Homework 1 Solutions

# Homework 1 Solutions - Problem 1 A 3-kg plastic tank that...

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Unformatted text preview: Problem 1: A 3-kg plastic tank that has a volume of 0.2 m3 is ﬁlled with liquid water. Assuming the density of water is 1000 kg/m3, determine the weight of the combined system. GWEN? ' gLHEWc/z YW : 150414 3 [’93: {wk 391 = (3.22 m” 8:430 = woo Leg/m3 V Do that A WW Scum-ism mugo : 8H9)“; Xvi = LtmOXOrﬂ = M iii; “MOM ’ wank + Mlle/0 ‘ 303 “3) ”than? 1 “/1ij = (Ros “MM-2?; My») : WOHH?) M Wrioile: MOM M Problem 2: One British thermal unit (Btu) is the amount of energy required to increase the temperature of one lbm of liquid water by one degree F (one degree R) at standard temperature and pressure (STP). This is equivalent to deﬁning the constant pressure speciﬁc heat, cp, of liquid water at STP to be: Cp = 1 Btu / lbm-R. (A) Using appropriate conversion factors, show that the corresponding value of cp in SI units is Cp = 4.187 kJ/kg-K. (B) The kinetic energy of a body of mass m is deﬁned by KE' = ész, where V is the velocity of the body. Determine VgivenKE = 4.187 kJ and m = 1 kg. . ' (C) The potential energy of a body of mass m is deﬁned by PE = mgz where g is the acceleration of gravity and z is the elevation of the body above a given reference location. Determine 2 given PE = 4.187 kJ, m = 1 kg, and g = 9.81 m/sz. : ‘i’ IXQXOOSM 5’5 CP . 4427 a?“ [4,. \/1 \/ (2 t es/wwc ‘5’!” [k7] / 4.4 (:7) l! . _ F_(2K“q,'rg'*‘751tooo‘T‘f ” \ t i) ' 'qa’jasqs‘c. _, W3 7' (12.5) “/5 < PQOBW 02 Lamb (C) r?! PE = “”5 2 (£4,1377Xl000) U > (a. a9 e) %[email protected] 73’ m 2*: “QM? m ‘ Problem 3: The mean free path of a gas , A, is deﬁned as the average distance traveled by molecules between 1 collisions. A commonly used formula for estimating ,1 of an ideal gas is: i=6L px/RT Where ,u is the Viscosity of the gas, p is the density of air, T is the-temperature in Kelvin, and C is an experimentally determined constant. Calculate the mean ﬁee path of air (in units of nm) at 25 °C and standard atmospheric pressure if the viscosity of air is 1.8003 x10'5 N—s/mz, the density of air is 1.169 kg/m3 the constant C is equal to 1.3. (Hint: use R = 0.287 kJ/kg—K for air) I GWEAA] C: t3 , g i ‘ M: L300} XLJS “IS/ma : . j 3 HM V3/m3 {Q : 0,927 ”7/3.-“ T = 83+ 973.1; : QQXJS k SQW‘WM‘, M ARI/50W 'U/IJQ'S need) «Lo ’\2 C ‘———-" Mir/(4 (Nit j)\/ )QT (/mq’s {0F [75): ML I ‘ VT : KLB )( ’8063 ﬂops ) WK UM) v/W I‘m/7+ mm 44> [7] so meoui’f * \[E‘bf—‘g: I; 0.000 00 o 0&8le ' m ~ ,\ 2 (338.14% mm Problem 4: A Ford Taurus driven 15,000 miles a year Will use about 715 gallons of gasoline compared to a Ford Explorer that would use 940 gallons. About 19.7 lbm of C02, which causes global warming, is released to the atmosphere when a gallon of gasoline is burned. Determine the extra amount of C02 production a person is responsible for during a 5-year period if they trade their Taurus for an Explorer. Tatum/bi CV32 Fmdvcb’w P4” ‘IW (75 \$J>qu7 lb“ L052) I yr 36:} [I H CODI’PKUCk/bkzh‘ M S yeag 70qg’l 5' lbm we} Exﬂlorv: (3001 ,omde, igef YW? (Cltto 3%F>()0L7 [55041) 1 485’? ‘5‘“ (“OJ/Yr USA Pmdt/Uidn VIM Syea/s - qRSCZO ”‘14 COQ Extra 0% = 92‘ 16,255 m com2 Emt cor) .- 29‘ «so lbw. coQ Problem 5: The water in a tank is pressurized by air, and the pressure is measured by a multi-ﬂuid manometer as shown in the ﬁgure. Determine the gage'pressure of air in the tank if in = 0.2 m, h; = 0.3 m, and h3 = 0.46 m. Take the densities of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and 13,600 kg/m3, respectively. , _ ‘WOil ELL/air 14.: 0.2m ix“: Dv-BW. 143: (Wt m 3150 : .2003 ”fl/QB 1503 - 85% lei/m6 M ereury ’ 11’le 5 WP'/5“ﬁ€ 'Sew'nou; sﬂmpiy Pix/#054039. f/‘BSSW‘C x/Zn'Mh 40 60a. 3%.?! Comm 053: E‘Pa : it”? O) 03'. ' ‘ P‘4 id ”1 . » 7 7 We?) _ _ v 149,03 94 ’ Pi : 30w 3 M' £3) mewlhwi'e Ps4 PS 1CD”) WAN), W5! Adel (3)01?! Q3) doseW/ \$xbW m zest/H 4% Q) (Pi " PQ : i733 31”} _ 300i} 514:2 ~ 40010 31/11 "P’RoQME-m 5' gm“! ‘) 710% “Mama mm 9-933 as «a big {Jorfﬂon F3 pas/91w ow) We 6;} 554,9 waver Fowfnms are nejw‘ﬂre. (TWA/MW? ”(NM {Jon/ff a +9 pow/1' I m 4443 diam/mm W W JQWV) *H’Vlﬂﬁiq H‘S [cu/\$3 Pﬁasm) 04) MA W uﬁ Mg ‘4 Of] 04} hraﬁr @tmegr {De/35%) . “Pp P; : O3é007m-81K0MD -(§5©7(9.8D(o,3) ’ QoooXiMoM 56‘ qo 72/ Max 9% P; P) odmos (OM/L {IN/um 6). 3:95.91 T Pl ‘ P& I R)5a3-e.5 SQ‘CH Wm . Problem 6: The basic barometer can be used to measure the height of a building. If the barometric readings at the top and at the bottom of a building are 730 and 755 mmHg, respectively, determine the height of the building. Assume an average air density of 1.18 kg/m3 . P1 = ”33.0 mmHg '1 P3302: rssmmiég I) :‘ 3187, 01333761 \4 ‘— 337.Ci m Problem 7: The temperature of a system drops by 27 °F during a cooling process. Express this drop in temperature in K, R, and °C. «Meaty/E a WNW“ «t l Jig/u CUE/“vs (m) I Rea/m M M 5M Maud" also a éf’He/We or” M 021—)? I Mme MID-5mm! Wu: {25 AT = 97 °F AT: .27 re amt—Mm? 41412 L0 [dell/I’M OT ; 97R K L [3 k i3}? AT 2 [5 K ...
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