CONNECT FOR THERMODYNAMICS: AN ENGINEERI
9th Edition
ISBN: 9781260048636
Author: CENGEL
Publisher: MCG
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Chapter 13.3, Problem 8P
The composition of moist air is given on a molar basis to be 78 percent N2, 20 percent O2, and 2 percent water vapor. Determine the mass fractions of the constituents of air.
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An aluminum rod of length L
=
1m has mass density p = 2700 kg and
Young's modulus E = 70 GPa. The rod is fixed at both ends. The exact
natural eigenfrequencies of the rod are wexact
E
=
√
ρ
for n=1,2,3,. . . .
1. What is the minimum number of linear elements necessary to
determine the fundamental frequency w₁ of the system? Discretize
the rod in that many elements of equal length, assemble the global
system of equations KU = w² MU, and find the fundamental
frequency w₁. Compute the relative error e₁ = (w1 - wexact) /w exact
Sketch the fundamental mode of vibration.
2. Use COMSOL to solve the same problem. Show the steps necessary
to find the fundamental frequency and mode of the rod. What is the
relative error using linear elements and a normal mesh?
Chapter 13 Solutions
CONNECT FOR THERMODYNAMICS: AN ENGINEERI
Ch. 13.3 - What are mass and mole fractions?Ch. 13.3 - Consider a mixture of several gases of identical...Ch. 13.3 - The sum of the mole fractions for an ideal-gas...Ch. 13.3 - Somebody claims that the mass and mole fractions...Ch. 13.3 - Consider a mixture of two gases. Can the apparent...Ch. 13.3 - What is the apparent molar mass for a gas mixture?...Ch. 13.3 - Prob. 7PCh. 13.3 - The composition of moist air is given on a molar...Ch. 13.3 - Prob. 9PCh. 13.3 - Prob. 10P
Ch. 13.3 - A gas mixture consists of 20 percent O2, 30...Ch. 13.3 - Prob. 12PCh. 13.3 - Prob. 13PCh. 13.3 - Consider a mixture of two gases A and B. Show that...Ch. 13.3 - Is a mixture of ideal gases also an ideal gas?...Ch. 13.3 - Express Daltons law of additive pressures. Does...Ch. 13.3 - Express Amagats law of additive volumes. Does this...Ch. 13.3 - Prob. 18PCh. 13.3 - How is the P-v-T behavior of a component in an...Ch. 13.3 - Prob. 20PCh. 13.3 - Prob. 21PCh. 13.3 - Prob. 22PCh. 13.3 - Consider a rigid tank that contains a mixture of...Ch. 13.3 - Prob. 24PCh. 13.3 - Is this statement correct? The temperature of an...Ch. 13.3 - Is this statement correct? The volume of an...Ch. 13.3 - Is this statement correct? The pressure of an...Ch. 13.3 - A gas mixture at 300 K and 200 kPa consists of 1...Ch. 13.3 - Prob. 29PCh. 13.3 - Separation units often use membranes, absorbers,...Ch. 13.3 - Prob. 31PCh. 13.3 - The mass fractions of a mixture of gases are 15...Ch. 13.3 - The volumetric analysis of a mixture of gases is...Ch. 13.3 - An engineer has proposed mixing extra oxygen with...Ch. 13.3 - A rigid tank contains 0.5 kmol of Ar and 2 kmol of...Ch. 13.3 - A mixture of gases consists of 0.9 kg of oxygen,...Ch. 13.3 - Prob. 37PCh. 13.3 - One pound-mass of a gas whose density is 0.001...Ch. 13.3 - A 30 percent (by mass) ethane and 70 percent...Ch. 13.3 - Prob. 40PCh. 13.3 - Prob. 41PCh. 13.3 - A rigid tank that contains 2 kg of N2 at 25C and...Ch. 13.3 - Prob. 43PCh. 13.3 - Prob. 44PCh. 13.3 - Prob. 45PCh. 13.3 - Is the total internal energy of an ideal-gas...Ch. 13.3 - Prob. 47PCh. 13.3 - Prob. 48PCh. 13.3 - Prob. 49PCh. 13.3 - Prob. 50PCh. 13.3 - The volumetric analysis of a mixture of gases is...Ch. 13.3 - A mixture of nitrogen and carbon dioxide has a...Ch. 13.3 - The mass fractions of a mixture of gases are 15...Ch. 13.3 - A mixture of gases consists of 0.1 kg of oxygen, 1...Ch. 13.3 - An insulated tank that contains 1 kg of O2at 15C...Ch. 13.3 - An insulated rigid tank is divided into two...Ch. 13.3 - Prob. 59PCh. 13.3 - A mixture of 65 percent N2 and 35 percent CO2...Ch. 13.3 - Prob. 62PCh. 13.3 - Prob. 63PCh. 13.3 - Prob. 66PCh. 13.3 - Prob. 67PCh. 13.3 - Prob. 68PCh. 13.3 - Prob. 69PCh. 13.3 - The gas passing through the turbine of a simple...Ch. 13.3 - Prob. 71PCh. 13.3 - A pistoncylinder device contains 6 kg of H2 and 21...Ch. 13.3 - Prob. 73PCh. 13.3 - Prob. 74PCh. 13.3 - Prob. 75PCh. 13.3 - Prob. 76PCh. 13.3 - Prob. 77PCh. 13.3 - Prob. 78PCh. 13.3 - Prob. 79PCh. 13.3 - Prob. 81PCh. 13.3 - Fresh water is obtained from seawater at a rate of...Ch. 13.3 - Is it possible for an adiabatic liquid-vapor...Ch. 13.3 - Prob. 84PCh. 13.3 - Prob. 85RPCh. 13.3 - The products of combustion of a hydrocarbon fuel...Ch. 13.3 - A mixture of gases is assembled by first filling...Ch. 13.3 - Prob. 90RPCh. 13.3 - Prob. 91RPCh. 13.3 - Prob. 92RPCh. 13.3 - A rigid tank contains a mixture of 4 kg of He and...Ch. 13.3 - A spring-loaded pistoncylinder device contains a...Ch. 13.3 - Prob. 95RPCh. 13.3 - Reconsider Prob. 1395. Calculate the total work...Ch. 13.3 - Prob. 97RPCh. 13.3 - Prob. 100RPCh. 13.3 - Prob. 101RPCh. 13.3 - Prob. 102FEPCh. 13.3 - An ideal-gas mixture whose apparent molar mass is...Ch. 13.3 - An ideal-gas mixture consists of 2 kmol of N2and 4...Ch. 13.3 - Prob. 105FEPCh. 13.3 - Prob. 106FEPCh. 13.3 - An ideal-gas mixture consists of 3 kg of Ar and 6...Ch. 13.3 - Prob. 108FEPCh. 13.3 - Prob. 109FEPCh. 13.3 - Prob. 110FEPCh. 13.3 - Prob. 111FEP
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