! 0% “i 4“ J b. Jar ofneon We» VI VA Mugl in»? SQM‘WQ ' ® same number m 27rkBT What would be the appropriate integral to calculate how many molecules have speeds between 200 and 250 m/s? 250 3/2 The probability density function for the Maxwell-Boltzmaim velocity distribution is: f (v) = 47r[ ] vze—"WZ/ZkBT . ® N101>< (V)dV (fix. gist finch h §‘--.'i3:jiili-w‘§ 200 ' ‘ 250 b- Nmrx Jv'fO’MV 200 250 c. NWX Jvz-f(v)dv Phys 123 Exam 1 — pg 2 1.8. What would be the appropriate integral to calculate the average speed (not rms speed) of all molecules? a. j-f(v)dv 0 l7.) . I r r 3mm“?! v.‘»."‘}"V”’/Ca(i_‘ ) Iv.f(v)dv (Awe! .WL clog u was,» ’1 w, in s 3 ‘M; 0 00 0. I122 -f(v)dv 0 d. V - f(v)dv 0 1.9. Slabs of metal 1 (thermal conductivity k1) and metal 2 (log) are placed together so that their flat surfaces are in contact. The two slabs have identical dimensions. Metal 1 is in thermal contact with a reservoir at T1 and metal 2 is in contact with a reservoir at T2. What is the temperature at the interface between the metals? Tmavxlx a. (kl + k2 ) (1:11] + [62112) UK s9 b. (k1+k2)(/<:1T2 +k21]) 3M“ :1. «fifipk I glah Z.’ k17l +k2Tz I 161m2 k, Whack?) \ MK CV 243.1119.) T2 d leZ'I'kZYl y k v k1 k2 k1+k2 A a T 1 1‘1 ' \s\\“m'\‘\\\=\c1‘L”“*l m 6. 'k—+;— +k2T2) ‘ A \: —\\ 1 2 1 TmL\\\+}~1> ~1th L k 1 1 _ ,. . 1"...“ /........m A......... i . ... >1 « V,.,,.\, ., Una...“ f. —+— kT+kT T ,1», ix [kl k2] ( 1 2 2 ]) /|\W'\ : \Ki—w-L- Li-w/ "Wu; rt; (A qucknl) fig“ 1". \$\&\LL /\ Mi -wma.w._.-_«“ ,0 U , ml 1.10. First, a gas is compressed adiabatically. This heats up the gas,{whilemitspressure increases to 2.5x the original value. Next, more heat is added to the gas, this time as it is expanded isothermally, until it returns to its original pressure. Which of the following diagrams best represents the two processes on a standard P—V diagram? L— C) L d) e) f) g) h) 1.11. For the next three problems, consider the cyclic process described by the figure. For: A to B: does the internal energy increase, decrease, or stay the same? b Increase ’TWD >T“ tagfimwk d iii \\ If)er be Wx‘mfilmf \ Decrease c. Stays the same (AEmt = 0) V. 1.12. For B to C: is heat added or taken away from the gas? Added 5”. “1(3me ., Taken away CW} o Magnum, in WU“- C. Neither (Qadded = Q : A ETC“? \A Phys 123 Exam 1 — pg 3 _ TQLTG So «ii/1t). 1s. 09:50" V1 1.13. For C to A: is Won gas positive, negative, or zero? a Positive - . i ‘ u i c. Q Negative \NiWM- ‘8 dac’iaafij )‘Sa Hormfimmj é”? l" unfit; 33‘ 0. Zero 1.14. A heat engine performs x joules of work in each cycle and has an efficiency of e. For each cycle of operation, how much energy is absorbed by heat? @ 35/6 & Cr “’1‘” mi“) e tA N " c. xe Q)“ d (l-x) e (l-x)/e f (1-x)e 1.15. If you flip 10 coins, what is the probability of getting exactly 8 heads? 8! ~ ~ 8!2! 3' 10 dimc'flhk/S vx “ 8 have)? wmrosi‘ak f. 10 b_ __81_ MM at Maugham . g. 10! 2110128 lelzs 8! to 10! c' 101210 3 ‘9» @mml" l0 8!2! . 10! d' 212128 7“ 1' 8!8!28 e 812! fi (0'. l ' 2110!28 ‘ 24%; {(8 1.16. 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? (If you like, you can consider the “signal” to be 3 volts and the “noise” to be a standard deviation of 0.112 V, like in the homework problem.) a. the same \ _ "e @ «5 times better 4: \u aka-ha“; m the FLA-C Raj \‘ g" c. 2 times better \0 Ji «Drag wad Maw/>9 3 \0 j 2» d. 4 times better \ l I e. 8 times better 5 waxy/“51; Cx UAWSQS by v: \FZ' 1.17. Suppose an atom has only two available energy levels, which are at these energies: state 1 = 0 J; state 2 = 2><10'20 J. If the temperature is 300 K, what is the probability that the atom is in the higher energy state? 20 —23. t 20 I 43. a. 1+e+210 /1.3810 300 (M; 1+e+210 A3810 300 —2-102°/138-10“23~300 Z 2 €40 “ f- —‘—'~__2.1020/1.38_10—23'300 b' 1+6 Cxle' Q A ALT e 1 ‘ Q 6—2.1020/1.38-10“’3-300 c. 1+ -2.1020/1.38-lo—23.300 7 g. —————_2‘1020/138'10_23_300 e -' 1+e ' 20 —23 d 1__e~2-10 /1.38-10 -300 E;D K h allow/1384043300 ' 20 723 1 Elm/138‘“) '300 Q R ‘3 1—-e+2-102°/1.38-10‘23-300 20 —23 1__ 8—210 /1.38-1o ~300 e+2l1020/1'38.10_23_300 i- —20 23 e ' 1p Luficrsiau 1__ 6—240 /1.3s-1o- .300 n QMLD/(QT a” ._mm... ado/(ch l t 6} Phys 123 Exam 1 — pg 4 (8 pts) Problem 2. (a) What is the upper limit to how far soda (density of soda w density of water) can be sucked through a vertical straw, assuming you can obtain a perfect vacuum in your mouth? 6/“ «NW g :9 , i , ix {:5 a rm , \ I a M 1: ~ if; Ciro! 9“ 1,o\~lo$ W 5 Cm” rn”)\ 5') walk...“ \ \A; [0"? :mv-r—m-t—gmwa ,vam-NM “mafia” ' ( \__ (b) A 13 kg block of metal is suspended fi‘om a scale and immersed in water as in the figure. The dimensions of the block are 12 cm x 10 cm X 9 cm. The 12 cm dimension is veltical, and the top of the block is 7 cm below the surface of the water. What is the reading of the spring scale (in Newtons)? Phys 123 Exam 1 — pg 5 (9 pts) Problem 3. A horizontal pipe 7 cm in diameter has a smooth reduction to a pipe 5 cm in diameter. If the pressure of the water in the larger pipe is 120 kPa and the pressure in the smaller pipe is 85 kPa, how fast (m/s) does wagerflownthroughm’ghempipgs? Hint: how does the velocity in the second section relate to the velocity in the first section? \Akow‘aljvuwx. 3’” Q Sal Vt “ft?! “N3 V3“ f\\\m_um W \sd 0%“55 Elk - itch T 97w \l “V M” K L I I)" “7 OZ, 4‘ (x V z" A I Q‘J< Mi‘ “Pi: M \l A\(_ ‘44wa ¢§¢memrxw was 40 rag}: V z» 4v V. k (‘59 [oh i \3 Se Q \ 'h 9 ‘fl \ A 2 on.) U\ _ Pt * PL : 3 £1“) Li."th My, ~ ww'w‘” l p Y A ZQF ‘FEHLJ »~ 1.. i if W “M” 8‘4ti "\ 5» nil/WA ~ \ K w" V n it“ calm" {WW m m (6’ WT; Phys 123 Exam 1 — pg 6 .. a b A Q 9 Q00 j/HXRQI ‘X Q 2% ‘° A; (10 pts) Problem 4. (a) An aluminum rod is exactly 20 cm long at 20°C, and has a mass of 300 g. If 11 k] of energy is added to the rod by heat, What will be the change in length of the rod? (Hint: the heat causes a change in temperature, which in turn causes a change in length.) (9 W\ a .25”? ‘1) AT 3" “W VV‘ (2,". {tech} “.5 Qfingjlfivo%§a) fi" nmmmmmfl A bLsedl,s’T <:(}lu§°§:)C2mhtwofl%Z> d. . r.» .M.=....M_.MM 3' lflb’éflo’qm MWWW“"V‘“ I AL: In outside temperature is 22°C. If it takes 3 hours for 1 kg of 0°C i e to melt in the container, determine the thermal conductivity of the (b) A Styrofoam box has a surface area of 0.8 m2 and a wall thickne f 2 cm. The temperature of the inner surface is 0°C, and the Styrofoam. Q0 ‘ L: LRAT t W X kStyrofoam : __ J/svm-°C Phys 123 Exam 1 — pg 7 (10 pts) Problem 5. (a) How many nitrogen molecules (N2) are required to fill a spherical balloon to a diameter of 35 cm at a temperature of 290K? Take the pressure to be exactly 1 atm. # molecules = (b) In one of the liquid nitrogen demos that I did, a small volume of liquid nitrogen turned abruptly to gas and expanded. The expanding gas was then trapped by a giant thin blue cylindrical plastic bag-type thing. Find the ratio of the volume of the expanded gas (now at 300K, 1 atm) to the original volume of liquid. P (a , gas ‘ U92 1m] Q ‘ gags MN A v .. __ o Hamid ‘v “91 ésws (9'3 8fog/ltj/b‘ q” \Q‘;; g l Q ‘ ink'i \m‘. 5 kg; r.” g p l 9"“? \‘3 \’\'$ “EJH u ,3 mu?!“ in’mac'i’ CL ‘k QWH‘O . \ML ‘ ‘ . SPK j < \/o\ 10 Vgas/Vliquid : Phys 123 Exam 1 — pg 8 (10 pts) Problem 6. (a) Find the average kinetic energy and rms speed of individual nitrogen molecules at 300K. W kb SCu‘iancwl 9” 3,026. \CE "~ K3: _\ \ =wl m/s (b) According to theqjulonngetit 15%, what should the specific heat of aluminum be? Note that the molar heat capacity C, in J /mol-°C, is related to‘the spégific'heat c, in J/kg°C, via the molar mass. Hint: You can compare your answer to the measured specific heat of aluminum, en on pg 1 of this exam. at ' {a i I fret.) Q“; Him as?" 4 ‘ l ( CA1 — J/kg-°C Phys 123 Exam 1 — pg 9 (6 pts) Problem 7. In the “cotton burner” demo, Wayne compressed a volume of air by a factor 31: about 10. That is, the final volume was 1/10 of the original volume. Treating air as an ideal diatomiQ 2 gas, find the final temperature of the gas (assuming it started at 300K). “W‘MM'” \ 1 V . E dig/r. in‘g J?“ 25/ 6‘ AVK E my 1”" T2 is ‘jé K g ‘1 g» “L Z“ . V2,, 101% Phys 123 Exam 1 ~pg 10 (12 pts) Problem 8. An engine using 0.0401 moles of diatomi ideal gas is driven by this cycle: starting from state A, the gas is cooled at constant pressure until it reaches state B. Then, thegas is heated at constant volume until it reaches state C. Finally, the gas is expanded isothermally back to the original state. The pressures, volumes, and temperature of all three states are given in the table. — "l :‘7 (s w (a) Find the heat added to the gas during each of the three legs. fl (Law‘in ‘6) 'nwbwrk ‘(pqmfigj M I) 800460) 2 F mm Q «SAM-W \ .. , _~ :N AE.':>U*“JMM>AE"+Q 9° Q" N” W “07 {WV} m H \ Hm; DZ KT 9% VWL/v (Wade M «9w “D a ' 0 Z V\ o : Qoioqb‘b'30RVKm‘ 9M3 .1 (b) How much net work is done by the gas each cycle? Q.“ ; 900 + 52%.: 1 K‘Z‘i-SI \Wci: 70503 V Wm : Ql",\QC/\ : \19:§\) (c) What is the efficiency of the engine? a : \L‘i’?~ a: \ g 61? 9Q“ QJZ'CZIS, - “a (d) What is the maximum theoretical efficiency for an engine operating between the same minimum and maximum temperatures? 7’3"? m“ r a. Qmmt. : \” Téfix‘k \/ ‘7‘” W $39)"? A) Phys 123 Exam 1 — pg 11 (10 pts) Problem 9. (a) Given the same gas and the same three states as in the last problem, calculate the entropy change of the gas in the isothermal change from C to A. . Q) 4“ (VGA @ww9 m imi phale CM; SS: t ‘ t“ l ASc—A = (b) Calculate the entropy change from C to B, and then from B to A, then add them together and show you get the same AS as found in part (a). (Note that OB and B—A are opposite the direction used by the gas in the previous problem; otherwise you’d get an answer that was the negative of the answer found in part (a) instead of the same as that answer.) . I}: mm bulwark} A T Chg AS“iH‘S “Cfi‘w‘C‘VQMD/n, ,. T - T M mmmmmmmm ___ 1 Coqb\xsi.%,‘gx)&v\ (é): ‘”,‘il$ 37;; m 33‘. N11 Q 40A: MW“? 3t}? r “:8: "x: r Phys 123 Exam 1 — pg 12 26%.. 2% k (8 pts) Problem 10. (a) Suppose you want to keep the inside of your fieezer at a temperature owhen your house is at What is the maximum possible coefficient of performance for a refrigerator operating between those two temperatures? W. ; MWW» C “‘0 WM" Cva "Wu COPmax = (b) If 400 J of heat leak from the environment into your freezer each second, what is the minimum theoretical power that your freezer will consume to keep the temperature inside the freezer at —5°C. «406"; 3 (9(— 5 2:va Waco» CVD‘A‘M “ 322* “"' Q: / ear? 6‘54 Pmin = W Phys 123 Exam 1 — pg 13 (5 pts, no partial credit) Extra Credit. You may pick one of the following extra credit problems to do. (If you work more than one, only the fu‘st one will be graded.) (a) A wooden cube, side length x and density p (p < pwater), bobs up and down in the water in simple harmonic motion. While bobbing, somehow it always continues to sit square in the water. In terms of x, p, pwmm and g, find the period of the harmonir m K \9215' motion. If?) XL? ‘2. V3) +11 ‘3 A W13 “Til/mm. » - ' (B I; M _-:: 4/ e fiWKfl midi? J 3 )9} (’w( W 3(J D t 6 N (X1 DX> (a 1: CsY‘S‘iDFJW 3” 6* X ED 1lSp/\;\g (amylaiik 5., €N‘i-2"8M (b) Make an estimate of the surface temperature of Mars the same way you did for Earth in HW problem 7 —4: The light from the sun reaches Mars’s orbit with an intensity of 580 W/m2. The radius of Mars is 3390 km. Wikipedia says the actual surface temperature varies between —87°C in the winter to —5°C in the summer; you should get an answer in between those two temperatures. a 9% <11qu £51 than, ~3—la14, KN A“ W ’ Q60 {gmvm'v‘th T q c) C)» we r '\ A I W| NNNN "i 2 ~ ; y *l .. “3 g ' “F (n .1 « low/rt r Mom Fat-Al?» " Qflfltj“ apt/“157 ‘i’ 1 P 0C, 9 : Ti (LIX SE50 “east 3 Q GQWKZJT J \: a. _ czY 9 ‘5 7"“ gums» ewloéll‘l "‘ W U . . . . . . mm at We‘- lea (c) 400 g of ice at —20°C 1s added to 50 g of steam at 160°C in a thermally—insulated contamer. Ignoring the heat capacrty of the container itself, find the final temperature of the combination. If it turns out that not all the ice melts, or not all the steam condenses, then give the amount of ice that melts (or steam that condenses) instead. 033m; 1;“, lg, L (Q [.99 L.‘ S‘i‘lmw\ \\ *Afifihl'mam (all “k-Q. l""€v-\‘m{ £- - L ’V C ( ‘6“ r’r‘g ) xcioflb) “K L J‘m‘cwt‘l’G) : “5 C54 WWW”) H“; MM “5 W WWW c awash») s at a...) nutrient?) QQMXWMJ + Qbaitwot} “ASXW‘M l "G “Tel Q , #209,312, H.710 + ‘7’ng 4 HWHN all ./ M30 + tl’éo 0’4 Le‘lgo { ’3 mead): % 03+ 6 nlfifilxlfiw, C C.\\:().c/' nu“ a“ EU; WQl—lu w} rm "‘3qu vs 0%. : Q0<)C1m°)¢eo\ + (,ei3){2.2c'ro‘9) +Qos)\q\8b)('°°) t u 1) “W” 0i W “W! Audi’s i3 Q'm Qv‘3L'LKV‘L“) L10) + m [533993) e 4 “Elam . "7) . {She Na 55m)» Mk" WA-k O.\l\«j) As$uvxpl“\ \r-Ws (er/«113'? Phys 123 Exam 1 ~ pg 14 ...
View Full Document

Page1 / 13

exam 1 - solutions - EX 0M l §nlo+WE “ Piqu_5ll'3...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online