'\ thermometer reading IF is brought ito a room where the temperature is 70°F; 1 min later the thermometer reading is 31°F. Determine the temperature reading as a function of time and, in particular, find the temperature reading 5 min after the thermometer is first brought into the room. ANS. u = 70 - 52 exp (-0.291); when t=5, u=58. ‘ ; jal 2 -u( TT.) Jat Te IGt tye Tot too ie (t sam te oF teImin ete Ts) vesmin {ah . bude een tesmin sete tert Jean K wat _’ - o-2vt 9) wate Te qo4 (-92)e oats cpa 8) ate ]e - ade fae eee te Inuwy jae i . 7 Ye > “$4 ( : ist Co “KW Cro Ts 19°92 ay gered ol = 10° SO ay 2 dic > ~Y 62 npr “1 ines) ! ‘A thermometer reading 75°F is taken out where the temperature is 20°F. The reading is 30°F 4min later. Find (a) the thermometer reading 7 min after the thermometer was brought outside, and (b) the time taken for the reading to drop from 75°F to within a half degree of the air temperature. ANS. (a) 23°F; (b) 11.5 min. to pee Weaae 0 yewtce te met eM yy Te mF comin 43° ani (gh oor apt S5u" 1 t= mia (EE ey \ rio = ee jh ne > : at in( B) = -Ab J Te wt ain ns)~ 5 T™ dot ev 4. ke 70 4202 te 0a Dt athe wor Te ts tte dose Wy soe ovtaot aye 0-202 © [Ih I ng J In [2 te th ogmn“3. At 1 :00 P.M, a thermometér reading 70°F is taken outside where the air temperature is -10°F (ten below zero). 1e reading is 26°F. At 1 :05 P.M., the thermometer is taken back indoors where the air is at 70°F. Att :02 PM What is the thermometer reading at 1 : 09 P.M.? ANS. 56°F. dene ee Tete Use PF £0 Tare toe HE TC ete Wee teamin 7 cade wu -w + G007*) Ts aut i tox “1d tY “34 -2k tepmin 0 0 [er Me Th dy ‘ ee tett Hes #) = Ke - 0-394: + 09903 (F ‘ -0 We oes) a e Te peu Tc=20 Tosue @ to T v1 Ce 8 egy = 104 ce -04- U4 : tes tC0%® @ tain 7 ppnel) = 70-4 7 ahd Tess [EF 6. At9 AM., a thermometer reading 70°F is taken outdoors where the temperature is ISF. At 9:05 AM., the thermometer reading is 45°F. At 9: 10 A.M., the thermometer is taken back indoors where the temperature is fixe and (b) when the reading, to the nearest degree, will show the correct at 70°F, Find (a) the reading at 9: 20 A. (70°F) indoor temperature. ANS. (a) 58°F; (b) 9:46 AM. Te wor Wscusr to Tate Cel TET EOE) -k Te4s¢ Gann we le tb He ts rss Tse t=lomin (2.98 s0- ge] In 5 Tx ts ete ao = gk - oie x ma ) . teist aoe °) Ls) Tete tle" T= ab 37 F a ~~ -O-1g1% SM = 104¢ » is oe 6) Troy “BUD = -orltite yage 40-48. 2 . > ~0-12In @ sea fee een ™ © Tstle7 = ais Tr Isthe 0. (aia( 10) la ure) = -o- Wye oda > 10 - WUT T= 38 sor | Kp.iue t* 36 $10 # Ws ¥o7. At2:00 PM., a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 py. temperature reading yielded by the thermometer is 42°F. Later, the thermometer is brought inside where the a ; at 80°F. At 2: 10 P.M,, the reading is 71°F. When was the thermometer brought indoors? & 0 Ts 3 Tots tae @ ta tz aman ; ee Bor 701 (HO #27 otal pe Fie T5760 F (2 60 inl 247 woo 1) Ia te fom Te UF Alte. ue @rt 42 soruor * fe (40) - be - 0-94 To dor gon whe / 2 2 meme ae ae tgtl T> yo4C Wt Gog -0-F944 & -¥02¢ C= Goro Ht _ C= goC e-em, mint? UF T Sop wolere mt) pK We B04 wooed ,) --eLI) MS Gos eo e-0-77 HUM 44 yg -KU) Assume Newton's Law of Cooling to solve the following problem: A bodyof temperature 100°F is placed at time t= O in a medium the temperatureof which is maintained at 40 deg * F At the end of 10 min, the body has cooled to a temperature of 90 deg * F (a) What is the temperature of the body at the end of 30 min? (b) When will the temperature of the body be 50°F? Tet, vlee eet et tle ) THMF 29 Ts=40 T-Tette in kl T40F tlom th > 40 ae ¥ )T=% — €2romin C~ to web a) Ts a ~ 9 -01829( 40) Te 7412 ( ) Ot? tro —w RP > 40 tuo o- 0-026 In f= ee rm yw 60e o 8. Assume Newton's Law of Cooling to solve the following problem: A body cools from 60 deg * C to 50 deg * C in 15 min in air which is maintained at 30°C. How Long will it take this body to cool from 100 deg * C to 80°C in air that is maintained at 50°C? 7 wet Tq Tsry tee Totes yp? oe sp Dot ade Tsp T3799 Grisman eos “FIT x. w 72 mM (=90 nl So Tr1m Tss0 G7 Bo apse WW (%, c2s “kez 509105 1 , © WS) + R. = 0-092 2118 -Gomin CT? 6 Tyas vette) ~ 800903 UE) 80> “yo 20 7 aye 207 LE) In 20 Se, tm wo may 9. Ahot pie is taken directly from an oven and placed outdoors on a porch table to cool on a day when the surrounding outdoor temperature is constant 80°F. The temperature of the pie was 350 deg * F at the instant t= 0 when it was placed on the table, and it was 300 deg * F 5 minutes later. (a) What was the temperature 10 minutes after it was placed on the table2(b) When was its temperature 100°F? Toe SOF 1290 too Tete ree pn Te bo E ZI KE @ 30 ban t=300 Exmin 30° corte 202 <¢0 ta70 7 * 18) c~ th a rol 1 temin [tas betel Ty ; L10 ET y) eI) bet ; J @ temo et aud Be) a> -p. one 4 3 in sae (eva taut 4) @ teiy TH? a te bore Ke ae ssl ~ o-o40ay (16) 0 T= wt [ Fo Cee a wD. oe ~o-vgotvt = In| 375 _ ‘ Tard. WP Sree 2 U4 C09: 54ming 10. At 10 A.M. a woman took a cup of hot instant coffee from her microwave oven and placed it on a nearby kitchen counter to cool. At this instant the temperature of the coffee was 180°F, and 10 minutes later it was 160°F. ‘Assume the constant temperature of the kitchen was 70° (a) What was the temperature of the coffee at 10:15 A.M.?(b) The woman of this problem likes to drink coffee when its temperature is between 130°F and 140°F. Between what times should she have drunk the coffee of this problem?To T3712 bey in etl : T+ Ts elev Te We line * t= luo 0 SOM tens! 70 + C97 tuo «70 e196 e') « a) 17 Ce ismnly Ww =¢ 3) tet hte? TBO 4 MO ! @ te oe te? Ie Te weine” la0<70 ta ¢: 207 Th In t: oO 20min @ t+ Hor tx? Te 70 F110 p- KE [4o «70 tno ¢- MOUNRE n[ 22s Dy wn? tOFeT,, ta. 99 Ilo Io 8) beeen 2959 min $0 2b-t0min ho i ao te In os We “001004 0 ) B teivmln ? T= 79 4)0-¢** T=10 +0 - vopert ©) Atank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at 2 gal/min, and the well-stired mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time, and (b) the time at which the brine leaving will contain 1 Ibi/gal of salt. ANS. (a) s = 160[1 - exp (-/40)}; (b) t= 40 In 2 min. [4 lect e aa (wo “Teen le © 4 fs 1uo-x~ “4H ads of de Xu0 ) Zo de te fine) = roe (Xwo) = ceat 4) xe Co Huo @t-o xed 9= Cera) 10 C= -140 X= toe Hed a Ly 4K dt 4 4p we tuo dudy\ A Pan of hot water is removed from the stove and placed nearby to cool. At ths instant the temperature of the water was 200°F, and five minutes later it was 190°F, Assuming that Newton's Law of Cooling applies and that the temperature surrounding the pan of cooling water is 60", what will be the temperature of the water 20 minutes Tepe | tzo after it was set down to cool? ae _ : Team 20 b> <0 t Wtte @ 40 teemin 19 termi Dev * bo tee bo ea, te? t= gami'n Wo? o Ro = tune, bo = wos") @ T+ 1 e=pomin \h toe ry 2 te yoecaoe F = (al ee - 6-062 £20) xe 6) o G0 tog k=o-pitey