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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A spring-loaded piston/cylinder arrangement contains R-134a at 20C, 24% quality with a volume 50 L. The setup is heated and thus expands, moving the piston. It is noted that when the last drop of liquid disappears the temperature is 40C. The heating is stopped when T
A cylinder containing 1 kg of ammonia has an externally loaded piston. Initially the ammonia is at 2 MPa, 180C and is now cooled to saturated vapor at 40C, and then further cooled to 20C, at which point the quality is 50%. Find the total work for the process, assuming a
A vertical cylinder has a 90-kg piston locked with a pin trapping 10 L of R-22 at 10C, 90% quality inside. Atmospheric pressure is 100 kPa, and the cylinder cross-sectional area is 0.006 m2. The pin is removed, allowing the piston to move and come to rest with a final temperature of
A piston/cylinder has 1 kg of R-134a at state 1 with 110C, 600 kPa, and is then brought to saturated vapor, state 2, by cooling while the piston is locked with a pin. Now the piston is balanced with an additional constant force and the pin is removed. The cooling continues to a state 3
Consider the process described in Problem 3.49. With the ammonia as a control mass, determine the boundary work during the process.
Find the work for Problem 3.52.
Find the work for Problem 3.53.
Find the work for Problem 3.55.
Find the work for Problem 3.56.
A spherical elastic balloon initially containing 5 kg ammonia as saturated vapor at 20C is connected by a valve to a 3-m3 evacuated tank. The balloon is made such that the pressure inside is proportional to the diameter. The valve is now opened, allowing ammonia to flow into the tank until
A 0.5-m-long steel rod with a 1-cm diameter is stretched in a tensile test. What is the required work to obtain a relative strain of 0.1%? The modulus of elasticity of steel is 2 108 kPa.
A film of ethanol at 20C has a surface tension of 22.3mN/m and is maintained on a wire frame. Consider the film with two surfaces as a control mass and find the work done when the wire is moved 10 mm to make the film 20 40 mm.
A simple magnetic substance is one involving only magnetic work, that is, a change in magnetization of a substance in the presence of a magnetic field. For such a substance undergoing a quasi equilibrium process at constant volume, the work is W = - Co H d M where H = magnetic field
For the magnetic substance described in Problem 4.41, determine the work done in a process at constant magnetic field intensity (temperature varies), instead of one at constant temperature.
A battery is well insulated while being charged by 12.3 V at a current of 6 A. Take the battery as a control mass and find the instantaneous rate of work and the total work done over 4 hours.
Two springs with same spring constant are installed in a mass less piston/cylinder with the outside air at 100 kPa. If the piston is at the bottom, both springs are relaxed and the second spring comes in contact with the piston at V 2 m3. The cylinder contains ammonia initially at
Consider the process of inflating a helium balloon, as described in Problem 3.14. For a control volume that consists of the space inside the balloon, determine the work done during the overall process.
A cylinder, Acyl 7.012 cm2, has two pistons mounted, the upper one, mp1 100 kg, initially resting on the stops. The lower piston, mp2 0 kg, has 2 kg water below it, with a spring in vacuum connecting the two pistons. The spring force is zero when the
The sun shines on a 150 m2 road surface so it is at 45C. Below the 5 cm thick asphalt, average conductivity of 0.06 W/m K, is a layer of compacted rubbles at a temperature of 15C. Find the rate of heat transfer to the rubbles.
A pot of steel, conductivity 50 W/m K, with a 5 mm thick bottom is filled with 15C liquid water. The pot has a diameter of 20 cm and is now placed on an electric stove that delivers 250 W as heat transfer. Find the temperature on the outer pot bottom surface assuming the inner surface is at
A water-heater is covered up with insulation boards over a total surface area of 3 m2. The inside board surface is at 75C and the outside surface is at 20C and the board material has a conductivity of 0.08 W/m K. How thick a board should it be to limit the heat transfer loss to 200
You drive a car on a winter day with the atmospheric air at –15C and you keep the outside front windshield surface temperature at + 2C by blowing hot air on the inside surface. If the windshield is 0.5 m2 and the outside convection coefficient is 250 W/m2K find the rate of energy
A large condenser (heat exchanger) in a power plant must transfer a total of 100 MW from steam running in a pipe to sea water being pumped through the heat exchanger. Assume the wall separating the steam and seawater is 4 mm of steel, conductivity 50 W/m K and that a maximum of 5C
The black grille on the back of a refrigerator has a surface temperature of 35C with a total surface area of 1 m2. Heat transfer to the room air at 20C takes place with an average convective heat transfer coefficient of 15 W/m2 K. How much energy can be removed during 15 minutes of
Due to a faulty door contact the small light bulb (25 W) inside a refrigerator is kept on and limited insulation lets 50 W of energy from the outside seep into the refrigerated space. How much of a temperature difference to the ambient at 20C must the refrigerator have in its heat exchanger
The brake shoe and steel drum on a car continuously absorbs 25 W as the car slows down. Assume a total outside surface area of 0.1 m2 with a convective heat transfer coefficient of 10 W/m2 K to the air at 20C. How hot does the outside brake and drum surface become when steady conditions are
A wall surface on a house is at 30C with an emissivity of = 0.7. The surrounding ambient to the house is at 15C, average emissivity of 0.9. Find the rate of radiation energy from each of those surfaces per unit area.
A log of burning wood in the fireplace has a surface temperature of 450C. Assume the emissivity is 1 (perfect black body) and find the radiant emission of energy per unit surface area.
A radiant heat lamp is a rod, 0.5 m long and 0.5 cm in diameter, through which 400 W of electric energy is deposited. Assume the surface has an emissivity of 0.9 and neglect incoming radiation. What will the rod surface temperature be?
Consider a window-mounted air conditioning unit used in the summer to cool incoming air. Examine the system boundaries for rates of work and heat transfer, including signs.
Consider a hot-air heating system for a home. Examine the following systems for heat transfer.
Consider a household refrigerator that has just been filled up with room temperature food. Define a control volume (mass) and examine its boundaries for rates of work and heat transfer, including sign.a. Immediately after the food is placed in the refrigeratorb. After a long period of time has
A room is heated with an electric space heater on a winter day. Examine the following control volumes, regarding heat transfer and work, including sign.
A cylinder fitted with a frictionless piston contains 10 lbm of superheated refrigerant R-134a vapor at 100 lbf/in 2, 300 F. The setup is cooled at constant pressure until the water reaches a quality of 25%. Calculate the work done in the process.
An escalator raises a 200 lbm bucket of sand 30 ft 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 = 35 lbf/ft, is stretched until it is 2.5 in. longer. Find the required force and work input.
The piston/cylinder shown in Fig P4.12 contains carbon dioxide at 50 lbf/in 2, 200 F with a volume of 5 ft3. Mass is added at such a rate that the gas compresses according to the relation PV1.2 constant to a final temperature of 350 F. Determine the work done during the process.
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 = 90 lbf/in 2, V = 0.4 ft3.The physical setup could be as in Problem 2.22. Find the boundary work done by the mass.
The gas space above the water in a closed storage tank contains nitrogen at 80 F, 15 lbf/in 2. Total tank volume is 150 ft3 and there is 1000 lbm of water at 80 F additional 1000 lbm water is now forced into the tank, assuming constant temperature throughout, find the final pressure of the nitrogen
A steam radiator in a room at 75 F has saturated water vapor at 16 lbf/in 2 flowing through it, when the inlet and exit valves are closed. What are the pressure and the quality of the water, when it has cooled to 75F? How much work is done?
Consider a two-part process with an expansion from 3 to 6 ft3 at a constant pressure of 20 lbf/in 2 followed by an expansion from 6 to 12 ft3 with a linearly rising pressure from 20 lbf/in 2 ending at 40 lbf/in 2. Show the process in a P-V diagram and find the boundary work.
A cylinder having an initial volume of 100 ft3 contains 0.2 lbm of water at 100 F. 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 assuming water vapor is an ideal gas.
Air at 30 lbf/in 2, 85 F is contained in a cylinder/piston arrangement with initial volume 3.5 ft3. The inside pressure balances ambient pressure of 14.7 lbf/in 2 plus an externally imposed force that is proportional to V0.5. Now heat is transferred to the system to a final pressure of 40 lbf/in 2.
A cylinder containing 2 lbm of ammonia has an externally loaded piston. Initially the ammonia is at 280 lbf/in 2, 360 F and is now cooled to saturated vapor at 105 F, and then further cooled to 65 F, at which point the quality is 50%. Find the total work for the process, assuming a piecewise linear
A piston/cylinder has 2 lbm of R-134a at state 1 with 200 F, 90 lbf/in 2, and is then brought to saturated vapor, state 2, by cooling while the piston is locked with a pin. Now the piston is balanced with an additional constant force and the pin is removed. The cooling continues to a state 3 where
Find the work for Problem 3.82.
Find the work for Problem 3.83.
A 1-ft-long steel rod with a 0.5-in. diameter is stretched in a tensile test. What is the required work to obtain a relative strain of 0.1%? The modulus of elasticity of steel is 30 106 lbf/in 2.
The sun shines on a 1500 ft2 road surface so it is at 115 F. Below the 2 inch thick asphalt, average conductivity of 0.035 Btu/h ft F, is a layer of compacted rubbles at a temperature of 60 F. Find the rate of heat transfer to the rubbles.
A water-heater is covered up with insulation boards over a total surface area of 30 ft2. The inside board surface is at 175 F and the outside surface is at 70 F and the board material has a conductivity of 0.05 Btu/h ft F. How thick a board should it be to limit the heat transfer loss to 720 Btu/h?
The black grille on the back of a refrigerator has a surface temperature of 95 F with a total surface area of 10 ft2. Heat transfer to the room air at 70 F takes place with an average convective heat transfer coefficient of 3 Btu/h ft2 R. How much energy can be removed during 15 minutes of
A hydraulic hoist raises a 1750 kg car 1.8 m in an auto repair shop. The hydraulic pump has a constant pressure of 800 kPa on its piston. What is the increase in potential energy of the car and how much volume should the pump displace to deliver that amount of work?
Airplane takeoff from an aircraft carrier is assisted by a steam driven piston/cylinder with an average pressure of 750 kPa. A 3500 kg airplane should be accelerated from zero to a speed of 30 m/s with 25% of the energy coming from the steam piston. Find the needed piston displacement volume.
Solve Problem 5.2, but assume the steam pressure in the cylinder starts at 1000 kPa, dropping linearly with volume to reach 100 kPa at the end of the process.
A piston motion moves a 25 kg hammerhead vertically down 1 m from rest to a velocity of 50 m/s in a stamping machine. What is the change in total energy of the hammerhead?
A 25 kg piston is above a gas in a long vertical cylinder. Now the piston is released from rest and accelerates up in the cylinder reaching the end 5 m higher at a velocity of 25 m/s. The gas pressure drops during the process so the average is 600 kPa with an outside atmosphere at 100 kPa. Neglect
Find the missing properties a. H2O T 250C, v 0.02 m3/kg P ? u ? b. N2 T 277C, P 0.5 MPa x ? h ? c. H2O T 2C, P
Find the missing properties and give the phase of the substance a. H2O u 2390 kJ/kg, T 90C h ? v ? x ? b. H2O u 1200 kJ/kg, P 10 MPa T ? x ? v
Find the missing properties and give the phase of the substance a. H2O T = 120C, v = 0.5 m3/kg u = ? P = ? x = ? b. H2O T 100C, P 10 MPa u ? x ? v ? c. N2 T 800 K, P
Find the missing properties among (P, T, v, u, h) together with x if applicable and give the phase of the substance. a. R-22 T 10C, u 200 kJ/kg b. H2O T 350C, h 3150 kJ/kg c. R-12 P 600 kPa, h
A 100-L rigid tank contains nitrogen (N2) at 900 K, 6 MPa. The tank is now cooled to 100 K. What are the work and heat transfer for this process?
Water in a 150-L closed, rigid tank is at 100C, 90% quality. The tank is then cooled to 10C. Calculate the heat transfer during the process.
A cylinder fitted with a frictionless piston contains 2 kg of superheated refrigerant R- 134a vapor at 350 kPa, 100C. The cylinder is now cooled so the R-134a remains at constant pressure until it reaches a quality of 75%. Calculate the heat transfer in the process.
A test cylinder with constant volume of 0.1 L contains water at the critical point. It now cools down to room temperature of 20C. Calculate the heat transfer from the water.
Ammonia at 0C, quality 60% is contained in a rigid 200-L tank. The tank and ammonia is now heated to a final pressure of 1 MPa. Determine the heat transfer for the process.
A 10-L rigid tank contains R-22 at 10C, 80% quality. A 10-A electric current (from a 6-V battery) is passed through a resistor inside the tank for 10 min, after which the R-22 temperature is 40C. What was the heat transfer to or from the tank during this process?
A piston/cylinder arrangement contains 1 kg of water, shown in Fig. P5.16. The piston is spring loaded and initially rests on some stops. A pressure of 300 kPa will just float the piston and, at a volume of 1.5 m3, a pressure of 500 kPa will balance the piston. The initial state of the water is 100
A closed steel bottle contains ammonia at 20C, x 20% and the volume is 0.05 m3. It has a safety valve that opens at a pressure of 1.4 MPa. By accident, the bottle is heated until the safety valve opens. Find the temperature and heat transfer when the valve first
A piston/cylinder arrangement B is connected to a 1-m3 tank A by a line and valve, shown in Fig. P5.18. Initially both contain water with A at 100 kPa, saturated vapor and B at 400C, 300 kPa, 1 m3. The valve is now opened and, the water in both A and B comes to a uniform state. a. Find the
Consider the same setup and initial conditions as in the previous problem, assuming that the process is adiabatic find the final temperature and work.
A vertical cylinder fitted with a piston contains 5 kg of R-22 at 10C. Heat is transferred to the system, causing the piston to rise until it reaches a set of stops at which point the volume has doubled. Additional heat is transferred until the temperature inside reaches 50C, at
A piston/cylinder contains 50 kg of water at 200 kPa with a volume of 0.1 m3. Stops in the cylinder are placed to restrict the enclosed volume to 0.5 m3 similar to Fig. P5.20, the water is now heated until the piston reaches the stops. Find the necessary heat transfer.
Ten kilograms of water in a piston/cylinder with constant pressure is at 450C and a volume of 0.633 m3. It is now cooled to 20C. Show the P–v diagram and find the work and heat transfer for the process.
Find the heat transfer in Problem 4.10.
Find the heat transfer in Problem 4.24.
A piston/cylinder contains 1 kg of liquid water at 20C 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 and plot the P-v diagram for the process. b. Calculate
An insulated cylinder fitted with a piston contains R-12 at 25C with a quality of 90% and a volume of 45 L. The piston is allowed to move, and the R-12 expands until it exists as saturated vapor. During this process the R-12 does 7.0 kJ of work against the piston. Determine the final
Two kilograms of nitrogen at 100 K, x 0.5 is heated in a constant pressure process to 300 K in a piston/cylinder arrangement. Find the initial and final volumes and the total heat transfer required.
A piston/cylinder arrangement has the piston loaded with outside atmospheric pressure and the piston mass to a pressure of 150 kPa. It contains water at 2C, which is then heated until the water becomes saturated vapor. Find the final temperature and specific work and heat transfer
Consider the system shown in Fig. P5.29. Tank A has a volume of 100 L and contains saturated vapor R-134a at 30C. When the valve is cracked open, R-134a flows slowly into cylinder B, the piston mass requires a pressure of 200 kPa in cylinder B to raise the piston. The process ends when the
A spherical balloon contains 2 kg of R-22 at 0C, 30% quality. This system is heated until the pressure in the balloon reaches 600 kPa. For this process, it can be assumed that the pressure in the balloon is directly proportional to the balloon diameter. How does pressure vary with volume
A piston held by a pin in an insulated cylinder contains 2 kg water at 100C, quality 98%. The piston has a mass of 102 kg, with cross-sectional area of 100 cm2, and the ambient pressure is 100 kPa. The pin is released, which allows the piston to move. Determine the final state of the water,
A piston/cylinder arrangement has a linear spring and the outside atmosphere acting on the piston, shown in Fig. P5.32. It contains water at 3 MPa, 400C with the volume being 0.1 m3. If the piston is at the bottom, the spring exerts a force such that a pressure of 200 kPa inside is required
A vertical piston/cylinder has a linear spring mounted. The spring is mounted so at zero cylinder volume a balancing pressure inside is 100 kPa. The cylinder contains 0.5 kg of water at 125C, 70% quality. Heat is now transferred to the water until the cylinder pressure reaches 300 kPa. How
Two heavily insulated tanks are connected by a valve. Tank A contains 0.6 kg of water at 300 kPa 300C. Tank B has a volume of 300 L and contains water at 600 kPa, 80% quality. The valve is opened, and the two tanks eventually come to a uniform state. Assuming the process to be adiabatic,
A piston/cylinder contains 1 kg of ammonia 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, so a pressure of 1400 kPa is required to lift it. To what temperature should the ammonia be heated to lift the piston? If it
A rigid tank is divided into two rooms by a membrane, both containing water. Room A is at 200 kPa, v 0.5 m3/kg, VA 1 m3, and room B contains 3.5 kg at 0.5 MPa, 400C. The membrane now ruptures and heat transfer takes place so the water comes to a uniform state
A cylinder/piston arrangement contains 5 kg of water at 100C with x 20% and the piston, mP 75 kg, resting on some stops, similar to Fig. P5.35, the outside pressure is 100 kPa, and the cylinder area is A 24.5 cm2. Heat is now added until the
Two tanks are connected by a valve and line. The volumes are both 1 m3 with R-134a at 20C, quality 15% in A and tank B is evacuated. The valve is opened and saturated vapor flows from A into B until the pressures become equal. The process occurs slowly enough that all temperature stay at
Consider the same system as in the previous problem. Let the valve be opened and transfer enough heat to both tanks so all the liquid disappears. Find the necessary heat transfer.
A cylinder having a piston restrained by a linear spring contains 0.5 kg of saturated vapor water at 120C. Heat is transferred to the water, causing the piston to rise, and with a spring constant of 15 kN/m, piston cross-sectional area 0.05 m2, the pressure varies linearly with volume until
A water-filled reactor with volume of 1 m3 is at 20 MPa, 360C and placed inside a containment room. The room is well insulated and initially evacuated. Due to a failure, the reactor ruptures and the water fill the containment room. Find the minimum room volume so the final pressure does not
Assume the same setup as the previous problem, but the room has a volume of 100 m3. Show that the final state is two-phase and find the final pressure by trial and error.
Refrigerant-12 is contained in a piston/cylinder arrangement at 2 MPa, 150C with a mass less piston against the stops, at which point V 0.5 m3. The side above the piston is connected by an open valve to an air line at 10C, 450 kPa. The whole setup now cools to the
A 10-m high open cylinder, Acyl 0.1 m2, contains 20C water above and 2 kg of 20C water below a 198.5-kg thin insulated floating piston. Assume standard g, Po. Now heat is added to the water below the piston so that it expands, pushing the piston up, causing the water
A rigid container has two rooms filled with water, each 1 m3 separated by a wall. Room A has P = 200 kPa with a quality x = 0.80. Room B has P = 2 MPa and T = 400C. The partition wall is removed and the water comes to a uniform state which after a while due to heat transfer has a
A piston/cylinder arrangement of initial volume 0.025 m3 contains saturated water vapor at 180C. The steam now expands in a polytropic process with exponent n 1 to a final pressure of 200 kPa, while it does work against the piston. Determine the heat transfer in this process.
Calculate the heat transfer for the process described in Problem 4.23.
Consider the piston/cylinder arrangement. A frictionless piston is free to move between two sets of stops. When the piston rests on the lower stops, the enclosed volume is 400 L. When the piston reaches the upper stops, the volume is 600L. The cylinder initially contains water at 100 kPa, 20%
Calculate the heat transfer for the process described in Problem 4.30. A cylinder containing 1 kg of ammonia has an externally loaded piston. Initially the ammonia is at 2 MPa, 180C and is now cooled to saturated vapor at 40C, and then further cooled to 20C, at which point
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