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physics
thermodynamics
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
A water storage tank contains liquid and vapor in equilibrium at 110°C. The distance from the bottom of the tank to the liquid level is 8 m. What is the absolute pressure at the bottom of the tank?
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 and the temperature if the water is cooled to occupy half the original volume?
Two tanks are connected as shown in Fig. P3.49, both containing water. Tank A is at 200 kPa, v = 0.5 m3/kg, VA = 1 m3 and tank B contains 3.5 kg at 0.5 MPa, 400°C. The valve is now opened and the two come to a uniform state. Find the final specific volume.
Some tools should be cleaned in water at a least 150oC. How high a P is needed?
Determine the mass of methane gas stored in a 2 m3 tank at −30°C, 3 MPa. Estimate the percent error in the mass determination if the ideal gas model is used.
Saturated water vapor at 60°C has its pressure decreased to increase the volume by 10% keeping the temperature constant. To what pressure should it be expanded?
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 and the temperature if the water is heated to occupy twice the original volume?
A boiler feed pump delivers 0.05 m3/s of water at 240°C, 20 MPa. What is the mass flowrate (kg/s)? What would be the percent error if the properties of saturated liquid at 240°C were used in the calculation? What if the properties of saturated liquid at 20 MPa were used?
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 volume.
A storage tank holds methane at 120 K, with a quality of 25 %, and it warms up by 5°C per hour due to a failure in the refrigeration system. How long time will it take before the methane becomes single phase and what is the pressure then?
A glass jar is filled with saturated water at 500 kPa, quality 25%, and a tight lid is put on. Now it is cooled to −10°C. What is the mass fraction of solid at this temperature?
Saturated (liquid + vapor) ammonia at 60°C is contained in a rigid steel tank. It is used in an experiment, where it should pass through the critical point when the system is heated. What should the initial mass fraction of liquid be?
A steel tank contains 6 kg of propane (liquid + vapor) at 20°C with a volume of 0.015 m3. The tank is now slowly heated. Will the liquid level inside eventually rise to the top or drop to the bottom of the tank? What if the initial mass is 1 kg instead of 6 kg?
A 400-m3 storage tank is being constructed to hold LNG, liquified natural gas, which may be assumed to be essentially pure methane. If the tank is to contain 90% liquid and 10% vapor, by volume, at 100 kPa, what mass of LNG (kg) will the tank hold? What is the quality in the tank?
A sealed rigid vessel of 2 m3 contains a saturated mixture of liquid and vapor R-134a at 10°C. If it is heated to 50°C, the liquid phase disappears. Find the pressure at 50°C and the initial mass of the liquid.
A pressure cooker (closed tank) contains water at 100°C with the liquid volume being 1/10 of the vapor volume. It is heated until the pressure reaches 2.0 MPa. Find the final temperature. Has the final state more or less vapor than the initial state?
A pressure cooker has the lid screwed on tight. A small opening with A = 5 mm2 is covered with a petcock that can be lifted to let steam escape. How much mass should the petcock have to allow boiling at 120oC with an outside atmosphere at 101.3 kPa?
Ammonia at 10oC and mass 0.1 kg is in a piston cylinder 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. Now the ammonia is slowly heated to 50oC. Find the final pressure and volume.
A cylinder fitted with a frictionless piston contains butane at 25°C, 500 kPa. Can the butane reasonably be assumed to behave as an ideal gas at this state?
A spherical helium balloon of 10 m in diameter is at ambient T and P, 15oC and 100 kPa. How much helium does it contain? It can lift a total mass that equals the mass of displaced atmospheric air. How much mass of the balloon fabric and cage can then be lifted?
Is it reasonable to assume that at the given states the substance behaves as an ideal gas?
A 1-m3 tank is filled with a gas at room temperature 20°C and pressure 100 kPa. How much mass is there if the gas is a) Air. b) Neon. c) Propane?
A rigid tank of 1 m3 contains nitrogen gas at 600 kPa, 400 K. By mistake someone lets 0.5 kg flow out. If the final temperature is 375 K what is then the final pressure?
A cylindrical gas tank 1 m long, inside diameter of 20 cm, is evacuated and then filled with carbon dioxide gas at 25°C. To what pressure should it be charged if there should be 1.2 kg of carbon dioxide?
If I have 1 L ammonia at room pressure and temperature (100 kPa, 20oC) how much mass is that?
A glass is cleaned in 45oC hot water and placed on the table bottom up. The room air at 20oC that was trapped in the glass gets heated up to 40oC and some of it leaks out so the net resulting pressure inside is 2 kPa above ambient pressure of 101 kPa. Now the glass and the air inside cools down to
A hollow metal sphere of 150-mm inside diameter is weighed on a precision beam balance when evacuated and again after being filled to 875 kPa with an unknown gas. The difference in mass is 0.0025 kg, and the temperature is 25°C. What is the gas, assuming it is a pure substance listed in Table A.5?
A vacuum pump is used to evacuate a chamber where some specimens are dried at 50°C. The pump rate of volume displacement is 0.5 m3/s with an inlet pressure of 0.1 kPa and temperature 50°C. How much water vapor has been removed over a 30-min period?
A 1 m3 rigid tank has propane at 100 kPa, 300 K and connected by a valve to another tank of 0.5 m3 with propane at 250 kPa, 400 K. The valve is opened and the two tanks come to a uniform state at 325 K. What is the final pressure?
Verify the accuracy of the ideal gas model when it is used to calculate specific volume for saturated water vapor as shown in Fig. 3.9. Do the calculation for 10 kPa and 1 MPa.
Assume we have 3 states of saturated vapor R-134a at +40oC, 0oC and -40oC. Calculate the specific volume at the set of temperatures and corresponding saturated pressure assuming ideal gas behavior. Find the percent relative error = 100(v - vg)/vg with vg from the saturated R-134a table.
Do Problem 3.75, but for the substance R-12.
Do Problem 3.75, but for the substance ammonia.
Air in an automobile tire is initially at −10°C and 190 kPa. After the automobile is driven awhile, the temperature gets up to 10°C. Find the new pressure. You must make one assumption on your own.
An initially deflated and flat balloon is connected by a valve to a 12 m3 storage tank containing helium gas at 2 MPa and ambient temperature, 20°C. The valve is opened and the balloon is inflated at constant pressure, Po = 100 kPa, equal to ambient pressure, until it becomes spherical at D1 =
How much is the change in liquid specific volume for water at 20oC as you move up from state i towards state j in figure 3.12 reaching 15 000 kPa?
Argon is kept in a rigid 5 m3 tank at −30°C, 3 MPa. Determine the mass using the compressibility factor. What is the error (%) if the ideal gas model is used?
What is the percent error in specific volume if the ideal gas model is used to represent the behavior of superheated ammonia at 40°C, 500 kPa? What if the generalized compressibility chart, Fig. D.1, is used instead?
A new refrigerant R-125 is stored as a liquid at -20oC with a small amount of vapor. For a total of 1.5 kg R-125 find the pressure and the volume.
Many substances that normally do not mix well do so easily under supercritical pressures. A mass of 125 kg ethylene at 7.5 MPa, 296.5 K is stored for such a process. How much volume does it occupy?
Carbon dioxide at 330 K is pumped at a very high pressure, 10 MPa, into an oil-well. As it penetrates the rock/oil the oil viscosity is lowered so it flows out easily. For this process we need to know the density of the carbon dioxide being pumped.
To plan a commercial refrigeration system using R-123 we would like to know how much more volume saturated vapor R-123 occupies per kg at -30oC compared to the saturated liquid state.
A bottle with a volume of 0.1 m3 contains butane with a quality of 75% and a temperature of 300 K. Estimate the total butane mass in the bottle using the generalized compressibility chart.
Refrigerant R-32 is at -10oC with a quality of 15%. Find the pressure and specific volume.
A mass of 2 kg of acetylene is in a 0.045 m3 rigid container at a pressure of 4.3 MPa. Use the generalized charts to estimate the temperature. (This becomes trial and error).
A substance is at 2 MPa, 17°C in a 0.25-m3 rigid tank. Estimate the mass from the compressibility factor if the substance is a) Air. b) Butane. c) Propane.
For water at 100 kPa with a quality of 10% find the volume fraction of vapor.
Determine the quality (if saturated) or temperature (if superheated) of the following substances at the given two states:
Fill out the following table for substance ammonia: Discuss.
Find the phase, quality x if applicable and the missing property P or T.
Find the phase, quality x if applicable and the missing property P or T. Discuss.
Give the phase and the missing properties of P, T, v and x.
Give the phase and the missing properties of P, T, v and x. These may be a little more difficult if the appendix tables are used instead of the software.
A 5 m long vertical tube of cross sectional area 200 cm2 is placed in a water fountain. It is filled with 15oC water, the bottom closed and the top open to the 100 kPa atmosphere. a) How much water is in the tube? b) What is the pressure at the bottom of the tube
Consider two tanks, A and B, connected by a valve, as shown in Fig. P3.97. Each has a volume of 200 L and tank A has R-12 at 25°C, 10% liquid and 90% vapor by volume, while tank B is evacuated. The valve is now opened and saturated vapor flows from A to B until the pressure in B has reached that
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 becomes saturated vapor. Sketch the P-v diagram and find the final pressure.
A 1 m3 rigid tank has air at 1500 kPa and ambient 300 K connected by a valve to a piston cylinder. The piston of area 0.1 m2 requires 250 kPa below it to float. The valve is opened and the piston moves slowly 2 m up and the valve is closed. During the process air temperature remains at 300 K. What
The electric company charges the customers per kW-hour. What is that in SI units?
Helium gas expands from 125 kPa, 350 K and 0.25 m3 to 100 kPa in a polytropic process with n = 1.667. Is the work positive, negative or zero?
The black grille on the back of a refrigerator has a surface temperature of 35°C with a total surface area of 1 m2. Heat transfer to the room air at 20°C takes place with an average convective heat transfer coefficient of 15 W/m2 K. How much energy can be removed during 15 minutes of operation?
Due to a faulty door contact the small light bulb (25 W) inside a refrigerator is kept on and limited insulation lets 50 W of energy from the outside seep into the refrigerated space. How much of a temperature difference to the ambient at 20°C must the refrigerator have in its heat exchanger with
The brake shoe and steel drum on a car continuously absorbs 25 W as the car slows down. Assume a total outside surface area of 0.1 m2 with a convective heat transfer coefficient of 10 W/m2 K to the air at 20°C. How hot does the outside brake and drum surface become when steady conditions are
A wall surface on a house is at 30°C with an emissivity of ε = 0.7. The surrounding ambient to the house is at 15°C, average emissivity of 0.9. Find the rate of radiation energy from each of those surfaces per unit area.
A log of burning wood in the fireplace has a surface temperature of 450°C. Assume the emissivity is 1 (perfect black body) and find the radiant emission of energy per unit surface area.
A radiant heat lamp is a rod, 0.5 m long and 0.5 cm in diameter, through which 400 W of electric energy is deposited. Assume the surface has an emissivity of 0.9 and neglect incoming radiation. What will the rod surface temperature be?
A vertical cylinder (Fig. P4.106) has a 61.18-kg piston locked with a pin trapping 10 L of R-22 at 10°C, 90% quality inside. Atmospheric pressure is 100 kPa, and the cylinder cross-sectional area is 0.006 m2. The pin is removed, allowing the piston to move and come to rest with a final temperature
A piston/cylinder contains butane, C4H10, at 300°C, 100 kPa with a volume of 0.02 m3. The gas is now compressed slowly in an isothermal process to 300 kPa. a. Show that it is reasonable to assume that butane behaves as an ideal gas during this process. b. Determine the work done by the butane
A cylinder fitted with a piston contains propane gas at 100 kPa, 300 K with a volume of 0.2 m3. The gas is now slowly compressed according to the relation PV1.1 = constant to a final temperature of 340 K. Justify the use of the ideal gas model. Find the final pressure and the work done during the
The gas space above the water in a closed storage tank contains nitrogen at 25°C, 100 kPa. Total tank volume is 4 m3, and there is 500 kg of water at 25°C. An additional 500 kg water is now forced into the tank. Assuming constant temperature throughout, find the final pressure of the nitrogen and
An ideal gas goes through an expansion process where the volume doubles. Which process will lead to the larger work output: an isothermal process or a polytropic process with n = 1.25?
Two kilograms of water is contained in a piston/cylinder (Fig. P4.110) with a massless piston loaded with a linear spring and the outside atmosphere. Initially the spring force is zero and P1 = Po = 100 kPa with a volume of 0.2 m3. If the piston just hits the upper stops the volume is 0.8 m3 and T
A cylinder having an initial volume of 3 m3 contains 0.1 kg of water at 40°C. The water is then compressed in an isothermal quasi-equilibrium process until it has a quality of 50%. Calculate the work done in the process splitting it into two steps. Assume the water vapor is an ideal gas during the
Air at 200 kPa, 30°C is contained in a cylinder/piston arrangement with initial volume 0.1 m3. The inside pressure balances ambient pressure of 100 kPa plus an externally imposed force that is proportional to V0.5. Now heat is transferred to the system to a final pressure of 225 kPa. Find the
A spring-loaded piston/cylinder arrangement contains R-134a at 20°C, 24% quality with a volume 50 L. The setup is heated and thus expands, moving the piston. It is noted that when the last drop of liquid disappears the temperature is 40°C. The heating is stopped when T = 130°C. Verify the final
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 should the water be heated to lift the
Two springs with same spring constant are installed in a massless piston/cylinder with the outside air at 100 kPa. If the piston is at the bottom, both springs are relaxed and the second spring comes in contact with the piston at V = 2 m3. The cylinder (Fig. P4.115) contains ammonia initially at
Find the work for Problem 3.101. A piston/cylinder arrangement is loaded with a linear spring and the outside atmosphere. It contains water at 5 MPa, 400°C with the volume being 0.1 m3. If the piston is at the bottom, the spring exerts a force such that Plift = 200 kPa. The system now cools until
Show how the polytropic exponent n can be evaluated if you know the end state properties, (P1, V2) and (P2, V2).
A drag force on an object moving through a medium (like a car through air or a submarine through water) is Fd = 0.225 A ρV2. Verify the unit becomes Newton.
A force of 1.2 kN moves a truck with 60 km/h up a hill. What is the power?
Electric power is volts times ampere (P = V i). When a car battery at 12 V is charged with 6 amp for 3 hours how much energy is delivered?
Torque and energy and work have the same units (N m). Explain the difference.
Find the rate of conduction heat transfer through a 1.5 cm thick hardwood board, k = 0.16 W/m K, with a temperature difference between the two sides of 20oC.
A 2 m2 window has a surface temperature of 15oC and the outside wind is blowing air at 2oC across it with a convection heat transfer coefficient of h = 125 W/m2K. What is the total heat transfer loss?
A radiant heating lamp has a surface temperature of 1000 K with ε = 0.8. How large a surface area is needed to provide 250 W of radiation heat transfer?
A car engine is rated at 160 hp. What is the power in SI units?
A piston of mass 2 kg is lowered 0.5 m in the standard gravitational field. Find the required force and work involved in the process.
An escalator raises a 100 kg bucket of sand 10 m in 1 minute. Determine the total amount of work done during the process.
A bulldozer pushes 500 kg of dirt 100 m with a force of 1500 N. It then lifts the dirt 3 m up to put it in a dump truck. How much work did it do in each situation?
A hydraulic cylinder has a piston of cross sectional area 25 cm2 and a fluid pressure of 2 MPa. If the piston is moved 0.25 m how much work is done?
Two hydraulic cylinders maintain a pressure of 1200 kPa. One has a cross sectional area of 0.01 m2 the other 0.03 m2. To deliver a work of 1 kJ to the piston how large a displacement (V) and piston motion H is needed for each cylinder? Neglect Patm.
A linear spring, F = ks(x − x0), with spring constant ks = 500 N/m, is stretched until it is 100 mm longer. Find the required force and work input.
A nonlinear spring has the force versus displacement relation of F = kns(x − x0)n. If the spring end is moved to x1 from the relaxed state, determine the formula for the required work.
The rolling resistance of a car depends on its weight as: F = 0.006 mg. How long will a car of 1400 kg drive for a work input of 25 kJ?
A car drives for half an hour at constant speed and uses 30 MJ over a distance of 40 km. What was the traction force to the road and its speed?
The air drag force on a car is 0.225 A ρV2. Assume air at 290 K, 100 kPa and a car frontal area of 4 m2 driving at 90 km/h. How much energy is used to overcome the air drag driving for 30 minutes?
A 1200 hp dragster engine has a drive shaft rotating at 2000 RPM. How much torque is on the shaft?
Two hydraulic piston/cylinders are connected with a line. The master cylinder has an area of 5 cm2 creating a pressure of 1000 kPa. The slave cylinder has an area of 3 cm2. If 25 J is the work input to the master cylinder what is the force and displacement of each piston and the work out put of the
A constant pressure piston cylinder 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 work in the process.
A steam radiator in a room at 25°C has saturated water vapor at 110 kPa flowing through it, when the inlet and exit valves are closed. What is the pressure and the quality of the water, when it has cooled to 25oC? How much work is done?
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