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physics
thermodynamics
Fundamentals of Thermodynamics 6th edition Richard E. Sonntag, Claus Borgnakke, Gordon J. Van Wylen - Solutions
Separate the list P, F, V, v, ρ, T, a, m, L, t and V into intensive, extensive and non-properties.
Two vertical cylindrical storage tanks are full of liquid water, density 1000 kg/m3, the top open to the atmoshere. One is 10 m tall, 2 m diameter, the other is 2.5 m tall with diameter 4 m. What is the total force from the bottom of each tank to the water and what is the pressure at the bottom of
Blue manometer fluid of density 925 kg/m3 shows a column height difference of 6 cm vacuum with one end attached to a pipe and the other open to P0 = 101 kPa. What is the absolute pressure in the pipe?
The absolute pressure in a tank is 85 kPa and the local ambient absolute pressure is 97 kPa. If a U-tube with mercury, density 13550 kg/m3, is attached to the tank to measure the vacuum, what column height difference would it show?
The pressure gauge on an air tank shows 75 kPa when the diver is 10 m down in the ocean. At what depth will the gauge pressure be zero? What does that mean?
A submarine maintains 101 kPa inside it and it dives 240 m down in the ocean having an average density of 1030 kg/m3. What is the pressure difference between the inside and the outside of the submarine hull?
A barometer to measure absolute pressure shows a mercury column height of 725 mm. The temperature is such that the density of the mercury is 13 550 kg/m3. Find the ambient pressure.
An absolute pressure gauge attached to a steel cylinder shows 135 kPa. We want to attach a manometer using liquid water a day that Patm = 101 kPa. How high a fluid level difference must we plan for?
The difference in height between the columns of a manometer is 200 mm with a fluid of density 900 kg/m3. What is the pressure difference? What is the height difference if the same pressure difference is measured using mercury, density 13600 kg/ m3, as manometer fluid?
An exploration submarine should be able to go 4000 m down in the ocean. If the ocean density is 1020 kg/m3 what is the maximum pressure on the submarine hull?
Assume we use a pressure gauge to measure the air pressure at street level and at the roof of a tall building. If the pressure difference can be determined with an accuracy of 1 mbar (0.001 bar) what uncertainty in the height estimate does that corresponds to?
An escalator brings four people of total 300 kg, 25 m up in a building. Explain what happens with respect to energy transfer and stored energy.
A U-tube manometer filled with water, density 1000 kg/m3, shows a height difference of 25 cm. What is the gauge pressure? If the right branch is tilted to make an angle of 30° with the horizontal, as shown in Fig. P2.70, what should the length of the column in the tilted tube be relative to the
A barometer measures 760 mmHg at street level and 735 mmHg on top of a building. How tall is the building if we assume air density of 1.15 kg/m3?
A piece of experimental apparatus is located where g = 9.5 m/s2 and the temperature is 5°C. An air flow inside the apparatus is determined by measuring the pressure drop across an orifice with a mercury manometer (see Problem 2.77 for density) showing a height difference of 200 mm. What is the
Two piston/cylinder arrangements, A and B, have their gas chambers connected by a pipe. Cross-sectional areas are AA = 75 cm2 and AB = 25 cm2 with the piston mass in A being mA = 25 kg. Outside pressure is 100 kPa and standard gravitation. Find the mass mB so that none of the pistons have to rest
Two hydraulic piston/cylinders are of same size and setup as in Problem 2.73, but with negligible piston masses. A single point force of 250 N presses down on piston A. Find the needed extra force on piston B so that none of the pistons have to move.
A pipe flowing light oil has a manometer attached as shown in Fig. P2.75. What is the absolute pressure in the pipe flow?
Two cylinders are filled with liquid water, ρ = 1000 kg/m3, and connected by a line with a closed valve. A has 100 kg and B has 500 kg of water, their cross-sectional areas are AA = 0.1 m2 and AB = 0.25 m2 and the height h is 1 m. Find the pressure on each side of the valve. The valve is opened
The density of mercury changes approximately linearly with temperature as ρHg = 13595 − 2.5 T kg/ m3 T in Celsius so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of 100 kPa is measured in the summer at 35°C and in
A mercury thermometer measures temperature by measuring the volume expansion of a fixed mass of liquid Hg due to a change in the density, see problem 2.35. Find the relative change (%) in volume for a change in temperature from 10°C to 20°C.
Using the freezing and boiling point temperatures for water in both Celsius and Fahrenheit scales, develop a conversion formula between the scales. Find the conversion formula between Kelvin and Rankine temperature scales.
Water in nature exist in different phases like solid, liquid and vapor (gas). Indicate the relative magnitude of density and specific volume for the three phases.
The atmosphere becomes colder at higher elevation. As an average the standard atmospheric absolute temperature can be expressed as Tatm = 288 - 6.5 × 10−3 z, where z is the elevation in meters. How cold is it outside an airplane cruising at 12 000 m expressed in Kelvin and in Celsius?
Repeat problem 2.72 if the flow inside the apparatus is liquid water, ρ ≅ 1000 kg/m3, instead of air. Find the pressure difference between the two holes flush with the bottom of the channel. You cannot neglect the two unequal water columns.
The main waterline into a tall building has a pressure of 600 kPa at 5 m elevation below ground level. How much extra pressure does a pump need to add to ensure a water line pressure of 200 kPa at the top floor 150 m above ground?
A 5-kg piston in a cylinder with diameter of 100 mm is loaded with a linear spring and the outside atmospheric pressure of 100 kPa. The spring exerts no force on the piston when it is at the bottom of the cylinder and for the state shown, the pressure is 400 kPa with volume 0.4 L. The valve is
In the city water tower, water is pumped up to a level 25 m above ground in a pressurized tank with air at 125 kPa over the water surface. This is illustrated in Fig. P2.84. Assuming the water density is 1000 kg/m3 and standard gravity, find the pressure required to pump more water in at ground
Two cylinders are connected by a piston as shown in Fig. P2.85. Cylinder A is used as a hydraulic lift and pumped up to 500 kPa. The piston mass is 25 kg and there is standard gravity. What is the gas pressure in cylinder B?
A dam retains a lake 6 m deep. To construct a gate in the dam we need to know the net horizontal force on a 5 m wide and 6 m tall port section that then replaces a 5 m section of the dam. Find the net horizontal force from the water on one side and air on the other side of the port.
Is density a unique measure of mass distribution in a volume? Does it vary? If so, on what kind of scale (distance)?
What is the lowest temperature (approximately) at which water can be liquid?
Sketch two constant-pressure curves (500 kPa and 30 000 kPa) in a T-v diagram and indicate on the curves where in the water tables you see the properties.
A tank contains 2 kg of nitrogen at 100 K with a quality of 50%. Through a volume flowmeter 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. The
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 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. Find 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 carries on to −10°C (state 3). Illustrate the processes 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
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
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
A piston/cylinder arrangement, shown in Fig. P3.111, contains air at 250 kPa, 300°C. The 50-kg piston has a diameter of 0.1 m and initially pushes against the stops. The atmosphere is at 100 kPa and 20°C. The cylinder now cools as heat is transferred to the ambient. a. At what temperature does
Air in a tank is at 1 MPa and room temperature of 20°C. It is used to fill an initially empty balloon to a pressure of 200 kPa, at which point the radius is 2 m and the temperature is 20°C. Assume the pressure in the balloon is linearly proportional to its radius and that the air in the tank also
A cylinder is fitted with a 10-cm-diameter piston that is restrained by a linear spring (force proportional to distance) as shown in Fig. P3.113. The spring force constant is 80 kN/m and the piston initially rests on the stops, with a cylinder volume of 1 L. The valve to the air line is opened and
A 500-L tank stores 100 kg of nitrogen gas at 150 K. To design the tank the pressure must be estimated and three different methods are suggested. Which is the most accurate, and how different in percent are the other two? a. Nitrogen tables, Table B.6 b. Ideal gas c. Generalized compressibility
What is the percent error in pressure if the ideal gas model is used to represent the behavior of superheated vapor R-22 at 50°C, 0.03082 m3/kg? What if the generalized compressibility chart, Fig. D.1, is used instead (iterations needed)?
Find the pressure and temperature for saturated vapor R-12 with v = 0.1 m3/kg
Use a linear interpolation to estimate properties of ammonia to fill out the table below
Use a linear interpolation to estimate Tsat at 900 kPa for nitrogen. Sketch by hand the curve Psat(T) by using a few table entries around 900 kPa from table B.6.1. Is your linear interpolation over or below the actual curve?
Use a double linear interpolation to find the pressure for superheated R-134a at 13°C with v = 0.3 m3/kg.
Why are most of the compressed liquid or solid regions not included in the printed tables?
Find the specific volume of ammonia at 140 kPa and 0°C.
Find the pressure of water at 200°C and specific volume of 1.5 m3/kg.
Use the computer software to find the properties for water at the 4 states in Problem 3.33
Use the computer software to find the properties for ammonia at the 2 states listed in Problem 3.37
Use the computer software to find the properties for ammonia at the 3 states listed in Problem 3.117
Find the value of the saturated temperature for nitrogen by linear interpolation in table B.6.1 for a pressure of 900 kPa. Compare this to the value given by the computer software.
Write a computer program that lists the states P, T, and v along the process curve in Problem 3.111
Use the computer software to sketch the variation of pressure with temperature in Problem 3.41. Extend the curve a little into the single-phase region.
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
What is the percent change in volume as liquid water freezes? Mention some effects in nature and for our households the volume change can have.
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: a. CO2 at T = 40°C and P = 0.5 MPa b. Air at T = 20°C and P = 200 kPa c. NH3 at T = 170°C and P = 600 kPa
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
When you skate on ice a thin liquid film forms under the skate; how can that be?
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
Give the phase for the following states. Discuss.
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
An external water tap has the valve activated by a long spindle so the closing mechanism is located well inside the wall. Why is that?
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) 200oC b) 100oC.
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 -20oC 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 +40oC. For each location find the pressure and the change
In your refrigerator the working substance evaporates from liquid to vapor at -20oC 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 +40oC. For each location find the pressure and the change
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