Fundamentals of Engineering Thermodynamics
8th Edition
ISBN: 9781118832301
Author: SHAPIRO
Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT
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Chapter 1.9, Problem 12CU
To determine
To describe: the difference among specific volume expressed on a mass basis and a molar basis.
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Problem 2 (55 pts). We now consider the FEM solution of Problem 1.(a) [5pts] Briefly describe the 4 steps necessary to obtain the approximate solution of thatBVP using the Galerkin FEM. Use the minimum amount of math necessary to supportyour explanations.(b) [20pts] Derive the weak form of the BVP.(c) [10pts] Assuming a mesh of two equal elements and linear shape functions, sketch byhand how you expect the FEM solution to look like. Also sketch the analytical solutionfor comparison. In your sketch, identify the nodal degrees of freedom that the FEMsolution seeks to find.(d) [10pts] By analogy with the elastic rod problem and heat conduction problem considered in class, write down the stiffness matrix and force vector for each of the twoelements considered in (c).(e) [10pts] Assemble the global system of equations, and verbally explain how to solve it.
Chapter 1 Solutions
Fundamentals of Engineering Thermodynamics
Ch. 1.9 - Prob. 1ECh. 1.9 - Prob. 2ECh. 1.9 - 3. The driver’s compartment of race cars can reach...Ch. 1.9 - 4. What causes changes in atmospheric pressure?
Ch. 1.9 - 5. Why are passenger airplane cabins normally...Ch. 1.9 - 6. Laura takes an elevator from the tenth floor of...Ch. 1.9 - 7. How do dermatologists remove precancerous skin...Ch. 1.9 - 8. When one walks barefoot from a carpet onto a...Ch. 1.9 - 9. Why does ocean water temperature vary with...Ch. 1.9 - 10. Are the systolic and diastolic pressures...
Ch. 1.9 - 11. How do forehead temperature strips work?
Ch. 1.9 - 12. How does a pressure measurement of 14.7 psig...Ch. 1.9 - 13. What is a nanotubel
Ch. 1.9 - 14. If a system is at steady state, does this mean...Ch. 1.9 - For problems 1-10, match the appropriate...Ch. 1.9 - Prob. 11CUCh. 1.9 - 12. Describe the difference between specific...Ch. 1.9 - 13. A system is said to be at ___________ if none...Ch. 1.9 - 14. A control volume is a system that
(a) always...Ch. 1.9 - 15. What is the objective of an engineering model...Ch. 1.9 - 16. _______________ is pressure with respect to...Ch. 1.9 - 17. A gas contained within a piston–cylinder...Ch. 1.9 - 18. The statement, “When two objects are in...Ch. 1.9 - 19. SI base units include
(a) kilogram (kg), meter...Ch. 1.9 - 20. Explain why the value for gage pressure is...Ch. 1.9 - 21. A system is at steady state if
(a) none of its...Ch. 1.9 - Prob. 22CUCh. 1.9 - 23. Classify items a through g shown on the...Ch. 1.9 - 24. When a system is isolated,
(a) its mass...Ch. 1.9 - 25. The resultant pressure force acting on a body...Ch. 1.9 - 26. The list consisting only of intensive...Ch. 1.9 - 27. Gage pressure indicates the difference between...Ch. 1.9 - 28. Systems can be studied only from a macroscopic...Ch. 1.9 - 29. Kilogram, second, foot, and newton are all...Ch. 1.9 - Prob. 30CUCh. 1.9 - 31. Mass is an intensive property.
Ch. 1.9 - Prob. 32CUCh. 1.9 - 33. Intensive properties may be functions of both...Ch. 1.9 - 34. Devices that measure pressure include...Ch. 1.9 - Prob. 35CUCh. 1.9 - 36. If a system is isolated from its surroundings...Ch. 1.9 - 37. The specific volume is the reciprocal of the...Ch. 1.9 -
Indicate whether the following statements are...Ch. 1.9 - 39. The pound force, lbf, is equal to the pound...Ch. 1.9 - 40. The value of a temperature expressed using the...Ch. 1.9 - Prob. 41CUCh. 1.9 - 42. A closed system always contains the same...Ch. 1.9 - Prob. 43CUCh. 1.9 - 44. A control volume is a special type of closed...Ch. 1.9 - 45. When a closed system undergoes a process...Ch. 1.9 - Prob. 46CUCh. 1.9 - Prob. 47CUCh. 1.9 - 48. A vessel holding 0.5 kg of oxygen (O2)...Ch. 1.9 - Prob. 49CUCh. 1.9 - 50. In local surroundings at standard atmospheric...Ch. 1.9 - Prob. 51CUCh. 1.9 - 52. The Rankine degree is a smaller temperature...Ch. 1.9 - 53. If the value of any property of a system...Ch. 1.9 - Prob. 54CUCh. 1.9 - 55. The composition of a closed system cannot...Ch. 1.9 - 56. Temperature is the property that is the same...Ch. 1.9 - Prob. 57CUCh. 1.9 - 58. The pressure unit psia indicates an absolute...Ch. 1.9 - 1.4 Perform the following unit conversions:
(a) 1...Ch. 1.9 - 1.5 Perform the following unit conversions:
(a)...Ch. 1.9 - 1.6 Which of the following food items weighs...Ch. 1.9 - 1.7 A person whose mass is 150 lb weighs 144.4...Ch. 1.9 - 1.8 The Phoenix with a mass of 350 kg was a...Ch. 1.9 - Prob. 9PCh. 1.9 - 1.10 In severe head-on automobile accidents, a...Ch. 1.9 - Prob. 11PCh. 1.9 - 1.12 A spring compresses in length by 0.14 in, for...Ch. 1.9 - 1.13 At a certain elevation, the pilot of a...Ch. 1.9 - 1.14 Estimate the magnitude of the force, in Ibf,...Ch. 1.9 - 1.15 Determine the upward applied force, in Ibf,...Ch. 1.9 -
1.16 An object is subjected to an applied upward...Ch. 1.9 - 1.17 A communications satellite weighs 4400 N on...Ch. 1.9 - 1.18 Using local acceleration of gravity data from...Ch. 1.9 - 1.19 A town has a 1-million-gallon storage...Ch. 1.9 - 1.20 A closed system consists of 0.5 kmol of...Ch. 1.9 - 1.21 A 2-lb sample of an unknown liquid occupies a...Ch. 1.9 - Prob. 22PCh. 1.9 - 1.23 The specific volume of 5 kg of water vapor at...Ch. 1.9 - Prob. 24PCh. 1.9 - 1.25 As shown in Figure P1.25, a gas is contained...Ch. 1.9 - 1.26 As shown in Fig. P1.26, a vertical...Ch. 1.9 - 1.27 Three kg of gas in a piston-cylinder assembly...Ch. 1.9 - 1.28 A closed system consisting of 4 lb of a gas...Ch. 1.9 - 1.29 A system consists of carbon monoxide (CO) in...Ch. 1.9 - 1.30 Figure P1.30 shows a gas contained in a...Ch. 1.9 - 1.31 A gas contained within a piston-cylinder...Ch. 1.9 - Prob. 32PCh. 1.9 - 1.33 Figure P 1.33 shows a storage tank holding...Ch. 1.9 - 1.34 As shown in Figure PI.34, the exit of a gas...Ch. 1.9 - 1.35 The barometer shown in Fig. P1.35 contains...Ch. 1.9 - Prob. 36PCh. 1.9 - Figure P1.37 shows a tank within a tank, each...Ch. 1.9 - 1.38 As shown in Fig. PI.38, an underwater...Ch. 1.9 - 1.39 Show that a standard atmospheric pressure of...Ch. 1.9 - 1.40 A gas enters a compressor that provides a...Ch. 1.9 - 1.41 As shown in Figure P1.41. air is contained in...Ch. 1.9 - Prob. 42PCh. 1.9 - 1.43 The pressure from water mains located at...Ch. 1.9 - 1.44 Figure P1.44 shows a tank used to collect...Ch. 1.9 - 1.45 If the water pressure at the base of the...Ch. 1.9 - 1.46 As shown in Figure P1.46. an inclined...Ch. 1.9 - 1.47 Figure P1.47 shows a spherical buoy, having a...Ch. 1.9 - 1.48 Because of a break in a buried oil storage...Ch. 1.9 - 1.49 Figure P1.49 shows a closed tank holding air...Ch. 1.9 - 1.50 The 30-year average temperature in Toronto,...Ch. 1.9 - 1.51 Convert the following temperatures from °F to...Ch. 1.9 - Prob. 52PCh. 1.9 - 1.53 A cake recipe specifies an oven temperature...Ch. 1.9 - 1.54 Does the Rankine degree represent a larger or...Ch. 1.9 - 1.55 Figure P1.55 shows a system consisting of a...Ch. 1.9 - What is (a) the lowest naturally occurring...Ch. 1.9 - 1.57 Air temperature rises from a morning low of...Ch. 1.9 - 1.58 For liquid-in-glass thermometers, the...
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- An aluminum rod of length L = 1m has mass density ρ = 2700 kgm3 andYoung’s modulus E = 70GPa. The rod is fixed at both ends. The exactnatural eigenfrequencies of the rod are ωexactn =πnLqEρfor n=1,2,3,. . . .1. What is the minimum number of linear elements necessary todetermine the fundamental frequency ω1 of the system? Discretizethe rod in that many elements of equal length, assemble the globalsystem of equations KU = ω2MU, and find the fundamentalfrequency ω1. Compute the relative error e1 = (ω1 − ωexact1)/ωexact1.Sketch the fundamental mode of vibration.arrow_forwardProblem 1 (65 pts, suggested time 50 mins). An elastic string of constant line tension1T is pinned at x = 0 and x = L. A constant distributed vertical force per unit length p(with units N/m) is applied to the string. Under this force, the string deflects by an amountv(x) from its undeformed (horizontal) state, as shown in the figure below.The PDE describing mechanical equilibrium for the string isddx Tdvdx− p = 0 . (1)(a) [5pts] Identify the BCs for the string and identify their type (essential/natural). Writedown the strong-form BVP for the string, including PDE and BCs.(b) [10pts] Find the analytical solution of the BVP in (a). Compute the exact deflectionof the midpoint v(L/2).(c) [15pts] Derive the weak-form BVP.(d) [5pts] What is the minimum number of linear elements necessary to compute the deflection of the midpoint?(e) [15pts] Write down the element stiffness matrix and the element force vector for eachelement.arrow_forwardProblem 1 (35 pts). An elastic string of constant line tension1 T is pinned at x = 0 andx = L. A constant distributed vertical force per unit length p (with units N/m) is appliedto the string. Under this force, the string deflects by an amount v(x) from its undeformed(horizontal) state, as shown in the figure below.Force equilibrium in the string requires thatdfdx − p = 0 , (1)where f(x) is the internal vertical force in the string, which is given byf = Tdvdx . (2)(a) [10pts] Write down the BVP (strong form) that the string deflection v(x) must satisfy.(b) [2pts] What order is the governing PDE in the BVP of (a)?(c) [3pts] Identify the type (essential/natural) of each boundary condition in (a).(d) [20pts] Find the analytical solution of the BVP in (a).arrow_forward
- Problem 2 (25 pts, (suggested time 15 mins). An elastic string of line tension T andmass per unit length µ is pinned at x = 0 and x = L. The string is free to vibrate, and itsfirst vibration mode is shown below.In order to find the frequency of the first mode (or fundamental frequency), the string isdiscretized into a certain number of linear elements. The stiffness and mass matrices of thei-th element are, respectivelyESMi =TLi1 −1−1 1 EMMi =Liµ62 11 2 . (2)(a) [5pts] What is the minimum number of linear elements necessary to compute the fundamental frequency of the vibrating string?(b) [20pts] Assemble the global eigenvalue problem and find the fundamental frequency ofvibration of the stringarrow_forwardI need part all parts please in detail (including f)arrow_forwardProblem 3 (10 pts, suggested time 5 mins). In class we considered the mutiphysics problem of thermal stresses in a rod. When using linear shape functions, we found that the stress in the rod is affected by unphysical oscillations like in the following plot E*(ux-a*T) 35000 30000 25000 20000 15000 10000 5000 -5000 -10000 0 Line Graph: E*(ux-a*T) MULT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arc length (a) [10pts] What is the origin of this issue and how can we fix it?arrow_forward
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