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engineering
mechanical engineering
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
Oxygen at 300 kPa, 100°C is in a piston/cylinder arrangement with a volume of 0.1 m3. It is now compressed in a polytropic process with exponent, n = 1.2, to a final temperature of 200°C. Calculate the heat transfer for the process.
A piston/cylinder contains 0.001 m3 air at 300 K, 150 kPa. The air is now compressed in a process in which P V1.25 = C to a final pressure of 600 kPa. Find the work performed by the air and the heat transfer.
Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. How much heat transfer is involved?
A piston/cylinder in a car contains 0.2 L of air at 90 kPa, 20°C, shown in Fig. P5.107. The air is compressed in a quasi-equilibrium polytropic process with polytropic exponent n = 1.25 to a final volume six times smaller. Determine the final pressure, temperature, and the heat transfer for the
A piston/cylinder has nitrogen gas at 750 K and 1500 kPa. Now it is expanded in a polytropic process with n = 1.2 to P = 750 kPa. Find the final temperature, the specific work and specific heat transfer in the process.
A piston/cylinder arrangement of initial volume 0.025 m3 contains saturated water vapor at 180°C. 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.
Air is expanded from 400 kPa, 600 K in a polytropic process to 150 kPa, 400 K in a piston cylinder arrangement. Find the polytropic exponent n and the work and heat transfer per kg air using constant heat capacity from A.5.
A piston/cylinder has 1 kg propane gas at 700 kPa, 40°C. The piston cross-sectional area is 0.5 m2, and the total external force restraining the piston is directly proportional to the cylinder volume squared. Heat is transferred to the propane until its temperature reaches 700°C. Determine the
An air pistol contains compressed air in a small cylinder, shown in Fig. P5.112. Assume that the volume is 1 cm3, pressure is 1 MPa, and the temperature is 27°C when armed. A bullet, m = 15 g, acts as a piston initially held by a pin (trigger); when released, the air expands in an isothermal
A spherical balloon contains 2 kg of R-22 at 0°C, 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 and what
Calculate the heat transfer for the process described in Problem 4.55. Consider a piston cylinder with 0.5 kg of R-134a as saturated vapor at -10°C. 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
Calculate the heat transfer for the process described in Problem 4.55. Consider a piston cylinder with 0.5 kg of R-134a as saturated vapor at -10°C. 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
A crane lifts a load of 450 kg vertically up with a power input of 1 kW. How fast can the crane lift the load?
A computer in a closed room of volume 200 m3 dissipates energy at a rate of 10 kW. The room has 50 kg wood, 25 kg steel and air, with all material at 300 K, 100 kPa. Assuming all the mass heats up uniformly, how long will it take to increase the temperature 10°C?
The rate of heat transfer to the surroundings from a person at rest is about 400 kJ/h. Suppose that the ventilation system fails in an auditorium containing 100 people. Assume the energy goes into the air of volume 1500 m3 initially at 300 K and 101 kPa. Find the rate (degrees per minute) of the
A piston/cylinder of cross sectional area 0.01 m2 maintains constant pressure. It contains 1 kg water with a quality of 5% at 150oC. If we heat so 1 g/s liquid turns into vapor what is the rate of heat transfer needed?
The heaters in a spacecraft suddenly fail. Heat is lost by radiation at the rate of 100 kJ/h and the electric instruments generate 75 kJ/h. Initially, the air is at 100 kPa, 25°C with a volume of 10 m3. How long will it take to reach an air temperature of −20°C?
A steam generating unit heats saturated liquid water at constant pressure of 200 kPa in a piston cylinder. If 1.5 kW of power is added by heat transfer find the rate (kg/s) of saturated vapor that is made.
A small elevator is being designed for a construction site. It is expected to carry four 75-kg workers to the top of a 100-m tall building in less than 2 min. The elevator cage will have a counterweight to balance its mass. What is the smallest size (power) electric motor that can drive this unit?
As fresh poured concrete hardens, the chemical transformation releases energy at a rate of 2 W/kg. Assume the center of a poured layer does not have any heat loss and that it has an average heat capacity of 0.9 kJ/kg K. Find the temperature rise during 1 hour of the hardening (curing) process.
A 100 Watt heater is used to melt 2 kg of solid ice at −10oC to liquid at +5oC at a constant pressure of 150 kPa. a) Find the change in the total volume of the water. b) Find the energy the heater must provide to the water. c) Find the time the process will take assuming uniform T in the
Water is in a piston cylinder maintaining constant P at 700 kPa, quality 90% with a volume of 0.1 m3. A heater is turned on heating the water with 2.5 kW. What is the rate of mass (kg/s) vaporizing?
Ten kilograms of water in a piston/cylinder setup with constant pressure is at 450°C and a volume of 0.633 m3. It is now cooled to 20°C. Show the P–v diagram and find the work and heat transfer for the process.
Consider the system shown in Fig. P5.127. Tank A has a volume of 100 L and contains saturated vapor R-134a at 30°C. 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
Ammonia, NH3, is contained in a sealed rigid tank at 0°C, x = 50% and is then heated to 100°C. Find the final state P2, u2 and the specific work and heat transfer.
A piston/cylinder contains 1 kg of ammonia at 20°C with a volume of 0.1 m3, shown in Fig. P5.129. 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
A piston held by a pin in an insulated cylinder, shown in Fig. P5.130 contains 2 kg water at 100°C, 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
A piston/cylinder arrangement has a linear spring and the outside atmosphere acting on the piston, shown in Fig. P5.131. It contains water at 3 MPa, 400°C 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 to
Consider the piston/cylinder arrangement shown in Fig. P5.132. 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 600 L. The cylinder initially contains water
A piston/cylinder, shown in Fig P5.133, contains R-12 at − 30°C, x = 20%. The volume is 0.2 m3. It is known that Vstop = 0.4 m3, and if the piston sits at the bottom, the spring force balances the other loads on the piston. It is now heated up to 20°C. Find the mass of the fluid and show
A piston/cylinder arrangement B is connected to a 1-m3 tank A by a line and valve, shown in Fig. P5.134. Initially both contain water, with A at 100 kPa, saturated vapor and B at 400°C, 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
A small flexible bag contains 0.1 kg ammonia at –10oC and 300 kPa. The bag material is such that the pressure inside varies linear with volume. The bag is left in the sun with an incident radiation of 75 W, loosing energy with an average 25 W to the ambient ground and air. After a while the bag
Water at 150°C, quality 50% is contained in a cylinder/piston arrangement with initial volume 0.05 m3. The loading of the piston is such that the inside pressure is linear with the square root of volume as P = 100 + CV0.5 kPa. Now heat is transferred to the cylinder to a final pressure of 600 kPa.
A 1 m3 tank containing air at 25oC and 500 kPa is connected through a valve to another tank containing 4 kg of air at 60oC and 200 kPa. Now the valve is opened and the entire system reaches thermal equilibrium with the surroundings at 20oC. Assume constant specific heat at 25oC and determine the
A closed cylinder is divided into two rooms by a frictionless piston held in place by a pin, as shown in Fig. P5.138. Room A has 10 L air at 100 kPa, 30°C, and room B has 300 L saturated water vapor at 30°C. The pin is pulled, releasing the piston, and both rooms come to equilibrium at 30°C and
What is 1 cal in English units, what is 1 Btu in ft-lbf?
Work as F Δx has units of lbf-ft, what is that in Btu? Discuss.
A 2500 lbm car is accelerated from 25 mi/h to 40 mi/h. How much work is that?
A crane use 7000 Btu/h to raise a 200 lbm box 60 ft. How much time does it take?
I have 4 lbm of liquid water at 70 F, 15 psia. I now add 20 Btu of energy at a constant pressure. How hot does it get if it is heated? How fast does it move if it is pushed by a constant horizontal force? How high does it go if it is raised straight up?
Air is heated from 540 R to 640 R at V = C. Find 1q2? What if from 2400 to 2500 R?
Airplane takeoff from an aircraft carrier is assisted by a steam driven piston/cylinder with an average pressure of 200 psia. A 38 500 lbm airplane should be accelerated from zero to a speed of 100 ft/s with 30% of the energy coming from the steam piston. Find the needed piston displacement volume.
A hydraulic hoist raises a 3650 lbm car 6 ft in an auto repair shop. The hydraulic pump has a constant pressure of 100 lbf/in.2 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?
A piston motion moves a 50 lbm hammerhead vertically down 3 ft from rest to a velocity of 150 ft/s in a stamping machine. What is the change in total energy of the hammerhead?
Find the missing properties and give the phase of the substance. a. H2O u = 1000 Btu/lbm, T = 270 F h =? v =? x =? b. H2O u = 450 Btu/lbm, P = 1500 lbf/in.2 T =? x =? v =? c. R-22 T = 30 F, P = 75 lbf/in.2 h =? x =?
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 = 50 F, u = 85 Btu/lbm b. H2O T = 600 F, h = 1322 Btu/lbm c. R-22 P = 150 lbf/in.2, h = 115.5 Btu/lbm
Find the missing properties and give the phase of the substance. a. R-134a T = 140 F, h = 185 Btu/lbm v =? x =? b. NH3 T = 170 F, P = 60 lbf/in.2 u =? v =? x =? c. R-134a T = 100 F, u = 175 Btu/lbm
A cylinder fitted with a frictionless piston contains 4 lbm of superheated refrigerant R-134a vapor at 400 lbf/in.2, 200 F. 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.
Ammonia at 30 F, quality 60% is contained in a rigid 8-ft3 tank. The tank and ammonia are now heated to a final pressure of 150 lbf/in.2. Determine the heat transfer for the process.
Water in a 6-ft3 closed, rigid tank is at 200 F, 90% quality. The tank is then cooled to 20 F. Calculate the heat transfer during the process.
A constant pressure piston/cylinder has 2 lbm water at 1100 F and 2.26 ft3. It is now cooled to occupy 1/10 of the original volume. Find the heat transfer in the process.
A piston/cylinder arrangement has the piston loaded with outside atmospheric pressure and the piston mass to a pressure of 20 lbf/in2. It contains water at 25 F, which is then heated until the water becomes saturated vapor. Find the final temperature and specific work and heat transfer for the
A piston/cylinder arrangement has the piston loaded with outside atmospheric pressure and the piston mass to a pressure of 20 lbf/in2. It contains water at 25 F, which is then heated until the water becomes saturated vapor. Find the final temperature and specific work and heat transfer for the
A piston/cylinder contains 2 lbm of liquid water at 70 F, and 30 lbf/in.2. There is a linear spring mounted on the piston such that when the water is heated the pressure reaches 300 lbf/in.2 with a volume of 4 ft3. Find the final temperature and plot the P-v diagram for the process. Calculate the
A twenty pound-mass of water in a piston/cylinder with constant pressure is at 1100 F and a volume of 22.6 ft3. It is now cooled to 100 F. Show the P–v diagram and find the work and heat transfer for the process.
A vertical cylinder fitted with a piston contains 10 lbm of R-22 at 50 F. 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 120 F, at which point the
A vertical cylinder fitted with a piston contains 10 lbm of R-22 at 50 F. 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 120 F, at which point the
A piston/cylinder contains 2 lbm of water at 70 F with a volume of 0.1 ft3. Initially the piston rests on some stops with the top surface open to the atmosphere, Po, so a pressure of 40 lbf/in.2 is required to lift it. To what temperature should the water be heated to lift the piston? If it is
Two tanks are connected by a valve and line. The volumes are both 35 ft3 with R-134a at 70 F, quality 25% 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 temperatures stay at 70 F
Ammonia, NH3, is contained in a sealed rigid tank at 30 F, x = 50% and is then heated to 200 F. Find the final state P2, u2 and the specific work and heat transfer.
Water at 70 F, 15 lbf/in.2, is brought to 30 lbf/in.2, 2700 F. Find the change in the specific internal energy, using the water table and the ideal gas water table in combination.
A car with mass 3250 lbm drives with 60 mi/h when the brakes are applied to quickly decrease its speed to 20 mi/h. Assume the brake pads are 1 lbm mass with heat capacity of 0.2 Btu/lbm R and the brake discs/drums are 8 lbm steel where both masses are heated uniformly. Find the temperature increase
A 2 lbm steel pot contains 2 lbm liquid water at 60 F. It is now put on the stove where it is heated to the boiling point of the water. Neglect any air being heated and find the total amount of energy needed.
A copper block of volume 60 in.3 is heat treated at 900 F and now cooled in a 3-ft3 oil bath initially at 70 F. Assuming no heat transfer with the surroundings, what is the final temperature?
An engine consists of a 200 lbm cast iron block with a 40 lbm aluminum head, 40 lbm steel parts, 10 lbm engine oil and 12 lbm glycerine (antifreeze). Everything begins at 40 F and as the engine starts, it absorbs a net of 7000 Btu before it reaches a steady uniform temperature. We want to know how
A cylinder with a piston restrained by a linear spring contains 4 lbm of carbon dioxide at 70 lbf/in.2, 750 F. It is cooled to 75 F, at which point the pressure is 45 lbf/in.2. Calculate the heat transfer for the process.
An insulated cylinder is divided into two parts of 10 ft3 each by an initially locked piston. Side A has air at 2 atm, 600 R and side B has air at 10 atm, 2000 R as shown in Fig. P5.95. The piston is now unlocked so it is free to move, and it conducts heat so the air comes to a uniform temperature
A 65 gallons rigid tank contains methane gas at 900 R, 200 psia. It is now cooled down to 540 R. Assume ideal gas and find the needed heat transfer.
Air in a piston/cylinder at 30 lbf/in.2, 1080 R. It is expanded in a constant-pressure process to twice the initial volume (state 2). The piston is then locked with a pin, and heats is transferred to a final temperature of 1080 R. Find P, T, and h for states 2 and 3, and find the work and heat
A 30-ft high cylinder, cross-sectional area 1 ft2, has a mass less piston at the bottom with water at 70 F on top of it. Air at 540 R, volume 10 ft3 under the piston is heated so that the piston moves up, spilling the water out over the side. Find the total heat transfer to the air when all the
An air pistol contains compressed air in a small cylinder, as shown in Fig. P5.112. Assume that the volume is 1 in.3, pressure is 10 atm, and the temperature is 80 F when armed. A bullet, m = 0.04 lbm, acts as a piston initially held by a pin (trigger); when released, the air expands in an
A piston/cylinder in a car contains 12 in.3 of air at 13 lbf/in.2, 68 F. The air is compressed in a quasi-equilibrium polytropic process with polytropic exponent n = 1.25 to a final volume six times smaller. Determine the final pressure, temperature, and the heat transfer for the process.
Oxygen at 50 lbf/in.2, 200 F is in a piston/cylinder arrangement with a volume of 4 ft3. It is now compressed in a polytropic process with exponent, n = 1.2, to a final temperature of 400 F. Calculate the heat transfer for the process. Continuity: m2 = m1; Energy: E2 - E1 = m (u2 - u1) = 1Q2 - 1W2
Helium gas expands from 20 psia, 600 R and 9 ft3 to 15 psia in a polytropic process with n = 1.667. How much heat transfer is involved?
A cylinder fitted with a frictionless piston contains R-134a at 100 F, 80% quality, at which point the volume is 3 Gal. The external force on the piston is now varied in such a manner that the R-134a slowly expands in a polytropic process to 50 lbf/in.2, 80 F. Calculate the work and the heat
A piston cylinder contains argon at 20 lbf/in.2, 60 F, and the volume is 4 ft3. The gas is compressed in a polytropic process to 100 lbf/in.2, 550 F. Calculate the heat transfer during the process.
A small elevator is being designed for a construction site. It is expected to carry four 150 lbm workers to the top of a 300-ft-tall building in less than 2 min. The elevator cage will have a counterweight to balance its mass. What is the smallest size (power) electric motor that can drive this
Water is in a piston cylinder maintaining constant P at 330 F, quality 90% with a volume of 4 ft3. A heater is turned on heating the water with 10 000 Btu/h. What is the elapsed time to vaporize all the liquid?
A computer in a closed room of volume 5000 ft3 dissipates energy at a rate of 10 hp. The room has 100 lbm of wood, 50 lbm of steel and air, with all material at 540 R, 1 atm. Assuming all the mass heats up uniformly how long time will it take to increase the temperature 20 F?
A closed cylinder is divided into two rooms by a frictionless piston held in place by a pin, as shown in Fig. P5. 138. Room A has 0.3 ft3 air at 14.7 lbf/in.2, 90 F, and room B has 10 ft3 saturated water vapor at 90 F. The pin is pulled, releasing the piston and both rooms come to equilibrium at 90
A mass flow rate into a control volume requires a normal velocity component. Why?
A temperature difference drives a heat transfer. Does a similar concept apply to m.
Can a steady state device have boundary work?
Can you say something about changes in m. and V. through a steady flow device?
How does a nozzle or spray head generate kinetic energy?
Liquid water at 15oC flows out of a nozzle straight up 15 m. What is nozzle Vexit?
What is the difference between a nozzle flow and a throttle process?
If you throttle a saturated liquid what happens to the fluid state? If it is an ideal gas?
R-134a at 30oC, 800 kPa is throttled so it becomes cold at –10oC. What is exit P?
Air at 500 K, 500 kPa is expanded to 100 kPa in two steady flow cases. Case one is a throttle and case two is a turbine. Which has the highest exit T? Why?
A turbine at the bottom of a dam has a flow of liquid water through it. How does that produce power? Which terms in the energy equation are important?
A windmill takes a fraction of the wind kinetic energy out as power on a shaft. In what manner does the temperature and wind velocity influence the power? Hint: write the power as mass flow rate times specific work.
If you compress air the temperature goes up, why? When the hot air, high P flows in long pipes it eventually cools to ambient T. How does that change the flow?
In a boiler you vaporize some liquid water at 100 kPa flowing at 1 m/s. What is the velocity of the saturated vapor at 100 kPa if the pipe size is the same? Can the flow then be constant P?
A mixing chamber has all flows at the same P, neglecting losses. A heat exchanger has separate flows exchanging energy, but they do not mix. Why have both kinds?
In a co-flowing (same direction) heat exchanger 1 kg/s air at 500 K flows into one channel and 2 kg/s air flows into the neighboring channel at 300 K. If it is infinitely long what is the exit temperature? Sketch the variation of T in the two flows.
Air at 600 K flows with 3 kg/s into a heat exchanger and out at 100oC. How much (kg/s) water coming in at 100 kPa, 20oC can the air heat to the boiling point?
Steam at 500 kPa, 300oC is used to heat cold water at 15oC to 75oC for domestic hot water supply. How much steam per kg liquid water is needed if the steam should not condense?
Air at 20 m/s, 260 K, 75 kPa with 5 kg/s flows into a jet engine and it flows out at 500 m/s, 800 K, 75 kPa. What is the change (power) in flow of kinetic energy?
An initially empty cylinder is filled with air from 20oC, 100 kPa until it is full. Assuming no heat transfer is the final temperature larger, equal to or smaller than 20oC? Does the final T depend on the size of the cylinder?
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