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

Locate the state of ammonia at 200 kPa, -10oC. Indicate in both the P-v and the T-v diagrams the location of the nearest states listed in the printed table B.2
Why are most of the compressed liquid or solid regions not included in the printed tables?
Water at 120oC with a quality of 25% has its temperature raised 20oC in a constant volume process. What is the new quality and pressure?
Water at 200 kPa with a quality of 25% has its temperature raised 20oC in a constant pressure process. What is the new quality and volume?
Why is it not typical to find tables for Ar, He, Ne or air like an Appendix B table?
What is the relative (%) change in P if we double the absolute temperature of an ideal gas keeping mass and volume constant? Repeat if we double V having m, T constant.
Calculate the ideal gas constant for argon and hydrogen based on table A.2 and verify the value with Table A.5
How close to ideal gas behavior (find Z) is ammonia at saturated vapor, 100 kPa? How about saturated vapor at 2000 kPa?
Find the volume of 2 kg of ethylene at 270 K, 2500 kPa using Z from Fig. D.1
With Tr = 0.85 and a quality of 0.6 find the compressibility factor using Fig. D.1
Modern extraction techniques can be based on dissolving material in supercritical fluids such as carbon dioxide. How high are pressure and density of carbon dioxide when the pressure and temperature are around the critical point Repeat for ethyl alcohol?
Find the lowest temperature at which it is possible to have water in the liquid phase. At what pressure must the liquid exist?
Water at 27°C can exist in different phases dependent upon the pressure. Give the approximate pressure range in kPa for water being in each one of the three phases vapor, liquid or solid.
What is the lowest temperature in Kelvins for which you can see metal as a liquid if the metal is a. silver b. copper
If density of ice is 920 kg/m3, find the pressure at the bottom of a 1000 m thick ice cap on the North Pole. What is the melting temperature at that pressure?
Dry ice is the name of solid carbon dioxide. How cold must it be at atmospheric (100 kPa) pressure? If it is heated at 100 kPa what eventually happens?
A substance is at 2 MPa, 17°C in a rigid tank. Using only the critical properties can the phase of the mass be determined if the substance is nitrogen, water or propane?
Give the phase for the following states.
Determine the phase of the substance at the given state using Appendix B tables a) Water 100°C, 500 kPa b) Ammonia -10°C, 150 kPa c) R-12 0°C, 350 kPa
Determine whether water at each of the following states is a compressed liquid, a superheated vapor, or a mixture of saturated liquid and vapor. a. P = 10 MPa, v = 0.003 m3/kg b. 1 MPa, 190°C c. 200°C, 0.1 m3/kg d. 10 kPa, 10°C
Determine whether refrigerant R-22 in each of the following states is a compressed liquid, a superheated vapor, or a mixture of saturated liquid and vapor.
Fill out the following table for substance water
Place the four states a-d listed in Problem 3.33 as labeled dots in a sketch of the P-v and T-v diagrams.
Determine the phase and the specific volume for ammonia at these states using the Appendix B table. a. –10oC, 150 kPa b. 20oC, 100 kPa c. 60oC, quality 25%
Give the phase and the specific volume.
Fill out the following table for substance ammonia
Place the two states a-b listed in Problem 3.37 as labeled dots in a sketch of the P-v and T-v diagrams.
Calculate the following specific volumes a. R-134a: 50°C, 80% quality b. Water 4 MPa, 90% quality c. Nitrogen 120 K, 60% quality
Give the phase and the missing property of P, T, v and x. a. R-134a T = -20oC, P = 150 kPa b. R-134a P = 300 kPa, v = 0.072 m3/kg c. CH4 T = 155 K, v = 0.04 m3/kg d. CH4 T = 350 K, v = 0.25 m3/kg
A sealed rigid vessel has volume of 1 m3 and contains 2 kg of water at 100°C. The vessel is now heated. If a safety pressure valve is installed, at what pressure should the valve be set to have a maximum temperature of 200°C?
Saturated liquid water at 60°C is put under pressure to decrease the volume by 1% keeping the temperature constant. To what pressure should it be compressed?
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) 200 oC and b) 100 oC.?
You want a pot of water to boil at 105oC. How heavy a lid should you put on the 15 cm diameter pot when Patm = 101 kPa?
In your refrigerator the working substance evaporates from liquid to vapor at -20 oC inside a pipe around the cold section. Outside (on the back or below) is a black grille inside which the working substance condenses from vapor to liquid at +40 oC. For each location find the pressure and the
In your refrigerator the working substance evaporates from liquid to vapor at -20 oC inside a pipe around the cold section. Outside (on the back or below) is a black grille inside which the working substance condenses from vapor to liquid at +40 oC. For each location find the pressure and the
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.
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 flow rate (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, liquefied 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 10 oC 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 or 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?
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 +40 oC, 0 oC and -40 oC. 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 = 1
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 -20 oC 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 -30 oC 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 -10 oC 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 or c) propane.
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:
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
A tank contains 2 kg of nitrogen at 100 K with a quality of 50%. Through a volume flow meter and valve, 0.5 kg is now removed while the temperature remains constant. Find the final state inside the tank and the volume of nitrogen removed if the valve/meter is located at a. The top of the tank b.
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 P lift = 200 kPa. The system now cools until the pressure reaches 1200 kPa.
Water in a piston/cylinder is at 90°C, 100 kPa, and the piston loading is such that pressure is proportional to volume, P = CV. Heat is now added until the temperature reaches 200°C. Find the final pressure and also the quality if in the two-phase region.
A container with liquid nitrogen at 100 K has a cross sectional area of 0.5 m2. Due to heat transfer, some of the liquid evaporates and in one hour the liquid level drops 30 mm. The vapor leaving the container passes through a valve and a heater and exits at 500 kPa, 260 K. Calculate the volume
A cylinder containing ammonia is fitted with a piston restrained by an external force that is proportional to cylinder volume squared. Initial conditions are 10°C, 90% quality and a volume of 5 L. A valve on the cylinder is opened and additional ammonia flows into the cylinder until the mass
A cylinder/piston arrangement contains water at 105°C, 85% quality with a volume of 1 L. The system is heated, causing the piston to rise and encounter a linear spring as shown in Fig. P3.105. At this point the volume is 1.5 L, piston diameter is 150 mm, and the spring constant is 100 N/mm. The
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. Determine the final temperature and specific volume.
A 1-m3 rigid tank with air at 1 MPa, 400 K is connected to an air line as shown in Fig. P3.107. The valve is opened and air flows into the tank until the pressure reaches 5 MPa, at which point the valve is closed and the temperature inside is 450K. a. What is the mass of air in the tank before and
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). Demonstrate the procedures 1 to 2 and 2 to 3 on both a P–v and T–v
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 290 K. The metal piston has a density of 8000 kg/m3 and the atmospheric pressure is 101 kPa. The pin is now removed, allowing the piston to move
For a certain experiment, R-22 vapor is contained in a sealed glass tube at 20°C. It is desired to know the pressure at this condition, but there is no means of measuring it, since the tube is sealed. However, if the tube is cooled to −20°C small droplets of liquid are observed on the glass

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