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Fundamentals of Engineering Thermodynamics
8th Edition
ISBN: 9781118412930
Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey
Publisher: WILEY
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Question
Chapter 6.13, Problem 155P
(a)
To determine
The velocity of steam at the exit.
(b)
To determine
The amount of entropy produced.
Expert Solution & Answer
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Q.1. The press shown for Figure.1 has a rated load
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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.
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.
Chapter 6 Solutions
Fundamentals of Engineering Thermodynamics
Ch. 6.13 - Prob. 1ECh. 6.13 - Prob. 2ECh. 6.13 - Prob. 3ECh. 6.13 - Prob. 4ECh. 6.13 - Prob. 5ECh. 6.13 - 6. Is entropy produced within a system undergoing...Ch. 6.13 - 7. When a mixture of olive oil and vinegar...Ch. 6.13 - Prob. 8ECh. 6.13 - Prob. 9ECh. 6.13 - 10. Is Eq. 6.51a restricted to adiabatic processes...
Ch. 6.13 - Prob. 11ECh. 6.13 - 12. What is the ENERGY STAR® program?
Ch. 6.13 - Prob. 1CUCh. 6.13 - Prob. 2CUCh. 6.13 - Prob. 3CUCh. 6.13 - Prob. 4CUCh. 6.13 - Prob. 5CUCh. 6.13 - For Problems 1–6, a closed system undergoes a...Ch. 6.13 - For Problems 7–10, a gas flows through a...Ch. 6.13 - Prob. 8CUCh. 6.13 - Prob. 9CUCh. 6.13 - For Problems 7–10, a gas flows through a...Ch. 6.13 - Prob. 11CUCh. 6.13 - Prob. 12CUCh. 6.13 - Prob. 13CUCh. 6.13 - 14. A closed system undergoes a process for which...Ch. 6.13 - 15. Show that for phase change of water from...Ch. 6.13 - Prob. 16CUCh. 6.13 - Prob. 17CUCh. 6.13 - Prob. 18CUCh. 6.13 - Prob. 19CUCh. 6.13 - Prob. 20CUCh. 6.13 - Prob. 21CUCh. 6.13 - Prob. 22CUCh. 6.13 - Prob. 23CUCh. 6.13 - Prob. 24CUCh. 6.13 - Prob. 25CUCh. 6.13 - Prob. 26CUCh. 6.13 - Prob. 27CUCh. 6.13 - 28. Briefly explain the notion of microscopic...Ch. 6.13 - Prob. 29CUCh. 6.13 - Prob. 30CUCh. 6.13 - Prob. 31CUCh. 6.13 - Prob. 32CUCh. 6.13 - Prob. 33CUCh. 6.13 - Prob. 34CUCh. 6.13 - Prob. 35CUCh. 6.13 - 36. A closed system can experience a decrease in...Ch. 6.13 - 37. Entropy is produced in every internally...Ch. 6.13 - Prob. 38CUCh. 6.13 - Prob. 39CUCh. 6.13 - Prob. 40CUCh. 6.13 - Prob. 41CUCh. 6.13 - Prob. 42CUCh. 6.13 - Prob. 43CUCh. 6.13 - Prob. 44CUCh. 6.13 - Prob. 45CUCh. 6.13 - Prob. 46CUCh. 6.13 - Prob. 47CUCh. 6.13 - Prob. 48CUCh. 6.13 - Prob. 49CUCh. 6.13 - Prob. 50CUCh. 6.13 - 51. The increase of entropy principle states that...Ch. 6.13 - Prob. 52CUCh. 6.13 - Prob. 53CUCh. 6.13 - Prob. 54CUCh. 6.13 - 55. When a system undergoes a Carnot cycle, no...Ch. 6.13 - Prob. 1PCh. 6.13 - Prob. 2PCh. 6.13 - Prob. 3PCh. 6.13 - 6.4 Using the appropriate tables, determine the...Ch. 6.13 -
6.7 Using steam table data, determine the...Ch. 6.13 - 6.8 Using the appropriate table, determine the...Ch. 6.13 - Prob. 10PCh. 6.13 - 6.11 Air in a piston–cylinder assembly undergoes a...Ch. 6.13 - 6.12 Water contained in a closed, rigid tank,...Ch. 6.13 - Prob. 13PCh. 6.13 - 6.14 Five kg of nitrogen (N2) undergoes a process...Ch. 6.13 - Prob. 15PCh. 6.13 - Prob. 16PCh. 6.13 - Prob. 17PCh. 6.13 - 6.18 Steam enters a turbine operating at steady...Ch. 6.13 - Prob. 19PCh. 6.13 - 6.20 One kg of water in a piston–cylinder assembly...Ch. 6.13 - Prob. 21PCh. 6.13 - 6.22 A system consisting of 2 kg of water...Ch. 6.13 - Prob. 23PCh. 6.13 - 6.24 A gas within a piston–cylinder assembly...Ch. 6.13 - Prob. 25PCh. 6.13 - 6.26 A gas initially at 2.8 bar and 60°C is...Ch. 6.13 - Prob. 27PCh. 6.13 - Prob. 28PCh. 6.13 - Prob. 29PCh. 6.13 - Prob. 30PCh. 6.13 - Prob. 31PCh. 6.13 - Prob. 32PCh. 6.13 - 6.33 Air in a piston–cylinder assembly undergoes a...Ch. 6.13 - Prob. 34PCh. 6.13 - Prob. 35PCh. 6.13 - Prob. 36PCh. 6.13 - 6.37 Two m3 of air in a rigid, insulated container...Ch. 6.13 - Prob. 38PCh. 6.13 - 6.39 Air contained in a rigid, insulated tank...Ch. 6.13 - 6.40 Air contained in a rigid, insulated tank...Ch. 6.13 - 6.41 Air contained in a rigid, insulated tank...Ch. 6.13 - Prob. 42PCh. 6.13 - Prob. 43PCh. 6.13 - Prob. 44PCh. 6.13 - 6.45 Steam undergoes an adiabatic expansion in a...Ch. 6.13 - 6.46 Two kg of air contained in a piston-cylinder...Ch. 6.13 - Prob. 47PCh. 6.13 - Prob. 48PCh. 6.13 - 6.49 One kg of air contained in a piston-cylinder...Ch. 6.13 - Prob. 50PCh. 6.13 - Prob. 51PCh. 6.13 - Prob. 52PCh. 6.13 - Prob. 53PCh. 6.13 - Prob. 54PCh. 6.13 - 6.55 For the silicon chip of Example 2.5....Ch. 6.13 - Prob. 56PCh. 6.13 - Prob. 57PCh. 6.13 - Prob. 58PCh. 6.13 - Prob. 59PCh. 6.13 - Prob. 60PCh. 6.13 - 6.61 A 2.64-kg copper part, initially at 400 K, is...Ch. 6.13 - Prob. 62PCh. 6.13 - Prob. 63PCh. 6.13 - 6.64 As shown in Fig. P6.64, an insulated box is...Ch. 6.13 - Prob. 68PCh. 6.13 - Prob. 69PCh. 6.13 - Prob. 70PCh. 6.13 - Prob. 71PCh. 6.13 - Prob. 72PCh. 6.13 - Prob. 73PCh. 6.13 - Prob. 74PCh. 6.13 - Prob. 75PCh. 6.13 - Prob. 76PCh. 6.13 - Prob. 77PCh. 6.13 - Prob. 79PCh. 6.13 - 6.80 Water at 20 bar, 400°C enters a turbine...Ch. 6.13 - Prob. 81PCh. 6.13 - Prob. 82PCh. 6.13 - Prob. 83PCh. 6.13 - Prob. 84PCh. 6.13 - Prob. 85PCh. 6.13 - 6.86 Steam enters a well-insulated nozzle...Ch. 6.13 - Prob. 87PCh. 6.13 - 6.88 An open feedwater heater is a direct-contact...Ch. 6.13 - Prob. 89PCh. 6.13 - 6.90 Air at 600 kPa, 330 K enters a...Ch. 6.13 - Prob. 91PCh. 6.13 - Prob. 92PCh. 6.13 - Prob. 93PCh. 6.13 - Prob. 94PCh. 6.13 - Prob. 95PCh. 6.13 - Prob. 96PCh. 6.13 - Prob. 97PCh. 6.13 - Prob. 98PCh. 6.13 - 6.99 Ammonia enters the compressor of an...Ch. 6.13 - Prob. 100PCh. 6.13 - Prob. 101PCh. 6.13 - 6.102 Steam enters a turbine operating at steady...Ch. 6.13 - 6.103 Refrigerant 134a is compressed from 2 bar,...Ch. 6.13 - Prob. 104PCh. 6.13 - Prob. 105PCh. 6.13 - Prob. 106PCh. 6.13 - Prob. 107PCh. 6.13 - Prob. 108PCh. 6.13 - 6.109 Determine the rates of entropy production,...Ch. 6.13 - Prob. 110PCh. 6.13 - Prob. 111PCh. 6.13 - 6.112 Air as an ideal gas flows through the...Ch. 6.13 - 6.113 A rigid, insulated tank whose volume is 10 L...Ch. 6.13 - Prob. 114PCh. 6.13 - Prob. 115PCh. 6.13 - Prob. 116PCh. 6.13 - Prob. 117PCh. 6.13 - 6.118 Air in a piston–cylinder assembly expands...Ch. 6.13 - Prob. 119PCh. 6.13 - 6.120 Steam undergoes an isentropic compression in...Ch. 6.13 - Prob. 121PCh. 6.13 - Prob. 122PCh. 6.13 - Prob. 123PCh. 6.13 - 6.124 Air within a piston–cylinder assembly,...Ch. 6.13 - Prob. 125PCh. 6.13 - Prob. 127PCh. 6.13 - 6.128 A rigid, insulated tank with a volume of 20...Ch. 6.13 - 6.129 A rigid, insulated tank with a volume of...Ch. 6.13 - Prob. 130PCh. 6.13 - Prob. 131PCh. 6.13 - Prob. 132PCh. 6.13 - 6.133 Figure P6.133 shows a simple vapor power...Ch. 6.13 - Prob. 134PCh. 6.13 - Prob. 135PCh. 6.13 - Prob. 136PCh. 6.13 - 6.137 Air at 1600 K, 30 bar enters a turbine...Ch. 6.13 - Prob. 138PCh. 6.13 - Prob. 139PCh. 6.13 - Prob. 140PCh. 6.13 - Prob. 141PCh. 6.13 - Prob. 142PCh. 6.13 - Prob. 143PCh. 6.13 - Prob. 144PCh. 6.13 - Prob. 145PCh. 6.13 - Prob. 146PCh. 6.13 - Prob. 147PCh. 6.13 - Prob. 148PCh. 6.13 - Prob. 149PCh. 6.13 - Prob. 150PCh. 6.13 - Prob. 151PCh. 6.13 - Prob. 152PCh. 6.13 - Prob. 153PCh. 6.13 - Prob. 154PCh. 6.13 - Prob. 155PCh. 6.13 - Prob. 156PCh. 6.13 - Prob. 157PCh. 6.13 - Prob. 158PCh. 6.13 - Prob. 159PCh. 6.13 - Prob. 160PCh. 6.13 - Prob. 161PCh. 6.13 - Prob. 162PCh. 6.13 - Prob. 163PCh. 6.13 - Prob. 164PCh. 6.13 - 6.165. Steam enters a two-stage turbine with...Ch. 6.13 - Prob. 166PCh. 6.13 - Prob. 167PCh. 6.13 - Prob. 168PCh. 6.13 - Prob. 169PCh. 6.13 - Prob. 170PCh. 6.13 - 6.171. Carbon dioxide (CO2) expands isothermally...Ch. 6.13 - 6.172 Steam at 12.0 MPa, 480°C expands through a...Ch. 6.13 - Prob. 173PCh. 6.13 - Prob. 174PCh. 6.13 - Prob. 175PCh. 6.13 - Prob. 176PCh. 6.13 - Prob. 177PCh. 6.13 - Prob. 178PCh. 6.13 - Prob. 179PCh. 6.13 - Prob. 180PCh. 6.13 - Prob. 181PCh. 6.13 - 6.182 An electrically driven pump operating at...Ch. 6.13 - 6.183 As shown in Fig. P6.183, water behind a dam...Ch. 6.13 - Prob. 184PCh. 6.13 - Prob. 185PCh. 6.13 - Prob. 186P
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- Problem 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_forwardProblem 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_forward
- I 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_forwardanswer the questions and explain all of it in words. Ignore where it says screencast and in class explanationarrow_forward
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