Chapter Questions
Make a control volume around the whole power plant in Fig. 1.1 and list the flows of mass and energy in or out and any storage of energy. Make sure you know what is inside and what is outside your chosen control volume.
Make a control volume around the refrigerator in Fig. $1.3 .$ Identify the mass flow of external air and show where you have significant heat transfer and where storage changes.
Separate the list $P, F, V, v, \rho, T, a, m, L, t,$ and $\mathbf{V}$ into intensive properties, extensive properties, and nonproperties.
A tray of liquid water is placed in a freezer where it cools from $20^{\circ} \mathrm{C}$ to $-5^{\circ} \mathrm{C}$. Show the energy flow(s) and storage and explain what changes.
The overall density of fibers, rock wool insulation, foams, and cotton is fairly low. Why?
Is density a unique measure of mass distribution in a volume? Does it vary? If so, on what kind of scale (distance)?
Water in nature exists in three different phases: solid, liquid, and vapor (gas). Indicate the relative magnitude of density and the specific volume for the three phases.
What is the approximate mass of $1 \mathrm{~L}$ of gasoline? Of helium in a balloon at $T_{0}, P_{0} ?$
Can you carry $1 \mathrm{~m}^{3}$ of liquid water?
A heavy refrigerator has four height-adjustable feet. What feature of the feet will ensure that they do not make dents in the floor?
A swimming pool has an evenly distributed pressure at the bottom. Consider a stiff steel plate lying on the ground. Is the pressure below it just as evenly distributed?
What physically determines the variation of the atmospheric pressure with elevation?
Two divers swim at a depth of $20 \mathrm{~m}$. One of them swims directly under a supertanker; the other avoids the tanker. Who feels a greater pressure?
A manometer with water shows a $\Delta P$ of $P_{0} / 20$; what is the column height difference?
Does the pressure have to be uniform for equilibrium to exist?
A water skier does not sink too far down in the water if the speed is high enough. What makes that situation different from our static pressure calculations?
What is the lowest temperature in degrees Celsius? In degrees Kelvin?
Convert the formula for water density in In-Text Concept Problem $\mathrm{d}$ to be for $T$ in degrees Kelvin.
A thermometer that indicates the temperature with a liquid column has a bulb with a larger volume of liquid. Why?
What is the main difference between the macroscopic kinetic energy in a motion like the blowing of wind versus the microscopic kinetic energy of individual molecules? Which one can you sense with your hand?
How can you illustrate the binding energy between the three atoms in water as they sit in a triatomic water molecule. Hint: imagine what must happen to create three separate atoms.
An apple "weighs" $60 \mathrm{~g}$ and has a volume of $75 \mathrm{~cm}^{3}$ in a refrigerator at $8^{\circ} \mathrm{C}$. What is the apple's density? List three intensive and two extensive properties of the apple.
One kilopond ( $1 \mathrm{kp}$ ) is the weight of $1 \mathrm{~kg}$ in the standard gravitational field. What is the weight of $1 \mathrm{~kg}$ in newtons (N)?
A stainless steel storage tank contains $5 \mathrm{~kg}$ of oxygen gas and $7 \mathrm{~kg}$ of nitrogen gas. How many kmoles are in the tank?
A steel cylinder of mass 4 kg contains 4 L of water at $25^{\circ} \mathrm{C}$ at $100 \mathrm{kPa}$. Find the total mass and volume of the system. List two extensive and three intensive properties of the water.
The standard acceleration (at sea level and $45^{\circ}$ latitude) due to gravity is $9.80665 \mathrm{~m} / \mathrm{s}^{2} .$ What is the force needed to hold a mass of $2 \mathrm{~kg}$ at rest in this gravitational field? How much mass can a force of I N support?
An aluminum piston of $2.5 \mathrm{~kg}$ is in the standard gravitational field, and a force of $25 \mathrm{~N}$ is applied vertically up. Find the acceleration of the piston.
When you move up from the surface of the earth, the gravitation is reduced as $g=9.807-3.32 \times$ $10^{-6} z,$ with $z$ being the elevation in meters. By what percentage is the weight of an airplane reduced when it cruises at $11000 \mathrm{~m} ?$
A car rolls down a hill with a slope such that the gravitational "pull" in the direction of motion is one-tenth of the standard gravitational force (see Problem 1.26 ). If the car has a mass of $2500 \mathrm{~kg}$, find the acceleration.
A van moves at $60 \mathrm{~km} / \mathrm{h}$ and completely stops with constant deceleration in $5 \mathrm{~s}$. The mass of the van and driver is $2075 \mathrm{~kg}$, find the necessary force.
A $1500 \mathrm{~kg}$ car moving at $20 \mathrm{~km} / \mathrm{h}$ is accelerated at a constant rate of $4 \mathrm{~m} / \mathrm{s}^{2}$ up to a speed of $75 \mathrm{~km} / \mathrm{h}$. What are the force and total time required?
On the moon, the gravitational acceleration is approximately one-sixth that on the surface of the earth. A 5 -kg mass is "weighed" with a beam balance on the surface of the moon. What is the expected reading? If this mass is weighed with a spring scale that reads correctly for standard gravity on earth (see Problem 1.26 ), what is the reading?
The elevator in a hotel has a mass of $750 \mathrm{~kg}$, and it carries six people with a total mass of $450 \mathrm{~kg}$. How much force should the cable pull up with to have an acceleration of $1 \mathrm{~m} / \mathrm{s}^{2}$ in the upward direction?
One of the people in the previous problem weighs $80 \mathrm{~kg}$ standing still. How much weight does this person feel when the elevator starts moving?
A bottle of $12 \mathrm{~kg}$ steel has $1.75 \mathrm{kmoles}$ of liquid propane. It accelerates horizontally at a rate of $3 \mathrm{~m} / \mathrm{s}^{2} .$ What is the needed force?
A steel beam of $700 \mathrm{~kg}$ is raised by a crane with an acceleration of $2 \mathrm{~m} / \mathrm{s}^{2}$ relative to the ground at a location where the local gravitational acceleration is $9.5 \mathrm{~m} / \mathrm{s}^{2} .$ Find the required force.
A $1-\mathrm{m}^{3}$ container is filled with $400 \mathrm{~kg}$ of granite stone, $200 \mathrm{~kg}$ of dry sand, and $0.2 \mathrm{~m}^{3}$ of liquid $25^{\circ} \mathrm{C}$ water. Using properties from Tables $\mathrm{A} .3$ andA. 4 , find the average specific volume and density of the masses when you exclude air mass and volume.
A power plant that separates carbon dioxide from the exhaust gases compresses it to a density of 110 $\mathrm{kg} / \mathrm{m}^{3}$ and stores it in an unminable coal seam with a porous volume of $100000 \mathrm{~m}^{3}$. Find the mass that can be stored.
A $15-\mathrm{kg}$ steel gas tank holds $300 \mathrm{~L}$ of liquid gasoline with a density of $800 \mathrm{~kg} / \mathrm{m}^{3}$. If the system is decelerated with $2 g,$ what is the needed force?
A $5-\mathrm{m}^{3}$ container is filled with $900 \mathrm{~kg}$ of granite (density of $2400 \mathrm{~kg} / \mathrm{m}^{3}$ ). The rest of the volume is air, with density equal to $1.15 \mathrm{~kg} / \mathrm{m}^{3}$. Find the mass of air and the overall (average) specific volume.
A tank has two rooms separated by a membrane. Room A has $1 \mathrm{~kg}$ of air and a volume of $0.5 \mathrm{~m}^{3}$; room $\mathrm{B}$ has $0.75 \mathrm{~m}^{3}$ of air with density $0.8 \mathrm{~kg} / \mathrm{m}^{3}$. The membrane is broken, and the air comes to a uniform state. Find the final density of the air.
One kilogram of diatomic oxygen $\left(\mathrm{O}_{2},\right.$ molecular mass of 32 ) is contained in a 500 - $L$ tank. Find the specific volume on both a mass and a mole basis $(v$ and $\bar{v})$.
A $5000-\mathrm{kg}$ elephant has a cross-sectional area of $0.02 \mathrm{~m}^{2}$ on each foot. Assuming an even distribution, what is the pressure under its feet?
A valve in the cylinder shown in Fig. $\mathrm{P} 1.44$ has a cross-sectional area of $11 \mathrm{~cm}^{2}$ with a pressure of $735 \mathrm{kPa}$ inside the cylinder and $99 \mathrm{kPa}$ outside. How large a force is needed to open the valve?
The hydraulic lift in an auto repair shop has a cylinder diameter of $0.2 \mathrm{~m}$. To what pressure should the hydraulic fluid be pumped to lift $40 \mathrm{~kg}$ of piston/ arms and $700 \mathrm{~kg}$ of a car?
A hydraulic lift has a maximum fluid pressure of $500 \mathrm{kPa}$. What should the piston/cylinder diameter be in order to lift a mass of $850 \mathrm{~kg}$ ?
A laboratory room has a vacuum of $0.1 \mathrm{kPa}$. What net force does that put on the door of size $2 \mathrm{~m}$ by $1 \mathrm{~m} ?$
A vertical hydraulic cylinder has a $125-\mathrm{mm}-$ diameter piston with hydraulic fluid inside the cylinder and an ambient pressure of 1 bar. Assuming standard gravity, find the piston mass that will create an inside pressure of $1500 \mathrm{kPa}$.
A $75-\mathrm{kg}$ human total footprint is $0.05 \mathrm{~m}^{2}$ when the human is wearing boots. Suppose you want to walk on snow that can at most support an extra $3 \mathrm{kPa}$ what should the total snowshoe area be?
A piston/cylinder with a cross-sectional area of $0.01 \mathrm{~m}^{2}$ has a piston mass of $100 \mathrm{~kg}$ resting on the stops, as shown in Fig. $\mathrm{P} 1.50 .$ With an outside atmospheric pressure of $100 \mathrm{kPa}$, what should the water pressure be to lift the piston?
A large exhaust fan in a laboratory room keeps the pressure inside at $10 \mathrm{~cm}$ of water vacuum relative to the hallway. What is the net force on the door measuring $1.9 \mathrm{~m}$ by $1.1 \mathrm{~m} ?$
A tornado rips off a $100-\mathrm{m}^{2}$ roof with a mass of $1000 \mathrm{~kg}$. What is the minimum vacuum pressure needed to do that if we neglect the anchoring forces?
A 5 -kg cannonball acts as a piston in a cylinder with a diameter of $0.15 \mathrm{~m}$. As the gunpowder is burned, a pressure of $7 \mathrm{MPa}$ is created in the gas behind the ball. What is the acceleration of the ball if the cylinder (cannon) is pointing horizontally?
Repeat the previous problem for a cylinder (cannon) pointing $40^{\circ}$ up relative to the horizontal direction.
A $2.5-\mathrm{m}$ -tall steel cylinder has a cross-sectional area of $1.5 \mathrm{~m}^{2}$. At the bottom, with a height of $0.5 \mathrm{~m}$. is liquid water, on top of which is a $1-\mathrm{m}$ -high layer of gasoline. This is shown in Fig. $\mathrm{P} 1.55 .$ The gasoline surface is exposed to atmospheric air at $101 \mathrm{kPa}$. What is the highest pressure in the water?
An underwater buoy is anchored at the seabed with a cable, and it contains a total mass of $250 \mathrm{~kg}$. What should the volume be so that the cable holds it down with a force of $1000 \mathrm{~N} ?$
At the beach, atmospheric pressure is 1025 mbar. You dive $15 \mathrm{~m}$ down in the ocean, and you later climb a hill up to $250 \mathrm{~m}$ in elevation. Assume that the density of water is about $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and the density of air is $1.18 \mathrm{~kg} / \mathrm{m}^{3}$. What pressure do you feel at each place?
What is the pressure at the bottom of a $5-\mathrm{m}$ -tall column of fluid with atmospheric pressure of $101 \mathrm{kPa}$ on the top surface if the fluid isa. water at $20^{\circ} \mathrm{C}$ ?b. glycerine at $25^{\circ} \mathrm{C} ?$c. gasoline at $25^{\circ} \mathrm{C} ?$
A steel tank of cross-sectional area $3 \mathrm{~m}^{2}$ and height $16 \mathrm{~m}$ weighs $10000 \mathrm{~kg}$ and is open at the top, as shown in Fig. $\mathrm{P} 1.59 .$ We want to float it in the ocean so that it is positioned $10 \mathrm{~m}$ straight down by pouring concrete into its bottom. How much concrete should we use?
A piston, $m_{p}=5 \mathrm{~kg},$ is fitted in a cylinder, $A=$ $15 \mathrm{~cm}^{2},$ that contains a gas. The setup is in a centrifuge that creates an acceleration of $25 \mathrm{~m} / \mathrm{s}^{2}$ in the direction of piston motion toward the gas. Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
Liquid water with density $\rho$ is filled on top of a thin piston in a cylinder with cross-sectional area $A$ and total height $H,$ as shown in Fig. $\mathrm{P} 1.61 .$ Air is let in under the piston so that it pushes up, causing the water to spill over the edge. Derive the formula for the air pressure as a function of piston elevation from the bottom. $h$.
A probe is lowered $16 \mathrm{~m}$ into a lake. Find the absolute pressure there.
The density of atmospheric air is about $1.15 \mathrm{~kg} / \mathrm{m}^{3}$, which we assume is constant. How large an absolute pressure will a pilot encounter when flying $2000 \mathrm{~m}$ above ground level, where the pressure is $101 \mathrm{kPa}$ ?
The standard pressure in the atmosphere with elevation $(H)$ above sea level can be correlated as $P=$ $P_{0}(1-H / L)^{5.26}$ with $L=44300 \mathrm{~m} .$ With the local sea level pressure $P_{0}$ at $101 \mathrm{kPa}$, what is the pressure at $10000 \mathrm{~m}$ elevation?
A barometer to measure absolute pressure shows a mercury column height of $725 \mathrm{~mm}$. The temperature is such that the density of the mercury is $13550 \mathrm{~kg} / \mathrm{m}^{3}$. Find the ambient pressure.
A differential pressure gauge mounted on a vessel shows $1.25 \mathrm{MPa}$, and a local barometer gives atmospheric pressure as 0.96 bar. Find the absolute pressure inside the vessel.
A manometer shows a pressure difference of $1 \mathrm{~m}$ of liquid mercury. Find $\Delta P$ in $\mathrm{kPa}$.
Blue manometer fluid of density $925 \mathrm{~kg} / \mathrm{m}^{3}$ shows a column height difference of $3-\mathrm{cm}$ vacuum with one end attached to a pipe and the other open to $P_{0}=101 \mathrm{kPa}$. What is the absolute pressure in the pipe?
What pressure difference does a $10-\mathrm{m}$ column of atmospheric air show?
A barometer measures $760 \mathrm{~mm} \mathrm{Hg}$ at street level and $735 \mathrm{~mm} \mathrm{Hg}$ on top of a building. How tall is the building if we assume air density of $1.15 \mathrm{~kg} / \mathrm{m}^{3} ?$
The pressure gauge on an air tank shows $75 \mathrm{kPa}$ when the diver is $10 \mathrm{~m}$ down in the ocean. At whatdepth will the gauge pressure be zero? What does that mean?
An exploration submarine should be able to descend $1200 \mathrm{~m}$ down in the ocean. If the ocean density is $1020 \mathrm{~kg} / \mathrm{m}^{3},$ what is the maximum pressure on the submarine hull?
A submarine maintains an internal pressure of $101 \mathrm{kPa}$ and dives $240 \mathrm{~m}$ down in the ocean, which has an average density of $1030 \mathrm{~kg} / \mathrm{m}^{3}$. What is the pressure difference between the inside and the outside of the submarine hull?
Assume that 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 correspond to?
The absolute pressure in a tank is $115 \mathrm{kPa}$ and the local ambient absolute pressure is $97 \mathrm{kPa}$. If a U-tube with mercury (density $=13550 \mathrm{~kg} / \mathrm{m}^{3}$ ) is attached to the tank to measure the gauge pressure, what column height difference will it show?
An absolute pressure gauge attached to a steel cylinder shows $135 \mathrm{kPa}$. We want to attach a manometer using liquid water on a day that $P_{\text {atm }}=101$ $\mathrm{kPa}$. How high a fluid level difference must we plan for?
A U-tube manometer filled with water (density = $1000 \mathrm{~kg} / \mathrm{m}^{3}$ ) shows a height difference of $25 \mathrm{~cm} .$ What is the gauge pressure? If the right branch is tilted to make an angle of $30^{\circ}$ with the horizontal, as shown in Fig. $\mathrm{P} 1.77,$ what should the length of the column in the tilted tube be relative to the U-tube?
A pipe flowing light oil has a manometer attached, as shown in Fig. $P 1.78$. What is the absolute pressure in the pipe flow?
The difference in height between the columns of a manometer is $200 \mathrm{~mm}$, with a fluid of density 900 $\mathrm{kg} / \mathrm{m}^{3}$. What is the pressure difference? What is the height difference if the same pressure difference is measured using mercury (density $\left.=13600 \mathrm{~kg} / \mathrm{m}^{3}\right)$ as manometer fluid?
Two cylinders are filled with liquid water, $\rho=1000$ $\mathrm{kg} / \mathrm{m}^{3},$ and connected by a line with a closed valve, as shown in Fig. $\mathrm{P} 1.80 . A$ has $100 \mathrm{~kg}$ and $B$ has $500 \mathrm{~kg}$ of water, their cross-sectional areas are $A_{A}=0.1 \mathrm{~m}^{2}$ and $A_{B}=0.25 \mathrm{~m}^{2},$ and the height $h$ is 1$\mathrm{m}$. Find the pressure on either side of the valve. The valve is opened, and water flows to an equilibrium. Find the final pressure at the valve location.
Two piston/cylinder arrangements, $A$ and $B,$ have their gas chambers connected by a pipe, as shown in Fig. $\mathrm{P} 1.81$. The cross-sectional areas are $A_{A}=$ $75 \mathrm{~cm}^{2}$ and $A_{B}=25 \mathrm{~cm}^{2},$ with the piston mass in $A$ being $m_{A}=25 \mathrm{~kg} .$ Assume an outside pressure of $100 \mathrm{kPa}$ and standard gravitation. Find the mass $m_{B}$ so that none of the pistons have to rest on the bottom.
Two hydraulic piston/cylinders are of the same size and setup as in Problem $1.81,$ but with negligible piston masses. A single point force of $250 \mathrm{~N}$ presses down on piston $A$. Find the needed extra force on piston $B$ so that none of the pistons have to move.
A piece of experimental apparatus, Fig. $\mathrm{P} 1.83,$ is located where $g=9.5 \mathrm{~m} / \mathrm{s}^{2}$ and the temperature is $5^{\circ} \mathrm{C}$. Air flow inside the apparatus is determined by measuring the pressure drop across an orifice with a mercury manometer (see Problem 1.91 for density) showing a height difference of $200 \mathrm{~mm}$. What is the pressure drop in $\mathrm{kPa} ?$
An escalator brings four people, whose total mass is $300 \mathrm{~kg}, 25 \mathrm{~m}$ up in a building. Explain what happens with respect to energy transfer and stored energy.
A car moves at $75 \mathrm{~km} / \mathrm{h}$; its mass, including people, is $3200 \mathrm{~kg} .$ How much kinetic energy does the car have?
A $52-\mathrm{kg}$ package is lifted up to the top shelf in a storage bin that is $4 \mathrm{~m}$ above the ground floor. How much increase in potential energy does the package get?
A car of mass 1775 kg travels with a velocity of $100 \mathrm{~km} / \mathrm{h}$. Find the kinetic energy. How high should the car be lifted in the standard gravitational field to have a potential energy that equals the kinetic energy?
An oxygen molecule with mass $\mathrm{m}=\mathrm{M} \mathrm{m}_{\mathrm{o}}=$ $32 \times 1.66 \times 10^{-27} \mathrm{~kg}$ moves with a velocity of $240 \mathrm{~m} / \mathrm{s}$. What is the kinetic energy of the molecule? What temperature does that corresponds to if it has to equal $(3 / 2) k T,$ where $k$ is Boltzmans constant and $T$ is absolute temperature in Kelvin?
What is a temperature of $-5^{\circ} \mathrm{C}$ in degrees Kelvin?
The human comfort zone is between 18 and $24^{\circ} \mathrm{C}$. What is the range in Kelvin? What is the maximum relative change from the low to the high temperature?
The density of mercury changes approximately linearly with temperature as $\rho_{\mathrm{Hg}}=13595-2.5 \mathrm{~T}$ $\mathrm{kg} / \mathrm{m}^{3}(T$ in Celsius), so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of $100 \mathrm{kPa}$ is measured in the summer at $35^{\circ} \mathrm{C}$ and in the winter at $-15^{\circ} \mathrm{C}$, what is the difference in column height between the two measurements?
A mercury thermometer measures temperature by measuring the volume expansion of a fixed mass of liquid mercury due to a change in density (see Problem 1.91 ). Find the relative change $(\%)$ in volume for a change in temperature from $10^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$.
The density of liquid water is $\rho=1008-T / 2$ $\left[\mathrm{kg} / \mathrm{m}^{3}\right]$ with $T$ in ${ }^{\circ} \mathrm{C}$. If the temperature increases $10^{\circ} \mathrm{C},$ how much deeper does a $1-\mathrm{m}$ layer of water become?
Using the freezing and boiling point temperatures for water on both the Celsius and Fahrenheit scales, develop a conversion formula between the scales. Find the conversion formula between the Kelvin and Rankine temperature scales.
The atmosphere becomes colder at higher elevations. As an average, the standard atmospheric absolute temperature can be expressed as $T_{\mathrm{atm}}=$ $288-6.5 \times 10^{-3} z,$ where $z$ is the elevation in meters. How cold is it outside an airplane cruising at $12000 \mathrm{~m},$ expressed in degrees Kelvin and Celsius?
Repeat Problem 1.83 if the flow inside the apparatus is liquid water $\left(\rho=1000 \mathrm{~kg} / \mathrm{m}^{3}\right)$ 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.
A dam retains a lake $6 \mathrm{~m}$ deep, as shown in Fig. P1.97. To construct a gate in the dam, we need to know the net horizontal force on a $5-\mathrm{m}$ -wide, $6-\mathrm{m}$ -tall port section that then replaces a $5-\mathrm{m}$ section of the dam. Find the net horizontal force from the water on one side and air on the other side of the port.
In the city water tower, water is pumped up to a level $25 \mathrm{~m}$ above ground in a pressurized tank with air at 125 kPa over the water surface. This is illustrated in Fig. P1.98. Assuming water density of $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and standard gravity, find the pressure required to pump more water in at ground level.
The main waterline into a tall building has a pressure of $600 \mathrm{kPa}$ at 5 -m elevation below ground level. The building is shown in Fig. P1.99. How much extra pressure does a pump need to add to ensure a waterline pressure of $200 \mathrm{kPa}$ at the top floor $150 \mathrm{~m}$ aboveground?
Two cylinders are connected by a piston, as shown in Fig. $\mathrm{P} 1.100 .$ Cylinder $A$ is used as a hydraulic lift and pumped up to $500 \mathrm{kPa}$. The piston mass is $25 \mathrm{~kg},$ and there is standard gravity. What is the gas pressure in cylinder $B$ ?
A $5-\mathrm{kg}$ piston in a cylinder with a diameter of $100 \mathrm{~mm}$ is loaded with a linear spring and the outside atmospheric pressure is $100 \mathrm{kPa}$, as shown in Fig. $\mathrm{P} 1.101 .$ 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 $400 \mathrm{kPa}$ with volume $0.4 \mathrm{~L}$. The valve is opened to let some air in, causing the piston to rise $2 \mathrm{~cm}$. Find the new pressure.
A mass of 2 lbm has an acceleration of $5 \mathrm{ft} / \mathrm{s}^{2}$. What is the needed force in $\mathrm{lbf}$ ?
How much mass is in 1 gal of gasoline? In helium in a balloon at atmospheric $P$ and $T ?$
Can you easily carry a 1 -gal bar of solid gold?
What is the temperature of $-5 \mathrm{~F}$ in degrees Rankine?
What is the lowest possible temperature in degrees Fahrenheit? In degrees Rankine?
What is the relative magnitude of degree Rankine to degree Kelvin?
Chemical reaction rates generally double for a $10-\mathrm{K}$ increase in temperature. How large an increase is that in Fahrenheit?
An apple weighs $0.2 \mathrm{lbm}$ and has a volume of $6 \mathrm{in} .^{3}$ in a refrigerator at $38 \mathrm{~F}$. What is the apple's density? List three intensive and two extensive properties of the apple.
A steel piston of mass 10 lbm is in the standard gravitational field, where a force of $10 \mathrm{lbf}$ is applied vertically up. Find the acceleration of the piston.
A 2500-lbm car moving at $25 \mathrm{mi} / \mathrm{h}$ is accelerated at a constant rate of $15 \mathrm{ft} / \mathrm{s}^{2}$ up to a speed of $50 \mathrm{mi} / \mathrm{h}$. What are the force and total time required?
An escalator brings four people with a total mass of 600 lbm and a 1000 -lbm cage up with an acceleration of $3 \mathrm{ft} / \mathrm{s}^{2}$. What is the needed force in the cable?
A 1 -lbm of diatomic oxygen $\left(\mathrm{O}_{2}\right.$ molecular mass32) is contained in a 100 -gal tank. Find the specific volume on both a mass and a mole basis $(v$ and $\bar{v})$.
A30-lbm steel gas tank holds $10 \mathrm{ft}^{3}$ of liquid gasoline having a density of $50 \mathrm{lbm} / \mathrm{ft}^{3}$. What force is needed to accelerate this combined system at a rate of $15 \mathrm{ft} / \mathrm{s}^{2} ?$
A power plant that separates carbon dioxide from the exhaust gases compresses it to a density of $8 \mathrm{lbm} / \mathrm{ft}^{3}$ and stores it in an unminable coal seam with a porous volume of $3500000 \mathrm{ft}^{3}$. Find the mass that can be stored.
A laboratory room keeps a vacuum of 4 in. of water due to the exhaust fan. What is the net force on a door of size $6 \mathrm{ft}$ by $3 \mathrm{ft}$ ?
A 150 -lbm human total footprint is $0.5 \mathrm{ft}^{2}$ when the person is wearing boots. If snow can support an extra 1 psi, what should the total snowshoe area be?
A tornado rips off a $1000-\mathrm{ft}^{2}$ roof with a mass of $2000 \mathrm{lbm}$. What is the minimum vacuum pressure needed to do that if we neglect the anchoring forces?
A manometer shows a pressure difference of 3.5 in. of liquid mercury. Find $\Delta P$ in psi.
A 7 -ft tall steel cylinder has a cross-sectional area of $15 \mathrm{ft}^{2}$. At the bottom, with a height of $2 \mathrm{ft}$, is liquid water, on top of which is a 4 -ft-high layer of gasoline. The gasoline surface is exposed to atmospheric air at 14.7 psia. What is the highest pressure in the water?
A U-tube manometer filled with water, density $62.3 \mathrm{lbm} / \mathrm{ft}^{3},$ shows a height difference of 10 in.What is the gauge pressure? If the right branch is tilted to make an angle of $30^{\circ}$ with the horizontal, as shown in Fig. $\mathrm{P} 1.77,$ what should the length of the column in the tilted tube be relative to the U-tube?
A piston/cylinder with a cross-sectional area of $0.1 \mathrm{ft}^{2}$ has a piston mass of 200 lbm resting on the stops, as shown in Fig. $\mathrm{P} 1.50 .$ With an outside atmospheric pressure of 1 atm, what should the water pressure be to lift the piston?
The main waterline into a tall building has a pressure of 90 psia at $16 \mathrm{ft}$ elevation below ground level. How much extra pressure does a pump need to add to ensure a waterline pressure of 30 psia at the top floor $450 \mathrm{ft}$ above ground?
A piston, $m_{p}=10 \mathrm{lbm},$ is fitted in a cylinder, $A=2.5$ in. $^{2},$ that contains a gas. The setup is in a centrifuge that creates an acceleration of $75 \mathrm{ft} / \mathrm{s}^{2}$ Assuming standard atmospheric pressure outside the cylinder, find the gas pressure.
The human comfort zone is between 18 and $24^{\circ} \mathrm{C}$. What is the range in Fahrenheit?
The atmosphere becomes colder at higher elevations. As an average, the standard atmospheric absolute temperature can be expressed as $T_{\mathrm{atm}}=$ $518-3.84 \times 10^{-3} z,$ where $z$ is the elevation in feet. How cold is it outside an airplane cruising at $32000 \mathrm{ft}$ expressed in degrees Rankine and Fahrenheit?
The density of mercury changes approximately linearly with temperature as $\rho_{\mathrm{Hg}}=851.5-0.086$ $T \mathrm{lbm} / \mathrm{ft}^{3}$ ( $T$ in degrees Fahrenheit), so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of $14.7 \mathrm{lbf} / \mathrm{in} .{ }^{2}$ is measured in the summer at $95 \mathrm{~F}$ and in the winter at $5 \mathrm{~F}$, what is the difference in column height between the two measurements?
Write a program to list corresponding temperatures in ${ }^{\circ} \mathrm{C}, \mathrm{K}, \mathrm{F},$ and $\mathrm{R}$ from $-50^{\circ} \mathrm{C}$ to $100{ }^{\circ} \mathrm{C}$ in increments of 10 degrees.
Plot the atmospheric pressure as a function of elevation $(0-20000 \mathrm{~m})$ at a location where the ground pressure is $100 \mathrm{kPa}$ at $500 \mathrm{~m}$ elevation. Use the variation shown in Problem 1.64.
Write a program that will input pressure in $\mathrm{kPa}$, $\mathrm{atm},$ or $\mathrm{lbf} / \mathrm{in} .^{2}$ and write the pressure in $\mathrm{kPa}, \mathrm{atm}$, bar, and $1 \mathrm{bf} / \mathrm{in} .{ }^{2}$
Write a program to do the temperature correction on a mercury barometer reading (see Problem 1.70 ). Input the reading and temperature and output the corrected reading at $20^{\circ} \mathrm{C}$ and pressure in $\mathrm{kPa}$.
Make a list of different weights and scales that are used to measure mass directly or indirectly. Investigate the ranges of mass and the accuracy that can be obtained.
Thermometers are based on several principles. Expansion of a liquid with a rise in temperature is used in many applications. Electrical resistance, thermistors, and thermocouples are common in instrumentation and remote probes. Investigate a variety of thermometers and list their range, accuracy, advantages, and disadvantages.
Collect information for a resistance- and thermocouple-based thermometer suitable for the range of temperatures from $0^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$. For each of the two types, list the accuracy and response of the transducer (output per degree change). Is any calibration or correction necessary when it is used in an instrument?
A thermistor is used as a temperature transducer. Its resistance changes with temperature approximately as $R=R_{0} \exp \left[\alpha\left(1 / T-1 / T_{0}\right)\right]$ where it has resistance $R_{0}$ at temperature $T_{0}$. Select the constants as $R_{0}=3000 \Omega$ and $T_{0}=298 \mathrm{~K}$ and compute $\alpha$ so that it has a resistance of $200 \Omega$ at $100^{\circ} \mathrm{C}$. Write a program to convert a measured resistance, $R,$ into information about the temperature. Find information for actual thermistors and plot the calibration curves with the formula given in this problem and the recommended correction given by the manufacturer.
Investigate possible transducers for the measurement of temperature in a flame with temperatures near $1000 \mathrm{~K}$. Are any transducers available for a temperature of $2000 \mathrm{~K} ?$
Blood pressure is measured with a sphygmomanometer while the sound from the pulse is checked. Investigate how this works, list the range of pressures normally recorded as the systolic (high) and diastolic (low) pressures, and present your findings in a short report.
A micromanometer uses a fluid with density 1000 $\mathrm{kg} / \mathrm{m}^{3},$ and it is able to measure height difference with an accuracy of $\pm 0.5 \mathrm{~mm}$. Its range is a maximum height difference of $0.5 \mathrm{~m}$. Investigate to determined if any transducers are available to replace the micromanometer.