Solution Manual for Thermodynamics for Engineers 1st Edition by Kroos 1.1 (B) The utilization of energy is not of concern in our study If you use energy to power your car, or your car seat is your own decision 1.2 (C) All properties are assumed to be uniformly distributed throughout the volume 1.3 (D) 1.4 (B) When the working fluid crosses the boundary, it is a control volume, as during intake and exhaust The ice plus the water forms the system of (C) The entire atmosphere forms the system of (D) 1.5 (C) An extensive property doubles if the mass doubles Temperature is the same for the entire room or half the room 1.6 (D) A process may be very fast, humanly speaking, but molecules move very rapidly so an engine operating at 4000 rpm is not thermodynamically fast All sudden expansion processes and combustion processes are non-equilibrium processes Air leaving a balloon is thermodynamically slow 1.7 (B) If force, length, and time had been selected as the three primary dimensions, the newton would have been selected and mass expressed in terms of the other three But, in Thermo-dynamics, the newton is expressed as kg·m/s 1.8 (D) W = J/s = N ⋅ m/s = (kg ⋅ m/s ) ⋅ m/s = kg ⋅ m /s 1.9 (A) 34 000 000 000 N = 34 × 10 N = 34 GN (or 34 000 MN.) 1.10 (A) ρ= m = V 10 kg 8000×10 = 1250 kg/m −6 m 1 v=V = = 3 = 0.0008 m /kg ρ 1250 kg/m ρ 1250 kg/m Hg SG = = 1.25 = m ρ 1000 kg/m 1.11 (D) We must know if the surface is horizontal, vertical, on an angle? The surface cannot be assumed to be horizontal just because it is drawn that way on the paper (Sometimes problems aren’t fair This is an example of such a problem.) water F 1.12 (C) P = n = 36cos30° kN −4 2 = 1559 kN/m or 1560 kPa A 200 cm ×10 m /cm 1.13 (A) Use Eq 1.13 to convert to pascals: p = ρ gH = (13.6 × 1000 kg/m ) × 9.81 m/s × 0.42 m = 56 030 kg/m s or or 56.03ì10 N/m 56.03 kPa â 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 1.14 (C) ∑ F = PA + Kx = mg P × π × 0.05 + 400× 0.2 = 40× 9.81 ∴ P = 39 780 N/m or 39.8 kPa gage The atmospheric pressure acts down on the top and up on the bottom of the cylinder and hence cancels out 1.15 (B) We not sense the actual temperature but the temperature gradient between our skin and the water As our skin heats up, the water feels cooler so we increase the water temperature until it feels warm again This is done until out skin temperature ceases to change An object feels cool if its temperature is less than out skin temperature If that’s the case, a temperature difference occurs between our skin and the object over a very small distance, creating a temperature gradient (Tskin − Tobject ) / x 1.16 (B) The energy equation states that at the position of maximum compression, the kinetic energy of the vehicle will be zero and the potential energy of the spring will be maximum, that is, 2mV = 2 Kx (The velocity must be expressed in m/s.) 80×1000 × 2000 2 ∴ K = 98.8×10 N/m or 100 = × K × 0.1 MN/m × 3600 If the mass is in kg, the velocity in m/s, and x in meters, K will be in N/m But, check the units to make sure Get used to always using N, kg, m, and s and the units will work out You don’t have to always check all those units It takes time and on a multiple-choice test, there are usually problems left over when time runs out 1.17, 1.18, and 1.19 The Internet has the answers! 1.20 True Thermodynamics presents how energy is transferred, stored, and transformed from one form to another If you use it to dry your hair, power your car, or store it in a battery, we don’t really care Just use it any way that allows you to enjoy life! 1.21 Energy derived from coal is not sustainable since coal will eventually not be available, even though that may take 500 years If an energy source is not available indefinitely, it is not sustainable 1.22 Consult the Internet 1.23 A large number of engineers were required when the industrial revolution occurred 1.24 Trains were traveling the rails in the mid-1800s so mechanical engineers were needed, not to drive the trains, but to design them! Coal was mined with a pick and shovel until the late 1800’s Power plants and automobiles also came near the end of the 1800’s 1.25 It’s CO2 and it keeps things very cold Check it out on the Internet © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 1.26 i) A system, ii) a control volume, iii) a system, iv) a system No fluid crosses the boundary of a system Fluid crosses the boundary of a control volume Control surface 1.27 Before After The system and c.v are identical The system is the air inside plus that which has exited The c.v extends to the exit of the balloon nozzle 16 1.28 The number of molecules in a cubic meter of air at sea level is (3 × 10 V= πr 3 10 = 12 25 = ×10 molecules ∴ r = 0.00002 m or 0.02 mm 25 3×10 ) × 10 molecules/m 1.29 Catsup is not a fluid It is a pseudo plastic or a shear-thinning liquid, whatever that is! A fluid always moves if acted upon by a shear A plastic can resist a shear but then moves when the shear is sufficiently large Catsup is like that: first it won’t move, then it suddenly comes 1.30 From Wikipedia, stone = 6.35 kg (= 14 lbm) ∴6.3 stones = 6.3× 6.35 = 40 kg nd 1.31 The units using Newton’s law are simpler: ft lbf = slug × s 2 is simpler than lbf = lbm × 32.2 ft/s 32.2 ft-lbm/lbf-s The conversion between mass and weight does not require the use of a gravitational constant when using the slug as the mass unit in the English system 1.32 Volume is extensive since it increases when the mass is increased, other properties remaining constant 0.000998 − 0.001008 1.33 % change = × 100 = − 0.992% or −1 % 0.001008 3 = 57.2 lbm/ft ρwater = 62.4 lbm/ft So, ice is lighter than water at v 0.01747 32ºF, so ice floats If ice was heavier than water, it would freeze from the bottom up That would be rather disastrous Fish as well as skaters would have a problem You can speculate as to the consequences 1.34 ρ ice = = © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 1.35 SGHg = 13 600 = 13.6 1000 kg W = γ V = 13 600 m × 9.81 ×2m = 266 800 N m s W = 266 800 N × 0.2248 lbf = 59,980 lbf N 1.36 v ρ a ) ρ = = = 0.2 kg/m3, m = ρV = 0.2× = 0.4 kg, W = mg = 0.4× 9.8 = 3.92 N b ) v = = = 0.5 m /kg, m = ρV = 2× = kg, W = mg = 4× 9.8 = 39.2 N 3 c ) v = V = = 0.002 m /kg, ρ = = 500 kg/m , W = mg = 1000× 9.8 = 9800 N m 1000 0.002 102 d ) m = W = 1000 = 102 kg, ρ = m = = 51 kg/m , v = = =0.0196 m /kg g 9.8 1.37 a ) ρ = V ρ 51 = = 0.02 lbm/ft , m = ρV = 0.02× 20 = 0.4 lbm, 50 32.2 ft/s W = m g = 0.4 lbm × = 0.4 lbf v gc 32.2 ft-lbm/lbf-s b ) v = = = 50 ft /lbm, m = ρV = 0.02× 20 = 0.4 lbm, ρ 0.02 g 32.2 ft/s = 0.4 lbm × W=m = 0.4 lbf gc 32.2 ft/s c ) W = m g = 1000 lbm × = 1000 lbf gc 32.2 ft-lbm/lbf-s v = V = 20 =0.02 ft /lbm , ρ = m 1000 d)m=W g c = 500 lbf × g 3 = 500 lbm v = V = 20 = 0.04 ft /lbm, ρ = = m =50 lbm/ft v 0.02 32.2 ft-lbm/lbf-s 32.2 ft/s = = 25 lbm/ft v 0.04 500 This problem should demonstrate the difficulty using English units with lbm and lbf! Note that lbm and lbf are numerically equal at sea level where g = 32.2 ft/s , which will be true for problems of interest in our study In space travel, g is not 32.2 ft/s 1.38 ρ = v = =0.25 kg/m , SG = W = mg = kg × 9.81 s m ρx ρ = 0.25 = 0.00025 , m = V = 8m 3 water = 19.62 N 1000 (We used N = kg·m/s ) v m /kg = kg © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 1 1.39 v = ρ = 0.2 =5 ft /lbm ρ , SG = m = ρV = 0.2× 20 = lbm, ρx water 0.2 lbm/ft = 62.4 lbm/ft W = m g = lbm × = 0.00321 32.2 ft/s = lbf 32.2 ft-lbm/lbf-s gc 1.40 Only (ii) can be considered a quasi-equilibrium process Process (i) uses a temperature distribution in the room to move the heated air to other locations in the room, i.e., the temperature is not uniform When the membrane in process (iii) is removed, a sudden expansion occurs, which cannot be considered a quasi-equilibrium process 1.41 From Table B-1 in the Appendix, we observe that So, i) SG = 1.225 kg/m3 = 0.001225 1000 kg/m ii)SG = 0.6012×1.225 kg/m = 0.000 736 1000 kg/m iii)SG = 0.3376×1.225 kg/m = 0.000 414 1000 kg/m 1.42 From Table B-1 in the Appendix, we observe find the local atmospheric pressure First, P = 2.1 kg cm g × 1002 cm2 × 9.81m = 206 000 N/m or 206 kPa gage 2 m s (We used N = kg·m/s ) P = 206 kPa + 101 kPa = 307 kPa ii) P = 206 kPa + 101× 0.887 kPa = 296 kPa iii) P = 206 kPa + 101× 0.5334 kPa = 260 kPa i) (We could have used Patm = 101.3 kPa or even 100 kPa since extreme accuracy is not of interest) 1.43 Refer to Fig 1.6 and Eq 1.14 The pressure in the tire would be P2 and P1 would be open to the atmosphere: kg × 100 P = cm gage P − P = ρ g h 334 000 N m N 1.44 P = ρ gh 100 000 1.45 P = 10 atm ⋅ 100 kPa m2 2 = (1000 × 13.6 ) kg × 9.81 m × h ∴ h = 2.50 m or 2500 mm kg m s m = 786m3 × 9.81 s2 × h = 1000 kPa atm cm × 9.81 m = 334 000 kg ⋅ m/s = 334 000 N/m s2 m m ∴ h = 13.0 m (We used N = kg·m/s ) ∴ P = 1000 kPa − 100 kPa = 900 kPa g © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part = 1000 kg × 9.81m × 0.25 m = 2453 Pa = 2.45 kPa gage m s water P = ρHg g hHg 2453 = (1000× 13.6)× 9.81× hHg ∴ hHg = 0.0184m or 0.724 in 1.46 P = ρ g h 1.47 A measured pressure is a gage pressure a) P = ρ gh = 13 600 × 81× 0.10 = 13 340 Pa or 13.34 kPa gage b) P = ρ gh = 13 600 × 81× 0.28 = 37 360 Pa or 37.36 kPa gage P = P +P 1.48 a) abs gage atm = + 0.371× 14.7 = 10.45 psia or 1505 psfa P = P +P b) abs gage atm = 20 + 0.371× 14.7 = 25.45 psia or 3665 psfa 1.49 Consult the Internet 1.50 Consult the Internet 1.51 T ( °R ) = T( °F) + 460 = 120 + 460 = 580°R 1.52 T ( °C) = T(K) − 273 = − 273 = −270°C 1.53 T ( °R) = T(° F) + 460 = 400 + 460 = 860°R 1.54 T (K) = 37 + 273 = 310 K 1.55 Use Eq 1.20: a) R = R e β ( T −T )/T T = 3000e 0 b) R = R e β ( T −T )/T T 0 4220(25 − 60)/ 298 ×333 = 677 Ω = 3000e4220(25 −120)/ 298 ×393 = 97.8 Ω = 3000e4220(25 −180)/ 298 ×453 = 23.6 Ω c) R = R e β ( T0 −T )/T0T 1.56 Use V = β V T 0.00018 H = 0.00018× π × 0.003 × 20 ∴ H = 0.016 m or 16 mm 0.00018 b) π H = 0.00018× π × 0.003 × 40 0.00018 H = 0.00018× π × 0.003 × 60 c) π ∴ H = 0.032 m or 32 mm a) π 1.57 V = 60 mi ×5280 ft/mi = 88 ft/s , KE = m V 2gc hr 3600 s/hr × 88 = 300,600 ft-lbf 2500 lbm = ∴ H = 0.048 m or 48 mm 2 ì 32.2 ft-lbm/lbf-s â 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 300,600 ft-lbf = 386 Btu 778 ft-lbf/Btu or The English unit on energy is most often the Btu (some authors use BTU) 1 2 1.58 KE + PE = m V + mgh = × 5000 × 80 + 5000 × 9.81× 1000 = 65× 10 N ⋅ m = 65 MJ 1.59 At 10 000 m, g = 9.81 − 3.32 × 10 −6 × 10 000 = 9.777 m/s 6 Wsurface = mg = 140 000 × 9.81 = 1.373×10 N W10 km = mg = 140 000 × 9.777 = 1.369 ×10 N 10 000 PE = ∫ mgdh = m ∫ 140 000(9.81− 3.32 ×10 −6 = 140 000 = 10 000 9.81× 10 000 − 3.32 × 10 −6 10 000 h ) dh × = 1.373 10 × 10 10 − 0.0023×10 10 1.371× 10 N ⋅ or 13.71 GJ © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part 8 © 2015 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part ... 1.18, and 1.19 The Internet has the answers! 1.20 True Thermodynamics presents how energy is transferred, stored, and transformed from one form to another If you use it to dry your hair, power... Internet 1.23 A large number of engineers were required when the industrial revolution occurred 1.24 Trains were traveling the rails in the mid-1800s so mechanical engineers were needed, not to... the boundary of a system Fluid crosses the boundary of a control volume Control surface 1.27 Before After The system and c.v are identical The system is the air inside plus that which has exited