FUNDAMENTALS OF THERMODYNAMICS
10th Edition
ISBN: 9781119634928
Author: Borgnakke
Publisher: WILEY
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Chapter 2, Problem 2.105EP
Repeat the previous problem if the outlet valve is at the top taking saturated vapor out until no more liquid.
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The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L.
Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).
The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(4)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. Both ends of the bar are in contact with a heatreservoir at zero temperature.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
A heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
Chapter 2 Solutions
FUNDAMENTALS OF THERMODYNAMICS
Ch. 2 - Are the pressure in the tables absolute or gauge...Ch. 2 - What is the minimum pressure for liquid carbon...Ch. 2 - When you skate on ice, a thin liquid film forms...Ch. 2 - Is it possible to have water vapor at 5 ?Ch. 2 - At higher elevations, as in mountains, air...Ch. 2 - Water at room temperature and room pressure has...Ch. 2 - Can a vapor exist below the triple point...Ch. 2 - Ice cubes can disappear and food can dry out...Ch. 2 - In Example 2.lb, is there any mass at the...Ch. 2 - Prob. 2.10P
Ch. 2 - Locate the state of R410A at 500kPa,10C . Indicate...Ch. 2 - How does a constant-v process for an ideal an as...Ch. 2 - Prob. 2.13PCh. 2 - As the pressure of a gas becomes larger, Z becomes...Ch. 2 - Carbon dioxide at 280K can be in three different...Ch. 2 - Find the lowest temperature at which it is...Ch. 2 - Water at 27C can exist in different phases,...Ch. 2 - Dry ice is the name of solid carbon dioxide. How...Ch. 2 - A substance is at 2MPa and 17C in a rigid tank....Ch. 2 - Determine the phase for each of these cases a....Ch. 2 - Determine the phase of water at a. T260°C.P5MPa b....Ch. 2 - Determine the phase of the substance at the given...Ch. 2 - Give the missing property of PvT and x for water...Ch. 2 - Determine whether refrigerant R410A in each of the...Ch. 2 - Show the states in Problem 2.24 in a sketch of the...Ch. 2 - Fill out the following table for substance...Ch. 2 - Place the two states ab listed in Problem 2.26 as...Ch. 2 - Determine the specific volume for R410A at these...Ch. 2 - Place the three states ac listed in previous...Ch. 2 - Find P and x for CH4 at a. T=155K,v=0.04m3/kg b....Ch. 2 - Give the specific volume of carbon dioxide at 40C...Ch. 2 - You want a pot of water to boil at 105C . How...Ch. 2 - Water at 400kPa a quality of 75 has its pressure...Ch. 2 - Saturated water vapor at 200kPa is in a...Ch. 2 - Saturated liquid water at 60C is put under...Ch. 2 - A constant pressure piston cylinder has water at...Ch. 2 - A glass jar is filled with saturated water at...Ch. 2 - Saturated vapor R4l0A at 60C has to pressure...Ch. 2 - Ammonia at 20C with a quality of 50 and a total...Ch. 2 - Repeat the previous problem if the outlet valve is...Ch. 2 - R134a is in a sealed, rigid vessel of 2m3 as...Ch. 2 - A storage tank holds methane at 120K , with a...Ch. 2 - A 400m3 storage tank is being constructed to hold...Ch. 2 - Carbon dioxide at 6000kPa,40C is cooled in a...Ch. 2 - A pressure cooker has the lid screwed on tight. A...Ch. 2 - A 1m3 tank is filled with a gas at room...Ch. 2 - A pneumatic cylinder (a piston cylinder with air)...Ch. 2 - Is it reasonable to assume that at the given...Ch. 2 - Helium in a steel tank is at 250kPa,300K with a...Ch. 2 - A spherical helium balloon l0m in diameter is at...Ch. 2 - A glass is cleaned in hot water at 35°C and placed...Ch. 2 - Air in a car tire is initially at 10C and 190kPa ....Ch. 2 - A rigid tank of 1m3 contains nitrogen gas at...Ch. 2 - Assume we have three states of saturated vapor...Ch. 2 - Do Problem 2.54 for R-410A Assume we have three...Ch. 2 - Do problem 2.54 for the substance ammonia. Assume...Ch. 2 - A cy1inica1 gas tank 1m long, with an inside...Ch. 2 - Ammonia in a piston cylinder arrangement is at...Ch. 2 - Find the compressibility factor (Z) for saturated...Ch. 2 - Find the compressibility factor for methane at a....Ch. 2 - Find the compressibility for carbon dioxide at 60C...Ch. 2 - What is the percent error in specific volume if...Ch. 2 - Estimate the saturation pressure of R142b at 300K...Ch. 2 - A bottle a volume of 0.1m3 contains butane with a...Ch. 2 - Find the volume of 2kg of ethylene at 270K,2500kPa...Ch. 2 - Argon is kept in a rigid 5m3 tank at 30C and 3MPa...Ch. 2 - A new refrigerant, R152a . is stored as a liquid...Ch. 2 - Determine the pressure of nitrogen at...Ch. 2 - Determine the pressure of nitrogen at...Ch. 2 - Carbon dioxide at 60C is pumped at a very high...Ch. 2 - Solve Problem 2.70 using the Soave EOS. Notice...Ch. 2 - A tank contains 8.35kg of methane in 0.1m3 at 250K...Ch. 2 - Do the previous problem using the Redlich-Kwong...Ch. 2 - Do the Problem 2.72 using the Soave EOS.Ch. 2 - Determine the unknowns of T, v and x if two phase...Ch. 2 - Give the phase and the missing properties of P, T,...Ch. 2 - Refrigerant R410A in a piston/cylinder arrangement...Ch. 2 - Water in a piston cylinder is at 90C,100kPa , and...Ch. 2 - A tank contains 2kg of saturated ammonia vapor at...Ch. 2 - A container with liquid nitrogen at l00K has a...Ch. 2 - Determine the mass of methane gas stored in a 2m3...Ch. 2 - What is the percent error in pressure if the ideal...Ch. 2 - Prob. 2.83PCh. 2 - Use a linear interpolation to estimate the missing...Ch. 2 - Use a linear interpolation to estimate Tsat at...Ch. 2 - Use a double linear interpolation to find the...Ch. 2 - Cabbage needs to be cooked (boiled) at 250 F. What...Ch. 2 - Prob. 2.88EPCh. 2 - If I have 1ft3 of ammonia at 15psia,60F , what is...Ch. 2 - Locate the state of R410A at 30 psia, 20F ....Ch. 2 - A substance is at 300lbf/in.2,65F in a rigid tank....Ch. 2 - For water at 1 atm with a quality of 10 find the...Ch. 2 - Determine the phase of the substance at the given...Ch. 2 - Give the phase and the missing property of P, T,...Ch. 2 - Fill out the following table for substance...Ch. 2 - Give the phase and the specific volume for the...Ch. 2 - Give the missing property of P, T, v, and x for a....Ch. 2 - Saturated liquid water at 150F is put under...Ch. 2 - You want a pot of water to boil at 220F . How...Ch. 2 - Saturated water vapor 240F has its pressure...Ch. 2 - Saturated vapor R4l0A at 100F has its pressure...Ch. 2 - A glass jar is filled with saturated water at 300F...Ch. 2 - A pressure cooker has the lid screwed on tight. A...Ch. 2 - Prob. 2.104EPCh. 2 - Repeat the previous problem if the outlet valve is...Ch. 2 - A cylindrical gas tank 3ft long, with an inside...Ch. 2 - A spherical helium balloon 30ft in diameter is at...Ch. 2 - Helium in a steel tank s at 36psia , 540R with a...Ch. 2 - A 35ft3 rigid tank has propane at 25psia,540R and...Ch. 2 - What is the percent error in specific volume if...Ch. 2 - Air in a car tire is initially at 10F and 30psia ....Ch. 2 - R4l0A at 200psia , 100F is cooled in a closed...Ch. 2 - Refrigerant- 410A in a piston cylinder arrangement...Ch. 2 - A substance is at 70F,300Ibf/in.2 in a 10ft3 tank....Ch. 2 - Estimate the saturation pressure of R142b at 540R...Ch. 2 - Determine the mass of an ethane gas stored in a...Ch. 2 - Determine the pressure of R410Aat100F,v=0.2ft3/ibm...Ch. 2 - What is the percent error in pressure if the ideal...
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