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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A piston/cylinder arrangement, shown in Fig P3.111 contains air at 250 kPa, 300°C. The 50-kg piston has a diameter of 0.1 m and initially pushes against the stops. The atmosphere is at 100 kPa and 20°C. The cylinder now cools as heat is transferred to the ambient. a. At what temperature does the
Air in a tank is at 1 MPa and room temperature of 20°C. It is used to fill an initially empty balloon to a pressure of 200 kPa, at which point the radius is 2 m and the temperature is 20°C. Assume the pressure in the balloon is linearly proportional to its radius and that the air in the tank also
A cylinder is fitted with a 10-cm-diameter piston that is restrained by a linear spring (force proportional to distance) as shown in Fig. P3.113. The spring force constant is 80 kN/m and the piston initially rests on the stops, with a cylinder volume of 1 L. The valve to the air line is opened and
A 500-L tank stores 100 kg of nitrogen gas at 150 K. To design the tank the pressure must be estimated and three different methods are suggested. Which is the most accurate, and how different in percent are the other two?a. Nitrogen tables, Table B.6b. Ideal gasc. Generalized compressibility chart,
What is the percent error in pressure if the ideal gas model is used to represent the behavior of superheated vapor R-22 at 50°C, 0.03082 m3/kg? What if the generalized compressibility chart, Fig D.1, is used instead (iterations needed)?
Find the pressure and temperature for saturated vapor R-12 with v = 0.1 m3/kg
Use a linear interpolation to estimate properties of ammonia to fill out the table below P [kPa] T [ °C] v [m3/kg] x a) 550 0.75 b) 80 20 c) 10 0.4
Use a linear interpolation to estimate Tsat at 900 kPa for nitrogen. Sketch by hand the curve Psat (T) by using a few table entries around 900 kPa from table B.6.1. Is your linear interpolation over or below the actual curve?
Use a double linear interpolation to find the pressure for superheated R-134a at 13°C with v = 0.3 m3/kg.
Find the specific volume of ammonia at 140 kPa and 0°C.
Find the pressure of water at 200°C and specific volume of 1.5 m3/kg
Use the computer software to find the properties for water at the 4 states in Problem 3.33
Use the computer software to find the properties for ammonia at the 2 states listed in Problem 3.37
Use the computer software to find the properties for ammonia at the 3 states listed in Problem 3.117
Find the value of the saturated temperature for nitrogen by linear interpolation in table B.6.1 for a pressure of 900 kPa. Compare this to the value given by the computer software.
Write a computer program that lists the states P, T, and v along the process curve in Problem 3.111
Use the computer software to sketch the variation of pressure with temperature in Problem 3.41. Extend the curve a little into the single-phase region
Cabbage needs to be cooked (boiled) at 250 F. What pressure should the pressure cooker be set for?
If I have 1 ft3 of ammonia at 15 psia, 60 F how much mass is that?
For water at 1 atm with a quality of 10% find the volume fraction of vapor
Locate the state of R-134a at 30 psia, 20 F. Indicate in both the P-v and the T-v diagrams the location of the nearest states listed in the printed table F.10
Calculate the ideal gas constant for argon and hydrogen based on Table F.1 and verify the value with Table F.4
Air in a tank is at 1 MPa and room temperature of 20°C. It is used to fill an initially empty balloon to a pressure of 200 kPa, at which point the radius is 2 m and the temperature is 20°C. Assume the pressure in the balloon is linearly proportional to its radius and that the air in the tank also
A cylinder is fitted with a 10-cm-diameter piston that is restrained by a linear spring (force proportional to distance) as shown in Fig. P3.113. The spring force constant is 80 kN/m and the piston initially rests on the stops, with a cylinder volume of 1 L. The valve to the air line is opened and
A 500-L tank stores 100 kg of nitrogen gas at 150 K. To design the tank the pressure must be estimated and three different methods are suggested. Which is the most accurate, and how different in percent are the other two? a. Nitrogen tables, Table B.6 b. Ideal gas c. Generalized compressibility
What is the percent error in pressure if the ideal gas model is used to represent the behavior of superheated vapor R-22 at 50°C, 0.03082 m3/kg? What if the generalized compressibility chart, Fig D.1, is used instead (iterations needed)?
Find the pressure and temperature for saturated vapor R-12 with v = 0.1 m3/kg Discuss.
Use a linear interpolation to estimate properties of ammonia to fill out the table below P [kPa] T [°C] v [m3/kg] x a) 550 0.75 b) 80 20 c) 10 0.4
Water at 80 F can exist in different phases dependent on the pressure. Give the approximate pressure range in lbf/in2 for water being in each one of the three phases, vapor, liquid or solid.
A substance is at 300 lbf/in.2, 65 F in a rigid tank. Using only the critical properties can the phase of the mass be determined if the substance is nitrogen, water or propane?
Determine whether water at each of the following states is a compressed liquid, a superheated vapor, or a mixture of saturated liquid and vapor.
Determine whether water at each of the following states is a compressed liquid, a superheated vapor, or a mixture of saturated liquid and vapor. Discuss.
Give the phase and the missing property of P, T, v and x. a. R-134a T = -10 F, P = 18 psia b. R-134a P = 50 psia, v = 1.3 ft3/lbm c. NH3 T = 120 F, v = 0.9 ft3/lbm d. NH3 T = 200 F, v = 11 ft3/lbm
Give the phase and the specific volume. Discuss.
A water storage tank contains liquid and vapor in equilibrium at 220 F. The distance from the bottom of the tank to the liquid level is 25 ft. What is the absolute pressure at the bottom of the tank?
A sealed rigid vessel has volume of 35 ft3 and contains 2 lbm of water at 200 F. The vessel is now heated. If a safety pressure valve is installed, at what pressure should the valve be set to have a maximum temperature of 400 F?
You want a pot of water to boil at 220 F. How heavy a lid should you put on the 6 inch diameter pot when Patm = 14.7 psia?
Saturated water vapor at 200 F has its pressure decreased to increase the volume by 10%, keeping the temperature constant. To what pressure should it be expanded? Explain.
A boiler feed pump delivers 100 ft3/min of water at 400 F, 3000 lbf/in.2. What is the mass flow rate (lbm/s)? What would be the percent error if the properties of saturated liquid at 400 F were used in the calculation? What if the properties of saturated liquid at 3000 lbf/in.2 were used?
A pressure cooker has the lid screwed on tight. A small opening with A = 0.0075 in2 is covered with a petcock that can be lifted to let steam escape. How much mass should the petcock have to allow boiling at 250 F with an outside atmosphere at 15 psia?
A steel tank contains 14 lbm of propane (liquid + vapor) at 70 F with a volume of 0.25 ft3. The tank is now slowly heated. Will the liquid level inside eventually rise to the top or drop to the bottom of the tank? What if the initial mass is 2 lbm instead of 14 lbm?
A cylindrical gas tank 3 ft long, inside diameter of 8 in., is evacuated and then filled with carbon dioxide gas at 77 F. To what pressure should it be charged if there should be 2.6 lbm of carbon dioxide?
A spherical helium balloon of 30 ft in diameter is at ambient T and P, 60 F and 14.69 psia. How much helium does it contain? It can lift a total mass that equals the mass of displaced atmospheric air. How much mass of the balloon fabric and cage can then be lifted?
Give the phase and the specific volume for each of the following.
What is the percent error in specific volume if the ideal gas model is used to represent the behavior of superheated ammonia at 100 F, 80 lbf/in.2? What if the generalized compressibility chart, Fig D.1, is used instead?
A cylinder is fitted with a 4-in.-diameter piston that is restrained by a linear spring (force proportional to distance) as shown in Fig. P3.16. The spring force constant is 400 lbf/in. and the piston initially rests on the stops, with a cylinder volume of 60 in.3. The valve to the air line is
A 35 ft3 rigid tank has propane at 15 psia, 540 R and connected by a valve to another tank of 20 ft3 with propane at 40 psia, 720 R. The valve is opened and the two tanks come to a uniform state at 600 R. What is the final pressure?
Two tanks are connected together as shown in Fig. P3.49, both containing water. Tank A is at 30 lbf/in.2, v = 8 ft3/lbm, V = 40 ft3 and tank B contains 8 lbm at 80 lbf/in. 2, 750 F. The valve is now opened and the two come to a uniform state. Find the final specific volume.
A 35 ft3 rigid tank has air at 225 psia and ambient 600 R connected by a valve to a piston cylinder. The piston of area 1 ft2 requires 40 psia below it to float, Fig. P3.99. The valve is opened and the piston moves slowly 7 ft up and the valve is closed. During the process air temperature remains
Give the phase and the missing properties of P, T, v and x. These may be a little more difficult if the appendix tables are used instead of the software. Discuss.
A pressure cooker (closed tank) contains water at 200 F with the liquid volume being 1/10 of the vapor volume. It is heated until the pressure reaches 300 lbf/in.2. Find the final temperature. Has the final state more or less vapor than the initial state?
Refrigerant-22 in a piston/cylinder arrangement is initially at 120 F, x = 1. It is then expanded in a process so that P = Cv−1 to a pressure of 30 lbf/in.2. Find the final temperature and specific volume.
A substance is at 70 F, 300 lbf/in.2 in a 10 ft3 tank. Estimate the mass from the compressibility chart if the substance is a) air, b) butane or c) propane.
Determine the mass of an ethane gas stored in a 25 ft3 tank at 250 F, 440 lbf/in.2 using the compressibility chart. Estimate the error (%) if the ideal gas model is used.
Determine the mass of an ethane gas stored in a 25 ft3 tank at 250 F, 440 lbf/in.2 using the compressibility chart estimate the error (%) if the ideal gas model is used.
A car engine is rated at 160 hp. What is the power in SI units?
A 1200 hp dragster engine has a drive shaft rotating at 2000 RPM. Compute torque is on the shaft?
A 1200 hp dragster engine drives the car with a speed of 100 km/h. How much force is between the tires and the road?
Two hydraulic piston/cylinders are connected through a hydraulic line so they have roughly the same pressure. If they have diameters of D1 and D2 = 2D1 respectively, what can you say about the piston forces F1 and F2?
Normally pistons have a flat head, but in diesel engines pistons can have bowls in them and protruding ridges. Does this geometry influence the work term?
What is roughly the relative magnitude of the work in the process 1-2c versus the process 1-2a shown in figure 4.8?
A hydraulic cylinder of area 0.01 m2 must push a 1000 kg arm and shovel 0.5 m straight up. What pressure is needed and how much work is done?
A work of 2.5 kJ must be delivered on a rod from a pneumatic piston/cylinder where the air pressure is limited to 500 kPa. What diameter cylinder should I have to restrict the rod motion to maximum 0.5 m?
Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero?
Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero? Discuss.
Show how the polytropic exponent n can be evaluated if you know the end state properties, (P1, V1) and (P2, V2).
A drag force on an object moving through a medium (like a car through air or a submarine through water) is Fd = 0.225 A ρV2. Verify the unit becomes Newton?
A force of 1.2 kN moves a truck with 60 km/h up a hill. What is the power?
Electric power is volts times ampere (P = V i). When a car battery at 12 V is charged with 6 amp for 3 hours how much energy is delivered?
Torque and energy and work have the same units (N m). Explain the difference.
Find the rate of conduction heat transfer through a 1.5 cm thick hardwood board, k = 0.16 W/m K, with a temperature difference between the two sides of 20oC.
A 2 m2 window has a surface temperature of 15oC and the outside wind is blowing air at 2oC across it with a convection heat transfer coefficient of h = 125 W/m2K. What is the total heat transfer loss?
A radiant heating lamp has a surface temperature of 1000 K with ε = 0.8. How large a surface area is needed to provide 250 W of radiation heat transfer?
A piston of mass 2 kg is lowered 0.5 m in the standard gravitational field. Compute the required force and work involved in the process.
An escalator raises a 100 kg bucket of sand 10 m in 1 minute. Determine the total amount of work done during the process.
A bulldozer pushes 500 kg of dirt 100 m with a force of 1500 N. It then lifts the dirt 3 m up to put it in a dump truck. How much work did it do in each situation?
A hydraulic cylinder has a piston of cross sectional area 25 cm2 and a fluid pressure of 2 MPa. If the piston is moved 0.25 m how much work is done?
Two hydraulic cylinders maintain a pressure of 1200 kPa. One has a cross sectional area of 0.01 m2 the other 0.03 m2. To deliver a work of 1 kJ to the piston how large a displacement (V) and piston motion H is needed for each cylinder? Neglect Patm.
A linear spring, F = ks (x − x0), with spring constant ks = 500 N/m, is stretched until it is 100 mm longer. Find the required force and work input.
A nonlinear spring has the force versus displacement relation of F = kns(x − x0) n. If the spring end is moved to x1 from the relaxed state, determine the formula for the required work.
The rolling resistance of a car depends on its weight as: F = 0.006 mg. How long will a car of 1400 kg drive for a work input of 25 kJ?
A car drives for half an hour at constant speed and uses 30 MJ over a distance of 40 km. What was the traction force to the road and its speed?
The air drag force on a car is 0.225 A ρV2. Assume air at 290 K, 100 kPa and a car frontal area of 4 m2 driving at 90 km/h. How much energy is used to overcome the air drag driving for 30 minutes?
Two hydraulic piston/cylinders are connected with a line. The master cylinder has an area of 5 cm2 creating a pressure of 1000 kPa. The slave cylinder has an area of 3 cm2. If 25 J is the work input to the master cylinder what is the force and displacement of each piston and the work out put of the
A constant pressure piston cylinder contains 0.2 kg water as saturated vapor at 400 kPa. It is now cooled so the water occupies half the original volume. Find the work in the process.
A steam radiator in a room at 25°C has saturated water vapor at 110 kPa flowing through it, when the inlet and exit valves are closed. What is the pressure and the quality of the water, when it has cooled to 25oC? How much work is done?
A 400-L tank A, see figure P4.33, contains argon gas at 250 kPa, 30oC. Cylinder B, having a frictionless piston of such mass that a pressure of 150 kPa will float it, is initially empty. The valve is opened and argon flows into B and eventually reaches a uniform state of 150 kPa, 30oC throughout.
A piston cylinder contains air at 600 kPa, 290 K and a volume of 0.01 m3. A constant pressure process gives 54 kJ of work out. Find the final volume and temperature of the air.
Saturated water vapor at 200 kPa is in a constant pressure piston cylinder. At this state the piston is 0.1 m from the cylinder bottom and cylinder area is 0.25 m2. The temperature is then changed to 200oC. Find the work in the process.
A cylinder fitted with a frictionless piston contains 5 kg of superheated refrigerant R-134a vapor at 1000 kPa, 140°C. The setup is cooled at constant pressure until the R-134a reaches a quality of 25%. Calculate the work done in the process.
Find the specific work in Problem 3.54 for the case the volume is reduced. Saturated vapor R-134a at 50oC changes volume at constant temperature. Find the new pressure, and quality if saturated, if the volume doubles. Repeat the question for the case the volume is reduced to half the original
A piston/cylinder has 5 m of liquid 20oC water on top of the piston (m = 0) with cross-sectional area of 0.1 m2, see Fig. P2.57. Air is let in under the piston that rises and pushes the water out over the top edge. Find the necessary work to push all the water out and plot the process in a P-V
Air in a spring loaded piston/cylinder has a pressure that is linear with volume, P = A + BV. With an initial state of P = 150 kPa, V = 1 L and a final state of 800 kPa and volume 1.5 L it is similar to the setup in Problem 3.113. Find the work done by the air.
Find the specific work in Problem 3.43. Saturated water vapor at 200 kPa is in a constant pressure piston cylinder. At this state the piston is 0.1 m from the cylinder bottom. How much is this distance if the temperature is changed to a) 200 oC and b) 100 oC.
A piston/cylinder contains 1 kg water at 20oC with volume 0.1 m3. By mistake someone locks the piston preventing it from moving while we heat the water to saturated vapor. Find the final temperature, volume and the process work.
A piston cylinder contains 1 kg of liquid water at 20oC and 300 kPa. There is a linear spring mounted on the piston such that when the water is heated the pressure reaches 3 MPa with a volume of 0.1 m3. a) Find the final temperature b) Plot the process in a P-v diagram. c) Find the work in the
A piston cylinder contains 3 kg of air at 20oC and 300 kPa. It is now heated up in a constant pressure process to 600 K. a) Find the final volume b) Plot the process path in a P-v diagram c) Find the work in the process.
A piston cylinder contains 0.5 kg air at 500 kPa, 500 K. The air expands in a process so P is linearly decreasing with volume to a final state of 100 kPa, 300 K. Find the work in the process.
Consider the nonequilibrium process described in Problem 3.109. Determine the work done by the carbon dioxide in the cylinder during the process. A cylinder has a thick piston initially held by a pin as shown in Fig. P3.109. The cylinder contains carbon dioxide at 200 kPa and ambient temperature
Consider the problem of inflating the helium balloon, as described in problem 3.79. For a control volume that consists of the helium inside the balloon determine the work done during the filling process when the diameter changes from 1 m to 4 m.
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