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physics
thermodynamics
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
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.
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?
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) 200oC b) 100oC.
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 of
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.
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.
The piston/cylinder shown in Fig. P4.48 contains carbon dioxide at 300 kPa, 100°C 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 200°C. Determine the work done during the process.
A gas initially at 1 MPa, 500°C 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.
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?
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 work does it give out?
Air goes through a polytropic process from 125 kPa, 325 K to 300 kPa and 500 K. Find the polytropic exponent n and the specific work in the process.
A piston cylinder contains 0.1 kg air at 100 kPa, 400 K which goes through a polytropic compression process with n = 1.3 to a pressure of 300 kPa. How much work has the air done in the process?
A balloon behaves so the pressure is P = C2 V1/3, C2 = 100 kPa/m. The balloon is blown up with air from a starting volume of 1 m3 to a volume of 3 m3. Find the final mass of air assuming it is at 25oC and the work done by the air.
A balloon behaves such that the pressure inside is proportional to the diameter squared. It contains 2 kg of ammonia at 0°C, 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 done
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 done during the process.
Consider the process described in Problem 3.98. With 1 kg water as a control mass, determine the boundary work during the process. A spring-loaded piston/cylinder contains water at 500°C, 3 MPa. The setup is such that pressure is proportional to volume, P = CV. It is now cooled until the water
Find the work for Problem 3.106.Refrigerant-12 in a piston/cylinder arrangement is initially at 50°C, x = 1. It is then expanded in a process so that P = Cv−1 to a pressure of 100 kPa. Find the final temperature and specific volume.
A piston/cylinder contains water at 500°C, 3 MPa. It is cooled in a polytropic process to 200°C, 1 MPa. Find the polytropic exponent and the specific work in the 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.
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?
A cylinder containing 1 kg of ammonia has an externally loaded piston. Initially the ammonia is at 2 MPa, 180°C and is now cooled to saturated vapor at 40°C, and then further cooled to 20°C, at which point the quality is 50%. Find the total work for the process, assuming a piecewise linear
A piston/cylinder arrangement shown in Fig. P4.61 initially contains air at 150 kPa, 400°C. The setup is allowed to cool to the ambient temperature of 20°C. 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
A piston cylinder has 1.5 kg of air at 300 K and 150 kPa. It is now heated up in a two step process. First constant volume to 1000 K (state 2) then followed by a constant pressure process to 1500 K, state 3. Find the final volume and the work in the process.
A piston/cylinder assembly (Fig. P4.63) has 1 kg of R-134a at state 1 with 110°C, 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
The refrigerant R-22 is contained in a piston/cylinder as shown in Fig. P4.64, where the volume is 11 L when the piston hits the stops. The initial state is −30°C, 150 kPa with a volume of 10 L. This system is brought indoors and warms up to 15°C. a. Is the piston at the stops in the final
A piston/cylinder contains 50 kg of water at 200 kPa with a volume of 0.1 m3. Stops in the cylinder restricts the enclosed volume to 0.5 m3, similar to the setup in Problem 4.7. The water is now heated to 200°C. Find the final pressure, volume and the work done by the water.
Find the work for Problem 3.108. Ammonia in a piston/cylinder arrangement is at 700 kPa, 80°C. 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 −10°C (state 3). Show the processes 1 to 2 and 2 to 3 on
A piston/cylinder contains 1 kg of liquid water at 20°C and 300 kPa. Initially the piston floats, similar to the setup in Problem 4.64, 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 volume and
10 kg of water in a piston cylinder arrangement exists as saturated liquid/vapor at 100 kPa, with a quality of 50%. It is now heated so the volume triples. The mass of the piston is such that a cylinder pressure of 200 kPa will float it. a) Find the final temperature and volume of the water. b)
Find the work in Problem 3.43. Ammonia at 10oC with a mass of 10 kg is in a piston cylinder arrangement with an initial volume of 1 m3. The piston initially resting on the stops has a mass such that a pressure of 900 kPa will float it. The ammonia is now slowly heated to 50oC. Find the work in the
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 piston cylinder setup similar to Problem 4.68 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 300°C. Find the final pressure, volume and the work, 1W2.
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 copper wire of diameter 2 mm is 10 m long and stretched out between two posts. The normal stress (pressure) σ = E(L – Lo)/Lo , depends on the length L versus the unstretched length Lo and Young’s modulus E = 1.1 × 106 kPa. The force is F = Aσ and measured to be 110 N. How much Longer is
A film of ethanol at 20°C has a surface tension of 22.3 mN/m and is maintained on a wire frame as shown in Fig. P4.73. 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.
Assume a balloon material with a constant surface tension of S = 2 N/m. What is the work required to stretch a spherical balloon up to a radius of r = 0.5 m? Neglect any effect from atmospheric pressure.
A soap bubble has a surface tension of S = 3 × 10-4 N/cm as it sits flat on a rigid ring of diameter 5 cm. You now blow on the film to create a half sphere surface of diameter 5 cm. How much work was done?
Assume we fill a spherical balloon from a bottle of helium gas. The helium gas provides work ∫ PdV that stretches the balloon material ∫ S dA and pushes back the atmosphere ∫ Po dV. Write the incremental balance for dWhelium = dWstretch + dWatm to establish the connection between the helium
A sheet of rubber is stretched out over a ring of radius 0.25 m. I pour liquid water at 20oC on it so the rubber forms a half sphere (cup). Neglect the rubber mass and find the surface tension near the ring?
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. a) The combustion chamber and combustion gas side of the heat transfer area. b) The furnace as a whole, including the hot- and cold-air ducts and chimney.
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?
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 refrigerator b. 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) The space heater. b) Room c) The space heater and the room together
An escalator raises a 100 kg bucket of sand 10 m in 1 minute. Determine the rate of work done during the process.
A car uses 25 hp to drive at a horizontal level at constant 100 km/h. What is the traction force between the tires and the road?
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 work out?
A crane lifts a bucket of cement with a total mass of 450 kg vertically up with a constant velocity of 2 m/s. Find the rate of work needed to do that.
Consider the car with the rolling resistance as in problem 4.27. How fast can it drive using 30 hp?
Consider the car with the air drag force as in problem 4.29. How fast can it drive using 30 hp?
Consider a 1400 kg car having the rolling resistance as in problem 4.27 and air resistance as in problem 4.29. How fast can it drive using 30 hp?
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.
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?
A current of 10 amp runs through a resistor with a resistance of 15 ohms. Find the rate of work that heats the resistor up.
A pressure of 650 kPa pushes a piston of diameter 0.25 m with V = 5 m/s. What is the volume displacement rate, the force and the transmitted power?
Assume the process in Problem 4.37 takes place with a constant rate of change in volume over 2 minutes. Show the power (rate of work) as a function of time.
Air at a constant pressure in a piston cylinder is at 300 kPa, 300 K and a volume of 0.1 m3. It is heated to 600 K over 30 seconds in a process with constant piston velocity. Find the power delivered to the piston.
A torque of 650 Nm rotates a shaft of diameter 0.25 m with ω = 50 rad/s. What are the shaft surface speed and the transmitted power?
The sun shines on a 150 m2 road surface so it is at 45°C. Below the 5 cm thick asphalt, average conductivity of 0.06 W/m K, is a layer of compacted rubbles at a temperature of 15°C. 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 15°C 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 15°C.
A water-heater is covered up with insulation boards over a total surface area of 3 m2. The inside board surface is at 75°C and the outside surface is at 20°C 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 W?
You drive a car on a winter day with the atmospheric air at −15°C and you keep the outside front windshield surface temperature at +2°C 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 loos through
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 15 W/m K and that a maximum of 5°C difference
What is 1 cal in SI units and what is the name given to 1 N-m?
A pot of water is boiling on a stove supplying 325 W to the water. What is the rate of mass (kg/s) vaporizing assuming a constant pressure process?
A spring loaded piston/cylinder contains 1.5 kg of air at 27C and 160 kPa. It is now heated to 900 K in a process where the pressure is linear in volume to a final volume of twice the initial volume. Plot the process in a P-v diagram and find the work and heat transfer.
Air in a piston/cylinder at 200 kPa, 600 K, is expanded in a constant-pressure process to twice the initial volume (state 2), shown in Fig. P5.101. The piston is then locked with a pin and heat is transferred to a final temperature of 600 K. Find P, T, and h for states 2 and 3, and find the work
A vertical piston/cylinder has a linear spring mounted as shown so at zero cylinder volume a balancing pressure inside is zero. The cylinder contains 0.25 kg air at 500 kPa, 27oC. Heat is now added so the volume doubles. a) Show the process path in a P-V diagram b) Find the final pressure and
A piston cylinder contains 0.1 kg air at 300 K and 100 kPa. The air is now slowly compressed in an isothermal (T = C) process to a final pressure of 250 kPa. Show the process in a P-V diagram and find both the work and heat transfer in the process.
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.
A constant mass goes through a process where 100 W of heat transfer comes in and 100 W of work leaves. Does the mass change state?
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
A piston/cylinder setup contains argon gas at 140 kPa, 10°C, and the volume is 100 L. The gas is compressed in a polytropic process to 700 kPa, 280°C. Calculate the heat transfer during the process.
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?
I have 2 kg of liquid water at 20oC, 100 kPa. I now add 20 kJ 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?
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?
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