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physics
thermodynamics

Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions

Saturated water vapor has a maximum for u and h at around 235oC. Is it similar for other substances?
A rigid insulated tank is separated into two rooms by a stiff plate. Room A of 0.5 m3 contains air at 250 kPa, 300 K and room B of 1 m3 has air at 150 kPa, 1000 K. The plate is removed and the air comes to a uniform state without any heat transfer. Find the final pressure and temperature.
A rigid container has 2 kg of carbon dioxide gas at 100 kPa, 1200 K that is heated to 1400 K. Solve for the heat transfer using a. the heat capacity from Table A.5 and b. properties from Table A.8
Do the previous problem for nitrogen, N2, gas. A rigid container has 2 kg of carbon dioxide gas at 100 kPa, 1200 K that is heated to 1400 K. Solve for the heat transfer using a. the heat capacity from Table A.5 and b. properties from Table A.8
A 10-m high cylinder, cross-sectional area 0.1 m2, has a massless piston at the bottom with water at 20°C on top of it, shown in Fig. P5.93. Air at 300 K, volume 0.3 m3, under the piston is heated so that the piston moves up, spilling the water out over the side. Find the total heat transfer to
Find the heat transfer in Problem 4.43. 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.
An insulated cylinder is divided into two parts of 1 m3 each by an initially locked piston, as shown in Fig. P5.95. Side A has air at 200 kPa, 300 K, and side B has air at 1.0 MPa, 1000 K. The piston is now unlocked so it is free to move, and it conducts heat so the air comes to a uniform
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 temperature of the air and the heat transfer input.
A cylinder with a piston restrained by a linear spring contains 2 kg of carbon dioxide at 500 kPa, 400°C. It is cooled to 40°C, at which point the pressure is 300 kPa. Calculate the heat transfer for the process.
Water at 100 kPa, 400 K is heated electrically adding 700 kJ/kg in a constant pressure process. Find the final temperature using a) The water tables B.1 b) The ideal gas tables A.8 c) Constant specific heat from A.5
A piston/cylinder has 0.5 kg air at 2000 kPa, 1000 K as shown. The cylinder has stops so Vmin = 0.03 m3. The air now cools to 400 K by heat transfer to the ambient. Find the final volume and pressure of the air (does it hit the stops?) and the work and heat transfer in the process.
The air conditioner in a house or a car has a cooler that brings atmospheric air from 30oC to 10oC both states at 101 kPa. If the flow rate is 0.5 kg/s find the rate of heat transfer.
A flow of liquid glycerine flows around an engine, cooling it as it absorbs energy. The glycerine enters the engine at 60oC and receives 9 kW of heat transfer. What is the required mass flow rate if the glycerine should come out at maximum 95oC?
What is the difference between a nozzle flow and a throttle process?
A cryogenic fluid as liquid nitrogen at 90 K, 400 kPa flows into a probe used in cryogenic surgery. In the return line the nitrogen is then at 160 K, 400 kPa. Find the specific heat transfer to the nitrogen. If the return line has a cross sectional area 100 times larger than the inlet line what is
A small stream with 20oC water runs out over a cliff creating a 100 m tall waterfall. Estimate the downstream temperature when you neglect the horizontal flow velocities upstream and downstream from the waterfall. How fast was the water dropping just before it splashed into the pool at the bottom
A small water pump is used in an irrigation system. The pump takes water in from a river at 10oC, 100 kPa at a rate of 5 kg/s. The exit line enters a pipe that goes up to an elevation 20 m above the pump and river, where the water runs into an open channel. Assume the process is adiabatic and that
A steam pipe for a 300-m tall building receives superheated steam at 200 kPa at ground level. At the top floor the pressure is 125 kPa and the heat loss in the pipe is 110 kJ/kg. What should the inlet temperature be so that no water will condense inside the pipe?
The main waterline into a tall building has a pressure of 600 kPa at 5 m below ground level. A pump brings the pressure up so the water can be delivered at 200 kPa at the top floor 150 m above ground level. Assume a flow rate of 10 kg/s liquid water at 10oC and neglect any difference in kinetic
Consider a water pump that receives liquid water at 15oC, 100 kPa and delivers it to a same diameter short pipe having a nozzle with exit diameter of 1 cm (0.01 m) to the atmosphere 100 kPa. Neglect the kinetic energy in the pipes and assume constant u for the water. Find the exit velocity and the
A cutting tool uses a nozzle that generates a high speed jet of liquid water. Assume an exit velocity of 1000 m/s of 20oC liquid water with a jet diameter of 2 mm (0.002 m). How much mass flow rate is this? What size (power) pump is needed to generate this from a steady supply of 20oC liquid water
A pipe flows water at 15oC from one building to another. In the winter time the pipe loses an estimated 500 W of heat transfer. What is the minimum required mass flow rate that will ensure that the water does not freeze (i.e. reach 0oC)?
A steam turbine receives water at 15 MPa, 600°C at a rate of 100 kg/s, shown in Fig. P6.78. In the middle section 20 kg/s is withdrawn at 2 MPa, 350°C, and the rest exits the turbine at 75 kPa, and 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine
A steam turbine receives steam from two boilers. One flow is 5 kg/s at 3 MPa, 700°C and the other flow is 15 kg/s at 800 kPa, 500°C. The exit state is 10 kPa, with a quality of 96%. Find the total power out of the adiabatic turbine.
If you throttle a saturated liquid what happens to the fluid state? If it is an ideal gas?
Two steady flows of air enters a control volume, shown in Fig. P6.80. One is 0.025 kg/s flow at 350 kPa, 150°C, state 1, and the other enters at 450 kPa, 15°C, both flows with low velocity. A single flow of air exits at 100 kPa, −40°C, state 3. The control volume rejects 1 kW heat to the
A large expansion engine has two low velocity flows of water entering. High pressure steam enters at point 1 with 2.0 kg/s at 2 MPa, 500°C and 0.5 kg/s cooling water at 120 kPa, 30°C enters at point 2. A single flow exits at point 3 with 150 kPa, 80% quality, through a 0.15 m diameter exhaust
Cogeneration is often used where a steam supply is needed for industrial process energy. Assume a supply of 5 kg/s steam at 0.5 MPa is needed. Rather than generating this from a pump and boiler, the setup in Fig. P6.82 is used so the supply is extracted from the high-pressure turbine. Find the
A compressor receives 0.1 kg/s R-134a at 150 kPa, -10oC and delivers it at 1000 kPa, 40oC. The power input is measured to be 3 kW. The compressor has heat transfer to air at 100 kPa coming in at 20oC and leaving at 25oC. How much is the mass flow rate of air?
A condenser (heat exchanger) brings 1 kg/s water flow at 10 kPa from 300°C to saturated liquid at 10 kPa, as shown in Fig. P6.84. The cooling is done by lake water at 20°C that returns to the lake at 30°C. For an insulated condenser, find the flow rate of cooling water.
A cooler in an air conditioner brings 0.5 kg/s air at 35oC to 5oC, both at 101 kPa and it then mix the output with a flow of 0.25 kg/s air at 20oC, 101 kPa sending the combined flow into a duct. Find the total heat transfer in the cooler and the temperature in the duct flow.
A heat exchanger, shown in Fig. P6.86, is used to cool an air flow from 800 K to 360 K, both states at 1 MPa. The coolant is a water flow at 15°C, 0.1 MPa. If the water leaves as saturated vapor, find the ratio of the flow rates
A superheater brings 2.5 kg/s saturated water vapor at 2 MPa to 450oC. The energy is provided by hot air at 1200 K flowing outside the steam tube in the opposite direction as the water, which is a counter flowing heat exchanger. Find the smallest possible mass flow rate of the air so the air exit
An automotive radiator has glycerine at 95oC enter and return at 55oC as shown in Fig. P6.88. Air flows in at 20oC and leaves at 25oC. If the radiator should transfer 25 kW what is the mass flow rate of the glycerine and what is the volume flow rate of air in at 100 kPa?
A two fluid heat exchanger has 2 kg/s liquid ammonia at 20oC, 1003 kPa entering state 3 and exiting at state 4. It is heated by a flow of 1 kg/s nitrogen at 1500 K, state 1, leaving at 600 K, state 2 similar to Fig. P6.86. Find the total rate of heat transfer inside the heat exchanger. Sketch the
R-134a at 30oC, 800 kPa is throttled so it becomes cold at –10oC. What is exit P?
A copper wire has been heat treated to 1000 K and is now pulled into a cooling chamber that has 1.5 kg/s air coming in at 20oC; the air leaves the other end at 60oC. If the wire moves 0.25 kg/s copper, how hot is the copper as it comes out?
An open feedwater heater in a powerplant heats 4 kg/s water at 45oC, 100 kPa by mixing it with steam from the turbine at 100 kPa, 250oC. Assume the exit flow is saturated liquid at the given pressure and find the mass flow rate from the turbine.
A desuperheater mixes superheated water vapor with liquid water in a ratio that produces saturated water vapor as output without any external heat transfer. A flow of 0.5 kg/s superheated vapor at 5 MPa, 400°C and a flow of liquid water at 5 MPa, 40°C enter a desuperheater. If saturated water
Two air flows are combined to a single flow. Flow one is 1 m3/s at 20oC and the other is 2 m3/s at 200oC both at 100 kPa. They mix without any heat transfer to produce an exit flow at 100 kPa. Neglect kinetic energies and find the exit temperature and volume flow rate.
A mixing chamber with heat transfer receives 2 kg/s of R-22 at 1 MPa, 40°C in one line and 1 kg/s of R-22 at 30°C, quality 50% in a line with a valve. The outgoing flow is at 1 MPa, 60°C. Find the rate of heat transfer to the mixing chamber.
Two flows are mixed to form a single flow. Flow at state 1 is 1.5 kg/s water at 400 kPa, 200oC and flow at state 2 is 500 kPa, 100oC. Which mass flow rate at state 2 will produce an exit T3 = 150oC if the exit pressure is kept at 300 kPa?
An insulated mixing chamber receives 2 kg/s R-134a at 1 MPa, 100°C in a line with low velocity. Another line with R-134a as saturated liquid 60°C flows through a valve to the mixing chamber at 1 MPa after the valve. The exit flow is saturated vapor at 1 MPa flowing at 20 m/s. Find the flow rate
To keep a jet engine cool some intake air bypasses the combustion chamber. Assume 2 kg/s hot air at 2000 K, 500 kPa is mixed with 1.5 kg/s air 500 K, 500 kPa without any external heat transfer. Find the exit temperature by using constant heat capacity from Table A.5.
To keep a jet engine cool some intake air bypasses the combustion chamber. Assume 2 kg/s hot air at 2000 K, 500 kPa is mixed with 1.5 kg/s air 500 K, 500 kPa without any external heat transfer. Find the exit temperature by using values from Table A.7.
The following data are for a simple steam power plant as shown in Fig. P6.99.State 6 has x6 = 0.92, and velocity of 200 m/s. The rate of steam flow is 25 kg/s, with 300 kW power input to the pump. Piping diameters are 200 mm from steam generator to the turbine and 75 mm from the condenser to the
A mass flow rate into a control volume requires a normal velocity component. Why?
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?
For the same steam power plant as shown in Fig. P6.99 and Problem 6.99, assume the cooling water comes from a lake at 15°C and is returned at 25°C. Determine the rate of heat transfer in the condenser and the mass flow rate of cooling water from the lake.
For the same steam power plant as shown in Fig. P6.99 and Problem 6.99, determine the rate of heat transfer in the economizer, which is a low temperature heat exchanger. Find also the rate of heat transfer needed in the steam generator.
A somewhat simplified flow diagram for a nuclear power plant shown in Fig. 1.4 is given in Fig. P6.102. Mass flow rates and the various states in the cycle are shown in the accompanying table. The cycle includes a number of heaters in which heat is transferred from steam, taken out of the turbine
Consider the powerplant as described in the previous problem. a.Determine the quality of the steam leaving the reactor. b.What is the power to the pump that feeds water to the reactor?
A gas turbine setup to produce power during peak demand is shown in Fig. P6.104. The turbine provides power to the air compressor and the electric generator. If the electric generator should provide 5 MW what is the needed air flow at state 1 and the combustion heat transfer between state 2 and 3?
A proposal is made to use a geothermal supply of hot water to operate a steam turbine, as shown in Fig. P6.105. The high-pressure water at 1.5 MPa, 180°C, is throttled into a flash evaporator chamber, which forms liquid and vapor at a lower pressure of 400 kPa. The liquid is discarded while the
A R-12 heat pump cycle shown in Fig. P6.71 has a R-12 flow rate of 0.05 kg/s with 4 kW into the compressor. The following data are givenCalculate the heat transfer from the compressor, the heat transfer from the R-12 in the condenser and the heat transfer to the R-12 in the evaporator.
A modern jet engine has a temperature after combustion of about 1500 K at 3200 kPa as it enters the turbine setion, see state 3 Fig. P.6.107. The compressor inlet is 80 kPa, 260 K state 1 and outlet state 2 is 3300 kPa, 780 K; the turbine outlet state 4 into the nozzle is 400 kPa, 900 K and nozzle
A 1-m3, 40-kg rigid steel tank contains air at 500 kPa, and both tank and air are at 20°C. The tank is connected to a line flowing air at 2 MPa, 20°C. The valve is opened, allowing air to flow into the tank until the pressure reaches 1.5 MPa and is then closed. Assume the air and tank are always
An evacuated 150-L tank is connected to a line flowing air at room temperature, 25°C, and 8 MPa pressure. The valve is opened allowing air to flow into the tank until the pressure inside is 6 MPa. At this point the valve is closed. This filling process occurs rapidly and is essentially adiabatic.
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?
An initially empty bottle is filled with water from a line at 0.8 MPa, 350oC. Assume no heat transfer and that the bottle is closed when the pressure reaches the line pressure. If the final mass is 0.75 kg find the final temperature and the volume of the bottle.
A 25-L tank, shown in Fig. P6.111, that is initially evacuated is connected by a valve to an air supply line flowing air at 20°C, 800 kPa. The valve is opened, and air flows into the tank until the pressure reaches 600 kPa.Determine the final temperature and mass inside the tank, assuming the
Helium in a steel tank is at 250 kPa, 300 K with a volume of 0.1 m3. It is used to fill a balloon. When the tank pressure drops to 150 kPa the flow of helium stops by itself. If all the helium still is at 300 K how big a balloon did I get? Assume the pressure in the balloon varies linearly with
A rigid 100-L tank contains air at 1 MPa, 200°C. A valve on the tank is now opened and air flows out until the pressure drops to 100 kPa. During this process, heat is transferred from a heat source at 200°C, such that when the valve is closed, the temperature inside the tank is 50°C. What is the
A 1-m3 tank contains ammonia at 150 kPa, 25°C. The tank is attached to a line flowing ammonia at 1200 kPa, 60°C. The valve is opened, and mass flows in until the tank is half full of liquid, by volume at 25°C. Calculate the heat transferred from the tank during this process.
An empty cannister of volume 1 L is filled with R-134a from a line flowing saturated liquid R-134a at 0oC. The filling is done quickly so it is adiabatic. How much mass of R-134a is there after filling? The cannister is placed on a storage shelf where it slowly heats up to room temperature 20oC.
A piston cylinder contains 1 kg water at 20oC with a constant load on the piston such that the pressure is 250 kPa. A nozzle in a line to the cylinder is opened to enable a flow to the outside atmosphere at 100 kPa. The process continues to half the mass has flowed out and there is no heat
A 200 liter tank initially contains water at 100 kPa and a quality of 1%. Heat is transferred to the water thereby raising its pressure and temperature. At a pressure of 2 MPa a safety valve opens and saturated vapor at 2 MPa flows out. The process continues, maintaining 2 MPa inside until the
A 100-L rigid tank contains carbon dioxide gas at 1 MPa, 300 K. A valve is cracked open, and carbon dioxide escapes slowly until the tank pressure has dropped to 500 kPa. At this point the valve is closed. The gas remaining inside the tank may be assumed to have undergone a polytropic expansion,
A nitrogen line, 300 K and 0.5 MPa, shown in Fig. P6.119, is connected to a turbine that exhausts to a closed initially empty tank of 50 m3. The turbine operates to a tank pressure of 0.5 MPa, at which point the temperature is 250 K. Assuming the entire process is adiabatic, determine the turbine
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? write the power as mass flow rate times specific work.
A 2 m tall cylinder has a small hole in the bottom. It is filled with liquid water 1 m high, on top of which is 1 m high air column at atmospheric pressure of 100 kPa. As the liquid water near the hole has a higher P than 100 kPa it runs out. Assume a slow process with constant T. Will the flow
A 2-m3 insulated vessel, shown in Fig. P6.121, contains saturated vapor steam at 4 MPa. A valve on the top of the tank is opened, and steam is allowed to escape. During the process any liquid formed collects at the bottom of the vessel, so that only saturated vapor exits. Calculate the total mass
A 750-L rigid tank, shown in Fig. P6.122, initially contains water at 250°C, 50% liquid and 50% vapor, by volume. A valve at the bottom of the tank is opened, and liquid is slowly withdrawn. Heat transfer takes place such that the temperature remains constant. Find the amount of heat transfer
Consider the previous problem but let the line and valve be located in the top of the tank. Now saturated vapor is slowly withdrawn while heat transfer keeps the temperature inside constant. Find the heat transfer required to reach a state where half the original mass is withdrawn.
Two kg of water at 500 kPa, 20oC is heated in a constant pressure process to 1700oC. Find the best estimate for the heat transfer.
In a glass factory a 2 m wide sheet of glass at 1500 K comes out of the final rollers that fix the thickness at 5 mm with a speed of 0.5 m/s. Cooling air in the amount of 20 kg/s comes in at 17oC from a slot 2 m wide and flows parallel with the glass. Suppose this setup is very long so the glass
Assume a setup similar to the previous problem but the air flows in the opposite direction of the glass, it comes in where the glass goes out. How much air flow at 17oC is required to cool the glass to 450 K assuming the air must be at least 120 K cooler than the glass at any location?
Three air flows all at 200 kPa are connected to the same exit duct and mix without external heat transfer. Flow one has 1 kg/s at 400 K, flow two has 3 kg/s at 290 K and flow three has 2 kg/s at 700 K. Neglect kinetic energies and find the volume flow rate in the exit flow.
Consider the power plant as described in Problem 6.102. a. Determine the temperature of the water leaving the intermediate pressure heater, T13, assuming no heat transfer to the surroundings. b. Determine the pump work, between states 13 and 16.
Consider the powerplant as described in Problem 6.102. a. Find the power removed in the condenser by the cooling water (not shown). b. Find the power to the condensate pump. c. Do the energy terms balance for the low pressure heater or is there a heat transfer not shown?
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?
A 500-L insulated tank contains air at 40°C, 2 MPa. A valve on the tank is opened, and air escapes until half the original mass is gone, at which point the valve is closed. What is the pressure inside then?
A steam engine based on a turbine is shown in Fig. P6.131. The boiler tank has a volume of 100 L and initially contains saturated liquid with a very small amount of vapor at 100 kPa. Heat is now added by the burner, and the pressure regulator does not open before the boiler pressure reaches 700
An insulated spring-loaded piston/cylinder, shown in Fig. P6.132, is connected to an air line flowing air at 600 kPa, 700 K by a valve. Initially the cylinder is empty and the spring force is zero. The valve is then opened until the cylinder pressure reaches 300 kPa. By noting that u2 = uline +
A mass-loaded piston/cylinder, shown in Fig. P6.133, containing air is at 300 kPa, 17°C with a volume of 0.25 m3, while at the stops V = 1 m3. An air line, 500 kPa, 600 K, is connected by a valve that is then opened until a final inside pressure of 400 kPa is reached, at which point T = 350 K.
A 2-m3 storage tank contains 95% liquid and 5% vapor by volume of liquified natural gas (LNG) at 160 K, as shown in Fig. P6.65. It may be assumed that LNG has the same properties as pure methane. Heat is transferred to the tank and saturated vapor at 160 K flows into the a steady flow heater which
Liquid water at 80oC flows with 0.2 kg/s inside a square duct, side 2 cm insulated with a 1 cm thick layer of foam k = 0.1 W/m K. If the outside foam surface is at 25oC how much has the water temperature dropped for 10 m length of duct? Neglect the duct material and any corner effects (A = 4sL).
A counter-flowing heat exchanger conserves energy by heating cold outside fresh air at 10oC with the outgoing combustion gas (air) at 100oC. Assume both flows are 1 kg/s and the temperature difference between the flows at any point is 50oC. What is the incoming fresh air temperature after the heat
Saturated liquid water at 1000 kPa flows at 2 kg/s inside a 10 cm outer diameter steel pipe and outside of the pipe is a flow of hot gases at 1000 K with a convection coefficient of h = 150 W/m2 K. Neglect any ΔT in the steel and any inside convection h and find the length of pipe needed to bring
A flow of 1000 K, 100 kPa air with 0.5 kg/s in a furnace flows over a steel plate of surface temperature 400 K. The flow is such that the convective heat transfer coefficient is h = 125 W/m2 K. How much of a surface area does the air have to flow over to exit with a temperature of 800 K? How about
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?
A temperature difference drives a heat transfer. Does a similar concept apply to
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?
A cylinder has 0.1 kg air at 25oC, 200 kPa with a 5 kg piston on top. A valve at the bottom is opened to let the air out and the piston drops 0.25 m towards the bottom. What is the work involved in this process? What happens to the energy?
Air at 35°C, 105 kPa, flows in a 100 mm × 150 mm rectangular duct in a heating system. The volumetric flow rate is 0.015 m3/s. What is the velocity of the air flowing in the duct and what is the mass flow rate?

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