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physics
thermodynamics
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
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.
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
Water is heated from 100 kPa, 20oC to 1000 kPa, 200oC. In one case pressure is raised at T = C, then T is raised at P = C. In a second case the opposite order is done. Does that make a difference for 1Q2 and 1W2?
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 the
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 with an incident radiation of 75 W, loosing energy with an average 25 W to the ambient ground and air. After a while the
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
Two kg water at 120oC with a quality of 25% has its temperature raised 20oC in a constant volume process. What are the new quality and specific internal energy?
Two kg water at 200 kPa with a quality of 25% has its temperature raised 20oC in a constant pressure process. What is the change in enthalpy?
You heat a gas 10 K at P = C. Which one in table A.5 requires most energy? Why?
Air is heated from 300 to 350 K at V = C. Find 1q2? What if from 1300 to 1350 K?
A mass of 3 kg nitrogen gas at 2000 K, V = C, cools with 500 W. What is dT/dt?
A drag force on a car, with frontal area A = 2 m2, driving at 80 km/h in air at 20oC is Fd = 0.225 A ρairV2. How much power is needed and what is the traction force?
In a complete cycle what is the net change in energy and in volume?
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?
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?
Airplane takeoff from an aircraft carrier is assisted by a steam driven piston/cylinder device with an average pressure of 1250 kPa. A 17500 kg airplane should be accelerated from zero to a speed of 30 m/s with 30% of the energy coming from the steam piston. Find the needed piston displacement
Solve Problem 5.22, 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 1200 kg car accelerates from zero to 100 km/h over a distance of 400 m. The road at the end of the 400 m is at 10 m higher elevation. What is the total increase in the car kinetic and potential energy?
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
The rolling resistance of a car depends on its weight as: F = 0.006 mg. How far will a car of 1200 kg roll if the gear is put in neutral when it drives at 90 km/h on a level road without air resistance?
A mass of 5 kg is tied to an elastic cord, 5 m long, and dropped from a tall bridge. Assume the cord, once straight, acts as a spring with k = 100 N/m. Find the velocity of the mass when the cord is straight (5 m down). At what level does the mass come to rest after bouncing up and down?
Find the missing properties. a. H2O T = 250°C, v = 0.02 m3/kg P = ? u = ? b. N2 T = 120 K, P = 0.8 MPa x = ? h = ? c. H2O T = −2°C, P = 100 kPa u = ? v = ? d. R-134a P = 200 kPa, v = 0.12 m3/kg u = ? T = ?
Find the missing properties of T, P, v, u, h and x if applicable and plot the location of the three states as points in the T-v and the P-v diagrams a. Water at 5000 kPa, u = 800 kJ/kg b. Water at 5000 kPa, v = 0.06 m3/kg c. R-134a at 35oC, v = 0.01 m3/kg
Why do we write ΔE or E2 – E1 whereas we write 1Q2 and 1W2?
Find the missing properties and give the phase of the ammonia, NH3. a. T = 65oC, P = 600 kPa u = ? v = ? b. T = 20oC, P = 100 kPa u = ? v = ? x = ? c. T = 50oC, v = 0.1185 m3/kg u = ? P = ? x = ?
Find the phase and missing properties of P, T, v, u, and x. a. Water at 5000 kPa, u = 1000 kJ/kg (Table B.1 reference) b. R-134a at 20oC, u = 300 kJ/kg c. Nitrogen at 250 K, 200 kPa Show also the three states as labeled dots in a T-v diagram with correct position relative to the two-phase region.
Find the missing properties and give the phase of the substance a. H2O T = 120°C, v = 0.5 m3/kg u = ? P = ? x = ? b. H2O T = 100°C, P = 10 MPa u = ? x = ? v = ? c. N2 T = 200 K, P = 200 kPa v = ? u = ? d. NH3 T = 100°C, v = 0.1 m3/kg P = ? x = ? e. N2 T = 100 K, x = 0.75 v = ? u = ?
Find the missing properties among (T, P, v, u, h and x if applicable) and give the phase of the substance and indicate the states relative to the two-phase region in both a T-v and a P-v diagram. a. R-12 P = 500 kPa, h = 230 kJ/kg b. R-22 T = 10oC, u = 200 kJ/kg c. R-134a T = 40oC, h = 400 kJ/kg
Saturated liquid water at 20oC is compressed to a higher pressure with constant temperature. Find the changes in u and h from the initial state when the final pressure is a) 500 kPa. b) 2000 kPa. c) 20 000 kPa
A 100-L rigid tank contains nitrogen (N2) at 900 K, 3 MPa. The tank is now cooled to 100 K. What are the work and heat transfer for this process?
A rigid container has 0.75 kg water at 300oC, 1200 kPa. The water is now cooled to a final pressure of 300 kPa. Find the final temperature, the work and the heat transfer in the process.
A cylinder fitted with a frictionless piston contains 2 kg of superheated refrigerant R-134a vapor at 350 kPa, 100oC. 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 0°C, 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.
Water in a 150-L closed, rigid tank is at 100°C, 90% quality. The tank is then cooled to −10°C. Calculate the heat transfer during the process.
When you wind a spring up in a toy or stretch a rubber band what happens in terms of work, energy and heat transfer? Later when they are released, what happens then?
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 and the amount of 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 20°C. Calculate the heat transfer from the water.
A 10-L rigid tank contains R-22 at −10°C, 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 40°C. What was the heat transfer to or from the tank during this process?
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 a maximum of 0.5 m3. The water is now heated until the piston reaches the stops. Find the necessary heat transfer.
A constant pressure piston/cylinder assembly contains 0.2 kg water as saturated vapor at 400 kPa. It is now cooled so the water occupies half the original volume. Find the heat transfer in the process.
Two kg water at 120oC with a quality of 25% has its temperature raised 20oC in a constant volume process as in Fig. P5.45. What are the heat transfer and work in the process?
A 25 kg mass moves with 25 m/s. Now a brake system brings the mass to a complete stop with a constant deceleration over a period of 5 seconds. The brake energy is absorbed by 0.5 kg water initially at 20oC, 100 kPa. Assume the mass is at constant P and T. Find the energy the brake removes from the
An insulated cylinder fitted with a piston contains R-12 at 25°C 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 temperature,
A water-filled reactor with volume of 1 m3 is at 20 MPa, 360°C and placed inside a containment room as shown in Fig. P5.48. The room is well insulated and initially evacuated. Due to a failure, the reactor ruptures and the water fills the containment room. Find the minimum room volume so the final
A piston/cylinder arrangement contains water of quality x = 0.7 in the initial volume of 0.1 m3, where the piston applies a constant pressure of 200 kPa. The system is now heated to a final temperature of 200°C. Determine the work and the heat transfer in the process.
Explain in words what happens with the energy terms for the stone in Example 5.2. What would happen if it were a bouncing ball falling to a hard surface?
A piston/cylinder arrangement has the piston loaded with outside atmospheric pressure and the piston mass to a pressure of 150 kPa, shown in Fig. P5.50. It contains water at −2°C, which is then heated until the water becomes saturated vapor. Find the final temperature and specific work and heat
A piston/cylinder assembly 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 1 MPa with a volume of 0.1 m3. Find the final temperature and the heat transfer in the process.
A closed steel bottle contains ammonia at −20°C, 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 opens.
Two kg water at 200 kPa with a quality of 25% has its temperature raised 20oC in a constant pressure process. What are the heat transfer and work in the process?
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 1-L capsule of water at 700 kPa, 150°C is placed in a larger insulated and otherwise evacuated vessel. The capsule breaks and its contents fill the entire volume. If the final pressure should not exceed 125 kPa, what should the vessel volume be?
Superheated refrigerant R-134a at 20°C, 0.5 MPa is cooled in a piston/cylinder arrangement at constant temperature to a final two-phase state with quality of 50%. The refrigerant mass is 5 kg, and during this process 500 kJ of heat is removed. Find the initial and final volumes and the necessary
A cylinder having a piston restrained by a linear spring (of spring constant 15 kN/m) contains 0.5 kg of saturated vapor water at 120°C, as shown in Fig. P5.57. Heat is transferred to the water, causing the piston to rise. If the piston cross-sectional area is 0.05 m2, and the pressure varies
A rigid tank is divided into two rooms by a membrane, both containing water, shown in Fig. P5.58. 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, 400°C. The membrane now ruptures and heat transfer takes place so the water comes to a uniform state at 100°C.
A 10-m high open cylinder, Acyl = 0.1 m2, contains 20°C water above and 2 kg of 20°C water below a 198.5-kg thin insulated floating piston, shown in Fig. P5.59. 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 on
Make a list of at least 5 systems that store energy, explaining which form of energy.
Assume the same setup as in Problem 5.48, 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.
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, as in Fig. 4.68. Find the final temperature and the heat
Two tanks are connected by a valve and line as shown in Fig. P5.62. The volumes are both 1 m3 with R-134a at 20°C, 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
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 vertical cylinder fitted with a piston contains 5 kg of R-22 at 10°C, shown in Fig. P5.64. 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
Find the heat transfer in Problem 4.67. 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
Refrigerant-12 is contained in a piston/cylinder arrangement at 2 MPa, 150°C with a massless 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 10°C, 450 kPa, shown in Fig. P5.66. The whole setup now cools to the
Find the heat transfer in Problem 4.114. A piston/cylinder (Fig. P4.114) contains 1 kg of water at 20°C with a volume of 0.1 m3. Initially the piston rests on some stops with the top surface open to the atmosphere, Po and a mass so a water pressure of 400 kPa will lift it. To what temperature
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 = 400°C. The partition wall is removed and the water comes to a uniform state, which after a while due to heat transfer has a temperature of
The cylinder volume below the constant loaded piston has two compartments A and B filled with water. A has 0.5 kg at 200 kPa, 150oC and B has 400 kPa with a quality of 50% and a volume of 0.1 m3. The valve is opened and heat is transferred so the water comes to a uniform state with a total volume
A 1200 kg car is accelerated from 30 to 50 km/h in 5 s. How much work is that? If you continue from 50 to 70 km/h in 5 s is that the same?
A rigid tank A of volume 0.6 m3 contains 3 kg water at 120oC and the rigid tank B is 0.4 m3 with water at 600 kPa, 200oC. They are connected to a piston cylinder initially empty with closed valves. The pressure in the cylinder should be 800 kPa to float the piston. Now the valves are slowly opened
Calculate the heat transfer for the process described in Problem 4.60.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%.
Calculate the heat transfer for the process described in Problem 4.70. A piston cylinder setup similar to Problem 4.24 contains 0.1 kg saturated liquid and vapor water at 100 kPa with quality 25%. The mass of the piston is such that a pressure of 500 kPa will float it. The water is heated to
A cylinder/piston arrangement contains 5 kg of water at 100°C with x = 20% and the piston, mP = 75 kg, resting on some stops, similar to Fig. P5.73. The outside pressure is 100 kPa, and the cylinder area is A = 24.5 cm2. Heat is now added until the water reaches a saturated vapor state. Find the
Because a hot water supply must also heat some pipe mass as it is turned on so it does not come out hot right away. Assume 80oC liquid water at 100 kPa is cooled to 45oC as it heats 15 kg of copper pipe from 20 to 45oC. How much mass (kg) of water is needed?
A house is being designed to use a thick concrete floor mass as thermal storage material for solar energy heating. The concrete is 30 cm thick and the area exposed to the sun during the daytime is 4 m × 6 m. It is expected that this mass will undergo an average temperature rise of about 3°C
A copper block of volume 1 L is heat treated at 500°C and now cooled in a 200-L oil bath initially at 20°C, shown in Fig. P5.76. Assuming no heat transfer with the surroundings, what is the final temperature?
A 1 kg steel pot contains 1 kg liquid water both at 15oC. 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 car with mass 1275 kg drives at 60 km/h when the brakes are applied quickly to decrease its speed to 20 km/h. Assume the brake pads are 0.5 kg mass with heat capacity of 1.1 kJ/kg K and the brake discs/drums are 4.0 kg steel. Further assume both masses are heated uniformly. Find the temperature
Saturated, x=1%, water at 25°C is contained in a hollow spherical aluminum vessel with inside diameter of 0.5 m and a 1-cm thick wall. The vessel is heated until the water inside is saturated vapor. Considering the vessel and water together as a control mass, calculate the heat transfer for the
A crane use 2 kW to raise a 100 kg box 20 m. How much time does it take?
A 25 kg steel tank initially at –10oC is filled up with 100 kg of milk (assume properties as water) at 30oC. The milk and the steel come to a uniform temperature of + 5oC in a storage room. How much heat transfer is needed for this process?
An engine consists of a 100 kg cast iron block with a 20 kg aluminum head, 20 kg steel parts, 5 kg engine oil and 6 kg glycerine (antifreeze). Everything begins at 5oC and as the engine starts we want to know how hot it becomes if it absorbs a net of 7000 kJ before it reaches a steady uniform
Use the ideal gas air table A.7 to evaluate the heat capacity Cp at 300 K as a slope of the curve h(T) by Δh/ΔT. How much larger is it at 1000 K and 1500 K.
We want to find the change in u for carbon dioxide between 600 K and 1200 K. a) Find it from a constant Cvo from table A.5 b) Find it from a Cvo evaluated from equation in A.6 at the average T. c) Find it from the values of u listed in table A.8
We want to find the change in u for oxygen gas between 600 K and 1200 K.a) Find it from a constant Cvo from table A.5b) Find it from a Cvo evaluated from equation in A.6 at the average T.c) Find it from the values of u listed in table A.8
Water at 20°C, 100 kPa, is brought to 200 kPa, 1500°C. Find the change in the specific internal energy, using the water table and the ideal gas water table in combination.
We want to find the increase in temperature of nitrogen gas at 1200 K when the specific internal energy is increased with 40 kJ/kg. a) Find it from a constant Cvo from table A.5 b) Find it from a Cvo evaluated from equation in A.6 at 1200 K. c) Find it from the values of u listed in table A.8
For an application the change in enthalpy of carbon dioxide from 30 to 1500°C at 100 kPa is needed. Consider the following methods and indicate the most accurate one. a. Constant specific heat, value from Table A.5. b. Constant specific heat, value at average temperature from the equation in Table
An ideal gas is heated from 500 to 1500 K. Find the change in enthalpy using constant specific heat from Table A.5 (room temperature value) and discuss the accuracy of the result if the gas isa. Argon.b. Oxygen.c. Carbon dioxide
A 250 L rigid tank contains methane at 500 K, 1500 kPa. It is now cooled down to 300 K. Find the mass of methane and the heat transfer using a) ideal gas and b) the methane tables.
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