Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 3.8, Problem 45P
To determine
The boiling temperature of the water in the pan.
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If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass.
Let us then discuss the stability of the system by using Lyapunov stability theorem. Consider the system energy as a candidate Lyapunov function shown in the image.
Discuss the positive definiteness of V (x, x_dot).
Derive the Lyapunov rate of this system (i.e., V_dot ), and discuss the stability property of thesystem based on the information we gain from ̇V_dot .
In class, two approaches—Theorems 1 and 2 below—are discussed to prove asymptotic stability of asystem when ̇V = 0.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 1.
Show the asymptotic stability of the system given in Eq. (1) by applying Theorem 2.
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Chapter 3 Solutions
Thermodynamics: An Engineering Approach
Ch. 3.8 - Is iced water a pure substance? Why?Ch. 3.8 - What is the difference between saturated vapor and...Ch. 3.8 - 3–3C Is there any difference between the...Ch. 3.8 - 3–4C Why are the temperature and pressure...Ch. 3.8 - Is it true that water boils at higher temperature...Ch. 3.8 - What is the difference between the critical point...Ch. 3.8 -
3–7C Is it possible to have water vapor at ?
Ch. 3.8 - A househusband is cooking beef stew for his family...Ch. 3.8 - In what kind of pot will a given volume of water...Ch. 3.8 - It is well known that warm air in a cooler...
Ch. 3.8 - Does the amount of heat absorbed as 1 kg of...Ch. 3.8 - Does the reference point selected for the...Ch. 3.8 - What is the physical significance of hfg? Can it...Ch. 3.8 - Does hfg change with pressure? How?Ch. 3.8 - Is it true that it takes more energy to vaporize 1...Ch. 3.8 - What is quality? Does it have any meaning in the...Ch. 3.8 - Which process requires more energy: completely...Ch. 3.8 - In the absence of compressed liquid tables, how is...Ch. 3.8 - Prob. 19PCh. 3.8 - Complete this table for H2O:Ch. 3.8 - Prob. 21PCh. 3.8 - Complete this table for H2O:Ch. 3.8 - Complete this table for H2O:Ch. 3.8 - Prob. 26PCh. 3.8 - Complete this table for refrigerant-134a:Ch. 3.8 - A 1.8-m3 rigid tank contains steam at 220C....Ch. 3.8 - A pistoncylinder device contains 0.85 kg of...Ch. 3.8 - Prob. 30PCh. 3.8 -
3–31 10-kg of R-134a fill a 1.348-m3 rigid...Ch. 3.8 - Prob. 32PCh. 3.8 - Refrigerant-134a at 200 kPa and 25C flows through...Ch. 3.8 - Prob. 34PCh. 3.8 - The temperature in a pressure cooker during...Ch. 3.8 - Prob. 36PCh. 3.8 -
3–37E One pound-mass of water fills a 2.4264-ft3...Ch. 3.8 - Prob. 38PCh. 3.8 - Water is to be boiled at sea level in a...Ch. 3.8 - Repeat Prob. 340 for a location at an elevation of...Ch. 3.8 - 10 kg of R-134a at 300 kPa fills a rigid container...Ch. 3.8 - 100 kg of R-134a at 200 kPa are contained in a...Ch. 3.8 - Water initially at 200 kPa and 300C is contained...Ch. 3.8 -
3–44 Saturated steam coming off the turbine of a...Ch. 3.8 - Prob. 45PCh. 3.8 - Prob. 46PCh. 3.8 - Water is being heated in a vertical pistoncylinder...Ch. 3.8 - Prob. 49PCh. 3.8 - A rigid tank with a volume of 1.8 m3 contains 40...Ch. 3.8 - A pistoncylinder device contains 0.005 m3 of...Ch. 3.8 -
3–53E A 5-ft3 rigid tank contains 5 lbm of water...Ch. 3.8 - A 5-ft3 rigid tank contains a saturated mixture of...Ch. 3.8 - Superheated water vapor at 180 psia and 500F is...Ch. 3.8 - Prob. 57PCh. 3.8 - 3–58 A rigid tank contains water vapor at 250°C...Ch. 3.8 - A pistoncylinder device initially contains 1.4 kg...Ch. 3.8 - How much error would one expect in determining the...Ch. 3.8 - Prob. 61PCh. 3.8 -
3–62 A rigid vessel contains 8 kg of...Ch. 3.8 - A rigid tank initially contains 1.4 kg saturated...Ch. 3.8 - A pistoncylinder device initially contains 50 L of...Ch. 3.8 - Under what conditions is the ideal-gas assumption...Ch. 3.8 - Prob. 66PCh. 3.8 - Propane and methane are commonly used for heating...Ch. 3.8 - A 400-L rigid tank contains 5 kg of air at 25C....Ch. 3.8 - Prob. 69PCh. 3.8 - Prob. 70PCh. 3.8 - The pressure gage on a 2.5-m3 oxygen tank reads...Ch. 3.8 - A spherical balloon with a diameter of 9 m is...Ch. 3.8 - Reconsider Prob. 373. Using appropriate software,...Ch. 3.8 - Prob. 74PCh. 3.8 - Prob. 75PCh. 3.8 - A rigid tank whose volume is unknown is divided...Ch. 3.8 - Prob. 77PCh. 3.8 - Prob. 78PCh. 3.8 - Prob. 79PCh. 3.8 - Prob. 80PCh. 3.8 - Prob. 81PCh. 3.8 - Determine the specific volume of superheated water...Ch. 3.8 - Determine the specific volume of superheated water...Ch. 3.8 - Prob. 85PCh. 3.8 - Prob. 86PCh. 3.8 - Prob. 87PCh. 3.8 - Prob. 88PCh. 3.8 - Prob. 89PCh. 3.8 - Prob. 90PCh. 3.8 - Carbon dioxide gas enters a pipe at 3 MPa and 500...Ch. 3.8 - A 0.016773-m3 tank contains 1 kg of...Ch. 3.8 - What is the physical significance of the two...Ch. 3.8 - A 3.27-m3 tank contains 100 kg of nitrogen at 175...Ch. 3.8 - Prob. 95PCh. 3.8 - Refrigerant-134a at 400 psia has a specific volume...Ch. 3.8 - Nitrogen at 150 K has a specific volume of...Ch. 3.8 - A 1-m3 tank contains 2.841 kg of steam at 0.6 MPa....Ch. 3.8 - Prob. 102PCh. 3.8 - Prob. 103PCh. 3.8 - On a certain day, the temperature and relative...Ch. 3.8 - Prob. 105PCh. 3.8 - Consider two rooms that are identical except that...Ch. 3.8 - A thermos bottle is half-filled with water and is...Ch. 3.8 - Prob. 108RPCh. 3.8 - The combustion in a gasoline engine may be...Ch. 3.8 - A tank contains argon at 600C and 200 kPa gage....Ch. 3.8 - Prob. 111RPCh. 3.8 - Prob. 112RPCh. 3.8 - A rigid tank with a volume of 0.117 m3 contains 1...Ch. 3.8 - Prob. 114RPCh. 3.8 - Ethane at 10 MPa and 100C is heated at constant...Ch. 3.8 - Prob. 116RPCh. 3.8 - A 10-kg mass of superheated refrigerant-134a at...Ch. 3.8 - A 4-L rigid tank contains 2 kg of saturated...Ch. 3.8 - The gage pressure of an automobile tire is...Ch. 3.8 - Prob. 120RPCh. 3.8 - Steam at 400C has a specific volume of 0.02 m3/kg....Ch. 3.8 - A tank whose volume is unknown is divided into two...Ch. 3.8 - Prob. 123RPCh. 3.8 - Prob. 124RPCh. 3.8 - Prob. 125RPCh. 3.8 - A tank contains helium at 37C and 140 kPa gage....Ch. 3.8 - Prob. 127RPCh. 3.8 - Prob. 131RPCh. 3.8 - Consider an 18-m-diameter hot-air balloon that,...Ch. 3.8 - Prob. 134FEPCh. 3.8 - Water is boiled at 1 atm pressure in a coffeemaker...Ch. 3.8 - Prob. 136FEPCh. 3.8 - Prob. 137FEPCh. 3.8 - Water is boiled in a pan on a stove at sea level....Ch. 3.8 - Prob. 139FEPCh. 3.8 - Consider a sealed can that is filled with...Ch. 3.8 - A rigid tank contains 2 kg of an ideal gas at 4...Ch. 3.8 - The pressure of an automobile tire is measured to...
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- If you have a spring mass damper system, given by m*x_double_dot + c*x_dot + kx = 0 where m, c, k (all positive scalars) are the mass, damper coefficient, and spring coefficient, respectively. x ∈ R represents the displacement of the mass. Using linear stability analysis, show that the system is asymptotically stable. Hint: stability of a linear system z_dot = Az is characterized by the eigenvalues of A.arrow_forwardWhat would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like?arrow_forward### What would the electropneumatic diagram of a circuit with the sequence a+b+c+(a-b-c-) look like, with a counter, in the fluidsim?arrow_forward
- You are asked to design a unit to condense ammonia. The required condensation rate is 0.09kg/s. Saturated ammonia at 30 o C is passed over a vertical plate (10 cm high and 25 cm wide).The properties of ammonia at the saturation temperature of 30°C are hfg = 1144 ́10^3 J/kg andrv = 9.055 kg/m 3 . Use the properties of liquid ammonia at the film temperature of 20°C (Ts =10 o C):Pr = 1.463 rho_l= 610.2 kf/m^3 liquid viscosity= 1.519*10^-4 kg/ ms kinematic viscosity= 2.489*10^-7 m^2/s Cpl= 4745 J/kg C kl=0.4927 W/m CCalculate the surface temperature required to achieve the desired condensation rate of 0.09 kg/s( should be 688 degrees C) a) Show that if you use a bigger vertical plate (2.5 m-wide and 0.8 m-height), the requiredsurface temperature would be now 20 o C. You may use all the properties given as an initialguess. No need to iterate to correct for Tf. b) What if you still want to use small plates because of the space constrains? One way to getaround this problem is to use small…arrow_forwardA differential element on the bracket is subjected to plane strain that has the following components:, Ɛx = 300 × 10-6, Ɛy = 150 × 10-6, Ɛxy = -750 x 10-6. Use the strain-transformation equations and determine the normal strain Ɛx in the X/ direction on an element oriented at an angle of 0 = 40°. Note, a positive angle, 0, is counter clockwise. x Enter your answer in micro strain to a precision of two decimal places. eg. if your answer is 300.15X106, please enter 300.15.arrow_forwardIf the 50 mm diameter shaft is made from brittle material having an ultimate strength of σult=595 MPa for both tension and compression, determine the factor of safety of the shaft against rupture. The applied force, F, is 140 kN. The applied torque T, is 5.0 kN⚫m. Enter your answer to a precision of two decimal places. T Farrow_forwardЗіс 1 mH 10 Ω m 16 cos 2.5 × 104 A Lic 592 10 Ω 1 μFarrow_forwardHomework#5arrow_forwardHomework#5arrow_forwardOxygen (molar mass 32 kg/kmol) expands reversibly in a cylinder behind a piston at a constant pressure of 3 bar. The volume initially is 0.01 m3 and finally is 0.03 m3; the initial temperature is 17°C. Calculate the work input and the heat supplied during the expansion. Assume oxygen to be an ideal gas and take cp = 0.917 kJ/kg K. For 1 bonus mark explain why (using your understanding of thermodynamics) that oxygen is used in this context rather than water vapour.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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