FUNDAMENTALS OF THERMODYNAMICS
10th Edition
ISBN: 9781119803645
Author: Sonntag
Publisher: WILEY
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Chapter 2, Problem 2.43P
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
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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- Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of 6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If, initially, tank A contains pure water and tank B contains 20 kg of salt. A 6 L/min 0.2 kg/L x(t) 100 L 4 L/min x(0) = 0 kg 3 L/min B y(t) 100 L y(0) = 20 kg 2 L/min 1 L/min Figure Q1 - Mixing problem for interconnected tanks Determine the mass of salt in each tank at time t > 0: Analytically (hand calculations)arrow_forwardTwo springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its equilibrium position a distance 2 m and then releasing both masses. if m₁ = m₂ = 1 kg, k₁ = 3 N/m and k₂ = 2 N/m. www.m k₁ = 3 (y₁ = 0). m₁ = 1 k2=2 (y₂ = 0) |m₂ = 1 Y2 y 2 System in static equilibrium (Net change in spring length =32-31) System in motion Figure Q3 - Coupled mass-spring system Determine the equations of motion y₁(t) and y₂(t) for the two masses m₁ and m₂ respectively: Analytically (hand calculations)arrow_forward100 As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the spring constant at time t is k(t) = t sin N/m. If the mass-spring system has mass m = 2 kg and a damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is subjected to the harmonic external force f(t) = 100 cos 3t N. Find at least the first four nonzero terms in a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement: Analytically (hand calculations)arrow_forward
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