Fundamentals of Engineering Thermodynamics
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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Chapter 12.9, Problem 33P

(a)

To determine

The final temperature of the mixture of gases at equilibrium.

(b)

To determine

The final pressure of the mixture of gases at equilibrium.

(c)

To determine

The amount of entropy produced.

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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 12 Solutions

Fundamentals of Engineering Thermodynamics

Ch. 12.9 - Prob. 11ECh. 12.9 - Prob. 12ECh. 12.9 - Prob. 13ECh. 12.9 - Prob. 14ECh. 12.9 - Prob. 15ECh. 12.9 - Prob. 16ECh. 12.9 - Prob. 1CUCh. 12.9 - Prob. 12CUCh. 12.9 - Prob. 13CUCh. 12.9 - Prob. 14CUCh. 12.9 - Prob. 15CUCh. 12.9 - 16. The Dalton model assumes that each mixture...Ch. 12.9 - Prob. 17CUCh. 12.9 - Prob. 18CUCh. 12.9 - 19. For the steady-state dehumidification process...Ch. 12.9 - Prob. 20CUCh. 12.9 - Prob. 21CUCh. 12.9 - Prob. 22CUCh. 12.9 - Prob. 23CUCh. 12.9 - Prob. 24CUCh. 12.9 - Prob. 25CUCh. 12.9 - Prob. 26CUCh. 12.9 - Prob. 27CUCh. 12.9 - Prob. 28CUCh. 12.9 - Prob. 29CUCh. 12.9 - Prob. 30CUCh. 12.9 - Prob. 31CUCh. 12.9 - Indicate whether the following statements are true...Ch. 12.9 - Prob. 33CUCh. 12.9 - Prob. 34CUCh. 12.9 - Prob. 35CUCh. 12.9 - Prob. 36CUCh. 12.9 - Prob. 37CUCh. 12.9 - Prob. 38CUCh. 12.9 - Prob. 39CUCh. 12.9 - Prob. 40CUCh. 12.9 - Prob. 41CUCh. 12.9 - Prob. 42CUCh. 12.9 - Prob. 43CUCh. 12.9 - Prob. 44CUCh. 12.9 - Prob. 45CUCh. 12.9 - Prob. 46CUCh. 12.9 - Prob. 47CUCh. 12.9 - Prob. 48CUCh. 12.9 - Prob. 49CUCh. 12.9 - Prob. 50CUCh. 12.9 - Prob. 1PCh. 12.9 - Prob. 2PCh. 12.9 - Prob. 3PCh. 12.9 - Prob. 4PCh. 12.9 - Prob. 5PCh. 12.9 - Prob. 6PCh. 12.9 - Prob. 7PCh. 12.9 - Prob. 8PCh. 12.9 - Prob. 9PCh. 12.9 - Prob. 10PCh. 12.9 - Prob. 11PCh. 12.9 - Prob. 12PCh. 12.9 - Prob. 13PCh. 12.9 - Prob. 14PCh. 12.9 - Prob. 15PCh. 12.9 - Prob. 16PCh. 12.9 - Prob. 17PCh. 12.9 - Prob. 18PCh. 12.9 - Prob. 19PCh. 12.9 - Prob. 20PCh. 12.9 - Prob. 21PCh. 12.9 - Prob. 22PCh. 12.9 - Prob. 23PCh. 12.9 - Prob. 24PCh. 12.9 - Prob. 25PCh. 12.9 - Prob. 26PCh. 12.9 - Prob. 27PCh. 12.9 - Prob. 28PCh. 12.9 - Prob. 29PCh. 12.9 - Prob. 30PCh. 12.9 - Prob. 31PCh. 12.9 - Prob. 32PCh. 12.9 - Prob. 33PCh. 12.9 - Prob. 34PCh. 12.9 - Prob. 35PCh. 12.9 - Argon (Ar), at 300 K, 1 bar with a mass flow rate...Ch. 12.9 - Prob. 37PCh. 12.9 - Prob. 38PCh. 12.9 - Prob. 39PCh. 12.9 - Prob. 41PCh. 12.9 - Prob. 43PCh. 12.9 - 12.45 A water pipe at 5°C runs above ground...Ch. 12.9 - Prob. 46PCh. 12.9 - A lecture hall having a volume of 106 ft3 contains...Ch. 12.9 - Prob. 48PCh. 12.9 - Prob. 49PCh. 12.9 - Prob. 50PCh. 12.9 - Prob. 51PCh. 12.9 - Prob. 52PCh. 12.9 - Prob. 53PCh. 12.9 - Prob. 54PCh. 12.9 - Prob. 55PCh. 12.9 - Prob. 56PCh. 12.9 - Prob. 57PCh. 12.9 - Prob. 58PCh. 12.9 - Prob. 59PCh. 12.9 - Prob. 60PCh. 12.9 - Prob. 61PCh. 12.9 - Prob. 63PCh. 12.9 - A closed, rigid tank having a volume of 1 m3...Ch. 12.9 - Prob. 65PCh. 12.9 - Prob. 66PCh. 12.9 - Moist air enters a control volume operating at...Ch. 12.9 - Prob. 68PCh. 12.9 - A fixed amount of air initially at 52°C, 1 atm,...Ch. 12.9 - Prob. 73PCh. 12.9 - Prob. 74PCh. 12.9 - Prob. 75PCh. 12.9 - Prob. 76PCh. 12.9 - Prob. 80PCh. 12.9 - An air conditioner operating at steady state takes...Ch. 12.9 - Figure P12.82 shows a compressor followed by an...Ch. 12.9 - Prob. 83PCh. 12.9 - Prob. 84PCh. 12.9 - Prob. 87PCh. 12.9 - Prob. 88PCh. 12.9 - Prob. 89PCh. 12.9 - Prob. 91PCh. 12.9 - Air at 35°C, 1 bar, and 10% relative humidity...Ch. 12.9 - Prob. 93PCh. 12.9 - Prob. 95PCh. 12.9 - Prob. 96PCh. 12.9 - At steady state, moist air at 42°C, 1 atm. 30%...Ch. 12.9 - Prob. 98PCh. 12.9 - Prob. 99PCh. 12.9 - Figure P12.100 shows a device for conditioning...Ch. 12.9 - Prob. 101PCh. 12.9 - Prob. 102PCh. 12.9 - Prob. 103PCh. 12.9 - Prob. 104PCh. 12.9 - Liquid water at 120°F enters a cooling tower...Ch. 12.9 - Prob. 107PCh. 12.9 - Prob. 108P
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