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mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
Air in a tank is at 1 MPa and room temperature of 20C. It is used to fill an initially empty balloon to a pressure of 200 kPa, at which point the diameter is 2 m and the temperature is 20C. Assume the pressure in the balloon is linearly proportional to its diameter and that the air
A vacuum pump is used to evacuate a chamber where some specimens are dried at 50C. The pump rate of volume displacement is 0.5 m3/s with an inlet pressure of 0.1 kPa and temperature 50C, how much water vapor has been removed over a 30-min period?
An initially deflated and flat balloon is connected by a valve to a 12 m3 storage tank containing helium gas at 2 MPa and ambient temperature, 20C. The valve is opened and the balloon is inflated at constant pressure, Po = 100 kPa, equal to ambient pressure, until it becomes spherical at D1
The helium balloon described in Problem 3.14 is released into the atmosphere and rises to an elevation of 5000 m, with a local ambient pressure of Po = 50 kPa and temperature of 20C. What is then the diameter of the balloon?
A cylinder is fitted with a 10-cm-diameter piston that is restrained by a linear spring (force proportional to distance). 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 the piston begins to
Air in a tire is initially at 10C, 190 kPa. After driving awhile, the temperature goes up to 10C. Find the new pressure. You must make one assumption on your own.
A substance is at 2 MPa, 17C in a 0.25-m3 rigid tank. Estimate the mass from the compressibility factor if the substance is a) air, b) butane or c) propane.
Argon is kept in a rigid 5 m3 tank at 30C, 3 MPa. Determine the mass using the compressibility factor. What is the error (%) if the ideal gas model is used?
A bottle with a volume of 0.1 m3 contains butane with a quality of 75% and a temperature of 300 K. Estimate the total butane mass in the bottle using the generalized compressibility chart.
A mass of 2 kg of acetylene is in a 0.045 m3 rigid container at a pressure of 4.3 MPa. Use the generalized charts to estimate the temperature. (This becomes trial and error).
Is it reasonable to assume that at the given states the substance behaves as an ideal gas?
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 refrigerant R-22 in each of the following states is a compressed liquid, a superheated vapor, or a mixture of saturated liquid and vapor.
Verify the accuracy of the ideal gas model when it is used to calculate specific volume for saturated water vapor. Do the calculation for 10 kPa and 1 MPa.
Determine the quality (if saturated) or temperature (if superheated) of the following substances at the given two states:
Calculate the following specific volumes
Give the phase and the specific volume.
Give the phase and the specific volume. Discuss. Discuss.
Find the phase, quality x if applicable and the missing property P or T.
Give the phase and the missing properties of P, T, v and x.
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.
What is the percent error in specific volume if the ideal gas model is used to represent the behavior of superheated ammonia at 40C, 500 kPa? What if the generalized compressibility chart, Fig D.1, is used instead?
What is the percent error in pressure if the ideal gas model is used to represent the behavior of superheated vapor R-22 at 50C, 0.03082 m3/kg What if the generalized compressibility chart, Fig. D.1, is used instead (iterations needed)?
Determine the mass of methane gas stored in a 2 m3 tank at 30C, 3 MPa. Estimate the percent error in the mass determination if the ideal gas model is used.
A water storage tank contains liquid and vapor in equilibrium at 110C. The distance from the bottom of the tank to the liquid level is 8 m. What is the absolute pressure at the bottom of the tank?
A sealed rigid vessel has volume of 1 m3 and contains 2 kg of water at 100C. 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 200C?
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,
A 400-m3 storage tank is being constructed to hold LNG, liquefied natural gas, which may be assumed to be essentially pure methane. If the tank is to contain 90% liquid and 10% vapor, by volume, at 100 kPa, what mass of LNG (kg) will the tank hold? What is the quality in the tank?
A storage tank holds methane at 120 K, with a quality of 25 %, and it warms up by 5C per hour due to a failure in the refrigeration system. How long time will it take before the methane becomes single phase and what is the pressure then?
Saturated liquid water at 60C is put under pressure to decrease the volume by 1% keeping the temperature constant. To what pressure should it be compressed?
Saturated water vapor at 60C has its pressure decreased to increase the volume by 10% keeping the temperature constant. To what pressure should it be expanded?
A boiler feed pump delivers 0.05 m3/s of water at 240C, 20 MPa. What is the mass flow rate (kg/s)? What would be the percent error if the properties of saturated liquid at 240C were used in the calculation? What if the properties of saturated liquid at 20 MPa were used?
A glass jar is filled with saturated water at 500 kPa, quality 25%, and a tight lid is put on. Now it is cooled to 10C. What is the mass fraction of solid at this temperature?
A cylinder/piston arrangement contains water at 105C, 85% quality with a volume of 1 L. The system is heated, causing the piston to rise and encounter a linear spring. At this point the volume is 1.5 L, piston diameter is 150 mm, and the spring constant is 100 N/mm. The heating continues,
Saturated (liquid vapor) ammonia at 60C is contained in a rigid steel tank. It is used in an experiment, where it should pass through the critical point when the system is heated. What should the initial mass fraction of liquid be?
For a certain experiment, R-22 vapor is contained in a sealed glass tube at 20C. It is desired to know the pressure at this condition, but there is no means of measuring it, since the tube is sealed. However, if the tube is cooled to 20C small droplets of liquid are observed
A steel tank contains 6 kg of propane (liquid vapor) at 20C with a volume of 0.015 m3. 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 1 kg instead of 6 kg?
A cylinder containing ammonia is fitted with a piston restrained by an external force that is proportional to cylinder volume squared. Initial conditions are 10C, 90% quality and a volume of 5 L. A valve on the cylinder is opened and additional ammonia flows into the cylinder until the mass
A container with liquid nitrogen at 100 K has a cross sectional area of 0.5 m2. Due to heat transfer, some of the liquid evaporates and in one hour the liquid level drops 30 mm. The vapor leaving the container passes through a valve and a heater and exits at 500 kPa, 260 K. Calculate the volume
A pressure cooker (closed tank) contains water at 100C with the liquid volume being 1/10 of the vapor volume. It is heated until the pressure reaches 2.0 MPa. Find the final temperature. Has the final state more or less vapor than the initial state?
Ammonia in a piston/cylinder arrangement is at 700 kPa, 80C. It is now cooled at constant pressure to saturated vapor (state 2) at which point the piston is locked with a pin. The cooling continues to 10C (state 3). Show the processes 1 to 2 and 2 to 3 on both a P–v and
A piston/cylinder arrangement is loaded with a linear spring and the outside atmosphere. It contains water at 5 MPa, 400C with the volume being 0.1 m3. If the piston is at the bottom, the spring exerts a force such that Plift 200 kPa. The system now cools until the pressure
Water in a piston/cylinder is at 90C, 100 kPa, and the piston loading is such that pressure is proportional to volume, P CV. Heat is now added until the temperature reaches 200C. Find the final pressure and also the quality if in the two-phase region.
A spring-loaded piston/cylinder contains water at 500C, 3 MPa. The setup is such that pressure is proportional to volume, P CV. It is now cooled until the water becomes saturated vapor. Sketch the P-v diagram and find the final pressure.
Refrigerant-12 in a piston/cylinder arrangement is initially at 50C, x 1. It is then expanded in a process so that P Cv1 to a pressure of 100 kPa. Find the final temperature and specific volume.
A sealed rigid vessel of 2 m3 contains a saturated mixture of liquid and vapor R- 134a at 10C. If it is heated to 50C, the liquid phase disappears. Find the pressure at 50C and the initial mass of the liquid.
Two tanks are connected both containing water. Tank A is at 200 kPa, v 0.5 m3/kg, VA 1 m3 and tank B contains 3.5 kg at 0.5 MPa, 400C. The valve is now opened and the two come to a uniform state. Find the final specific volume.
A tank contains 2 kg of nitrogen at 100 K with a quality of 50%. Through a volume flow meter and valve, 0.5 kg is now removed while the temperature remains constant. Find the final state inside the tank and the volume of nitrogen removed if the valve/meter is located ata. The top of the tankb. The
Consider two tanks, A and B, connected by a valve. Each has a volume of 200 L and tank A has R-12 at 25C, 10% liquid and 90% vapor by volume, while tank B is evacuated. The valve is now opened and saturated vapor flows from A to B until the pressure in B has reached that in A, at which
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?
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 vacuum pump is used to evacuate a chamber where some specimens are dried at 120 F. The pump rate of volume displacement is 900 ft3/min with an inlet pressure of 1 mm Hg and temperature 120 F, how much water vapor has been removed over a 30-min period?
A cylinder is fitted with a 4-in.-diameter piston that is restrained by a linear spring (force proportional to distance). 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 opened and the piston begins
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.
Argon is kept in a rigid 100 ft3 tank at F, 450 lbf/in 2. Determine the mass using the compressibility factor. What is the error (%) if the ideal gas model is used?
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. Discuss.
Give the phase and the specific volume. Discuss in detail.
Give the phase and the specific volume. Discuss briefly.
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. Discuss.
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 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?
Saturated liquid water at 200 F is put under pressure to decrease the volume by 1%, keeping the temperature constant. To what pressure should it be compressed?
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?
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?
Saturated (liquid vapor) ammonia at 140 F is contained in a rigid steel tank. It is used in an experiment, where it should pass through the critical point when the system is heated. What should the initial mass fraction of liquid be?
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 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?
Two tanks are connected together 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/in2, 750 F. The valve is now opened and the two come to a uniform state. Find the final specific volume.
A spring-loaded piston/cylinder contains water at 900 F, 450 lbf/in 2. The setup is such that pressure is proportional to volume, P CV. It is now cooled until the water becomes saturated vapor. Find the final pressure.
Refrigerant-22 in a piston/cylinder arrangement is initially at 120 F, x 1. It is then expanded in a process so that P Cv1 to a pressure of 30 lbf/in 2. Find the final temperature and specific volume.
A piston of mass 2 kg is lowered 0.5 m in the standard gravitational field. Find 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 and the instantaneous rate of work during the process.
A linear spring, F ks(x xo), 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 xo)n. If the spring end is moved to x1 from the relaxed state, determine the formula for the required work.
A cylinder fitted with a frictionless piston contains 5 kg of superheated refrigerant R-134a vapor at 1000 kPa, 140C. The setup is cooled at constant pressure until the R-134a reaches a quality of 25%. Calculate the work done in the process.
A piston/cylinder arrangement initially contains air at 150 kPa, 400C. The setup is allowed to cool to the ambient temperature of 20C. a. Is the piston resting on the stops in the final state? What is the final pressure in the cylinder? b. What is the specific work done by the air
The refrigerant R-22 is contained in a piston/cylinder, where the volume is 11 L when the piston hits the stops, the initial state is 30C, 150 kPa with a volume of 10 L. This system is brought indoors and warms up to 15C. a. Is the piston at the stops in the final
Consider a mass going through a polytropic process where pressure is directly proportional to volume (n = 1). The process start with P = 0, V = 0 and ends with P = 600 kPa, V = 0.01 m3.The physical setup could be as in Problem 2.22. Find the boundary work done by the mass.
A piston/cylinder contains 50 kg of water at 200 kPa with a volume of 0.1 m3. Stops in the cylinder restrict the enclosed volume to 0.5 m3, similar to the setup in Problem 4.7. The water is now heated to 200C. Find the final pressure, volume and the work done by the water.
A piston/cylinder contains 1 kg of liquid water at 20C and 300 kPa. Initially the piston floats, similar to the setup in Problem 4.7, with a maximum enclosed volume of 0.002 m3 if the piston touches the stops. Now heat is added so a final pressure of 600 kPa is reached. Find the final
A piston/cylinder contains butane, C4H10, at 300C, 100 kPa with a volume of 0.02 m3. The gas is now compressed slowly in an isothermal process to 300 kPa. a. Show that it is reasonable to assume that butane behaves as an ideal gas during this process. b. Determine the work done by the
The piston/cylinder contains carbon dioxide at 300 kPa, 100C with a volume of 0.2 m3. Mass is added at such a rate that the gas compresses according to the relation PV1.2 constant to a final temperature of 200C. Determine the work done during the process.
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 3.16. Find the work done by the air.
A gas initially at 1 MPa, 500C is contained in a piston and cylinder arrangement with an initial volume of 0.1 m3. The gas is then slowly expanded according to the relation PV constant until a final pressure of 100 kPa is reached. Determine the work for this process.
Consider a two-part process with an expansion from 0.1 to 0.2 m3 at a constant pressure of 150 kPa followed by an expansion from 0.2 to 0.4 m3 with a linearly rising pressure from 150 kPa ending at 300 kPa. Show the process in a P-V diagram and find the boundary work. Discuss.
A cylinder fitted with a piston contains propane gas at 100 kPa, 300 K with a volume of 0.2 m3. The gas is now slowly compressed according to the relation PV1.1 constant to a final temperature of 340 K. Justify the use of the ideal gas model. Find the final pressure and the work
The gas space above the water in a closed storage tank contains nitrogen at 25C, 100 kPa. Total tank volume is 4 m3, and there is 500 kg of water at 25C. Additional 500 kg water is now forced into the tank, assuming constant temperature throughout find the final pressure of the
A steam radiator in a room at 25C 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 balloon behaves such that the pressure inside is proportional to the diameter squared. It contains 2 kg of ammonia at 0C, 60% quality. The balloon and ammonia are now heated so that a final pressure of 600 kPa is reached. Considering the ammonia as a control mass, find the amount of work
Consider a piston cylinder with 0.5 kg of R-134a as saturated vapor at -10C. It is now compressed to a pressure of 500 kPa in a polytropic process with n = 1.5. Find the final volume and temperature, and determine the work done during the process.
A cylinder having an initial volume of 3 m3 contains 0.1 kg of water at 40C. The water is then compressed in an isothermal quasi-equilibrium process until it has a quality of 50%. Calculate the work done in the process. Assume the water vapor is an ideal gas.
Consider the non-equilibrium process described in Problem 3.7. Determine the work done by the carbon dioxide in the cylinder during the process.
Two kilograms of water is contained in a piston/cylinder with a mass less piston loaded with a linear spring and the outside atmosphere. Initially the spring force is zero and P1 Po 100 kPa with a volume of 0.2 m3. If the piston just hits the upper stops the volume
A piston/cylinder contains 1 kg of water at 20C with a volume of 0.1 m3. Initially the piston rests on some stops with the top surface open to the atmosphere, Po and a mass so a water pressure of 400 kPa will lift it. To what temperature should the water be heated to lift the piston? If it
Assume the same system as in the previous problem, but let the piston be locked with a pin. If the water is heated to saturated vapor find the final temperature, volume and the work, 1W2.
A piston cylinder setup similar to Problem 4.24 contains 0.1 kg saturated liquid and vapor water at 100 kPa with quality 25%. The mass of the piston is such that a pressure of 500 kPa will float it. The water is heated to 300C. Find the final pressure, volume and the work, 1W2.
A 400-L tank, A contains argon gas at 250 kPa, 30C. 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, 30C throughout. What
Air at 200 kPa, 30C is contained in a cylinder/piston arrangement with initial volume 0.1 m3. The inside pressure balances ambient pressure of 100 kPa plus an externally imposed force that is proportional to V0.5. Now heat is transferred to the system to a final pressure of 225 kPa. Find
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