Physics 5th edition James S. Walker - Solutions

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A constant-volume gas thermometer is calibrated in dry ice (that is, carbon dioxide in the solid state, which has a temperature of - 80.0°C) and in boiling ethyl alcohol (78.0°C). The two pressures are 0.900 atm and 1.635 atm. (a) What Celsius value of absolute zero does the calibration yield?
In a constant-volume gas thermometer, the pressure at 20.0°C is 0.980 atm. (a) What is the pressure at 45.0°C? (b) What is the temperature if the pressure is 0.500 atm?
Liquid nitrogen has a boiling point of - 195.81°C at atmospheric pressure. Express this temperature (a) In degrees Fahrenheit and (b) In kelvins.
Convert the following to equivalent temperatures on the Celsius and Kelvin scales: (a) The normal human body temperature, 98.6°F; (b) The air temperature on a cold day, -5.00°F.
The temperature difference between the inside and the outside of an automobile engine is 450°C. Express this temperature difference on (a) The Fahrenheit scale and (b) The Kelvin scale.
On a Strange temperature scale, the freezing point of water is -15.0°S and the boiling point is + 60.0°S. Develop a linear conversion equation between this temperature scale and the Celsius scale.
The melting point of gold is 1 064°C, and the boiling point is 2 660°C. (a) Express these temperatures in kelvins. (b) Compute the difference between these temperatures in Celsius degrees and kelvins.
The New River Gorge bridge in West Virginia is a steel arch bridge 518 m in length. How much does the total length of the roadway decking change between temperature extremes of - 20.0°C and 35.0°C? The result indicates the size of the expansion joints that must be built into the structure
A copper telephone wire has essentially no sag between poles 35.0 m apart on a winter day when the temperature is - 20.0°C. How much longer is the wire on a summer day when TC # 35.0°C?
The concrete sections of a certain superhighway are designed to have a length of 25.0 m. The sections are poured and cured at 10.0°C. What minimum spacing should the engineer leave between the sections to eliminate buckling if the concrete is to reach a temperature of 50.0°C?
A pair of eyeglass frames is made of epoxy plastic. At room temperature (20.0°C), the frames have circular lens holes 2.20 cm in radius. To what temperature must the frames be heated if lenses 2.21 cm in radius are to be inserted in them? The average coefficient of linear expansion for epoxy is
Each year thousands of children are badly burned by hot tap water. Figure P19.12 shows a cross-sectional view of an anti scalding faucet attachment designed to prevent such accidents. Within the device, a spring made of material with a high coefficient of thermal expansion controls a movable
The active element of a certain laser is made of a glass rod 30.0 cm long by 1.50 cm in diameter. If the temperature of the rod increases by 65.0°C, what is the increase in (a) Its length, (b) Its diameter, and (c) Its volume? Assume that the average coefficient of linear expansion of the
Inside the wall of a house, an L-shaped section of hot-water pipe consists of a straight horizontal piece 28.0 cm long, an elbow, and a straight vertical piece 134 cm long (Figure P19.14). A stud and a second-story floorboard hold stationary the ends of this section of copper pipe. Find the
A brass ring of diameter 10.00 cm at 20.0°C is heated and slipped over an aluminum rod of diameter 10.01 cm at 20.0°C. Assuming the average coefficients of linear expansion are constant, (a) To what temperature must this combination be cooled to separate them? Is this attainable? (b) What If?
A square hole 8.00 cm along each side is cut in a sheet of copper. (a) Calculate the change in the area of this hole if the temperature of the sheet is increased by 50.0 K. (b) Does this change represent an increase or a decrease in the area enclosed by the hole?
The average coefficient of volume expansion for carbon tetrachloride is 5.81 X 10-4 (°C)-1. If a 50.0-gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 30.0°C?
At 20.0°C, an aluminum ring has an inner diameter of 5.000 0 cm and a brass rod has a diameter of 5.050 0 cm. (a) If only the ring is heated, what temperature must it reach so that it will just slip over the rod? (b) What If? If both are heated together, what temperature must they both reach
A volumetric flask made of Pyrex is calibrated at 20.0°C. It is filled to the 100-mL mark with 35.0°C acetone. (a) What is the volume of the acetone when it cools to 20.0°C? (b) How significant is the change in volume of the flask?
A concrete walk is poured on a day when the temperature is 20.0°C in such a way that the ends are unable to move. (a) What is the stress in the cement on a hot day of 50.0°C? (b) Does the concrete fracture? Take Young’s modulus for concrete to be 7.00 X 109 N/m2 and the compressive strength
A hollow aluminum cylinder 20.0 cm deep has an internal capacity of 2.000 L at 20.0°C. It is completely filled with turpentine and then slowly warmed to 80.0°C. (a) How much turpentine overflows? (b) If the cylinder is then cooled back to 20.0°C, how far below the cylinder’s rim does the
A beaker made of ordinary glass contains a lead sphere of diameter 4.00 cm firmly attached to its bottom. At a uniform temperature of - 10.0°C, the beaker is filled to the brim with 118 cm3 of mercury, which completely covers the sphere. How much mercury overflows from the beaker if the
A steel rod undergoes a stretching force of 500 N. Its cross-sectional area is 2.00 cm2. Find the change in temperature that would elongate the rod by the same amount as the 500-N force does. Tables 12.1 and 19.1 are available to you.
The Golden Gate Bridge in San Francisco has a main span of length 1.28 km—one of the longest in the world. Imagine that a taut steel wire with this length and a cross-sectional area of 4.00 X 10-6 m2 is laid on the bridge deck with its ends attached to the towers of the bridge, on a summer day
Gas is contained in an 8.00-L vessel at a temperature of 20.0°C and a pressure of 9.00 atm. (a) Determine the number of moles of gas in the vessel. (b) How many molecules are there in the vessel?
A certain telescope forms an image of part of a cluster of stars on a square silicon charge-coupled detector (CCD) chip 2.00 cm on each side. A star field is focused on the CCD chip when it is first turned on and its temperature is 20.0°C. The star field contains 5 342 stars scattered uniformly.
An automobile tire is inflated with air originally at 10.0°C and normal atmospheric pressure. During the process, the air is compressed to 28.0% of its original volume and the temperature is increased to 40.0°C. (a) What is the tire pressure? (b) After the car is driven at high speed, the
A tank having a volume of 0.100 m3 contains helium gas at 150 atm. How many balloons can the tank blow up if each filled balloon is a sphere 0.300 m in diameter at an absolute pressure of 1.20 atm?
An auditorium has dimensions 10.0 m X 20.0 m X 30.0 m. How many molecules of air fill the auditorium at 20.0°C and a pressure of 101 kPa?
Imagine a baby alien playing with a spherical balloon the size of the Earth in the outer solar system. Helium gas inside the balloon has a uniform temperature of 50.0 K due to radiation from the Sun. The uniform pressure of the helium is equal to normal atmospheric pressure on Earth. (a) Find the
Just 9.00 g of water is placed in a 2.00-L pressure cooker and heated to 500°C. What is the pressure inside the container?
One mole of oxygen gas is at a pressure of 6.00 atm and a temperature of 27.0°C. (a) If the gas is heated at constant volume until the pressure triples, what is the final temperature? (b) If the gas is heated until both the pressure and volume are doubled, what is the final temperature?
The mass of a hot-air balloon and its cargo (not including the air inside) is 200 kg. The air outside is at 10.0°C and 101 kPa. The volume of the balloon is 400 m3. To what temperature must the air in the balloon be heated before the balloon will lift off? (Air density at 10.0°C is 1.25 kg/m3.)
Your father and your little brother are confronted with the same puzzle. Your father’s garden sprayer and your brother’s water cannon both have tanks with a capacity of 5.00 L (Figure P19.34). Your father inserts a negligible amount of concentrated insecticide into his tank. They both pour in
(a) Find the number of moles in one cubic meter of an ideal gas at 20.0°C and atmospheric pressure. (b) For air, Avogadro’s number of molecules has mass 28.9 g. Calculate the mass of one cubic meter of air. Compare the result with the tabulated density of air
The void fraction of a porous medium is the ratio of the void volume to the total volume of the material. The void is the hollow space within the material; it may be filled with a fluid. A cylindrical canister of diameter 2.54 cm and height 20.0 cm is filled with activated carbon having a void
A cube 10.0 cm on each edge contains air (with equivalent molar mass 28.9 g/mol) at atmospheric pressure and temperature 300 K. Find (a) The mass of the gas, (b) its weight, and (c) The force it exerts on each face of the cube. (d) Comment on the physical reason why such a small sample can
At 25.0 m below the surface of the sea (p =1 025 kg/m3), where the temperature is 5.00°C, a diver exhales an air bubble having a volume of 1.00 cm3. If the surface temperature of the sea is 20.0°C, what is the volume of the bubble just before it breaks the surface?
The pressure gauge on a tank registers the gauge pressure, which is the difference between the interior and exterior pressure. When the tank is full of oxygen (O2), it contains 12.0 kg of the gas at a gauge pressure of 40.0 atm. Determine the mass of oxygen that has been withdrawn from the tank
Estimate the mass of the air in your bedroom. State the quantities you take as data and the value you measure or estimate for each.
On his honeymoon James Joule traveled from England to Switzerland. He attempted to verify his idea of the interconvertibility of mechanical energy and internal energy by measuring the increase in temperature of water that fell in a waterfall. If water at the top of an alpine waterfall has a
A popular brand of cola contains 6.50 g of carbon dioxide dissolved in 1.00 L of soft drink. If the evaporating carbon dioxide is trapped in a cylinder at 1.00 atm and 20.0°C, what volume does the gas occupy?
In state-of-the-art vacuum systems, pressures as low as 10-9 Pa are being attained. Calculate the number of molecules in a 1.00-m3 vessel at this pressure if the temperature is 27.0°C.
A room of volume V contains air having equivalent molar mass M (in g/mol). If the temperature of the room is raised from T1 to T2, what mass of air will leave the room? Assume that the air pressure in the room is maintained at P0.
A diving bell in the shape of a cylinder with a height of 2.50 m is closed at the upper end and opens at the lower end. The bell is lowered from air into sea water (p =| 1.025 g/cm3). The air in the bell is initially at 20.0°C. The bell is lowered to a depth (measured to the bottom of the bell) of
A student measures the length of a brass rod with a steel tape at 20.0°C. The reading is 95.00 cm. What will the tape indicate for the length of the rod when the rod and the tape are at (a) - 15.0°C and (b) 55.0°C?
Consider Joule’s apparatus described in Figure 20.1. The mass of each of the two blocks is 1.50 kg, and the insulated tank is filled with 200 g of water. What is the increase in the temperature of the water after the blocks fall through a distance of 3.00 m?
The temperature of a silver bar rises by 10.0°C when it absorbs 1.23 kJ of energy by heat. The mass of the bar is 525 g. Determine the specific heat of silver.
The density of gasoline is 730 kg/m3 at 0°C. Its average coefficient of volume expansion is 9.60 X 10-4 /°C. If 1.00 gal of gasoline occupies 0.003 80 m3, how many extra kilograms of gasoline would you get if you bought 10.0 gal of gasoline at 0°C rather than at 20.0°C from a pump that is not
A 50.0-g sample of copper is at 25.0°C. If 1 200 J of energy is added to it by heat, what is the final temperature of the copper?
Systematic use of solar energy can yield a large saving in the cost of winter space heating for a typical house in the north central United States. If the house has good insulation, you may model it as losing energy by heat steadily at the rate 6 000 W on a day in April when the average exterior
A mercury thermometer is constructed as shown in Figure P19.47. The capillary tube has a diameter of 0.004 00 cm, and the bulb has a diameter of 0.250 cm.
A liquid with a coefficient of volume expansion ' just fills a spherical shell of volume Vi at a temperature of Ti (see Fig. P19.47). The shell is made of a material that has an average coefficient of linear expansion &. The liquid is free to expand into an open capillary of area A projecting from
A cylinder is closed by a piston connected to a spring of constant 2.00 X 103 N/m (see Fig. P19.50). with the spring relaxed, the cylinder is filled with 5.00 L of gas at a pressure of 1.00 atm and a temperature of 20.0°C. (a) If the piston has a cross-sectional area of 0.010 0 m2 and negligible
An aluminum pipe, 0.655 m long at 20.0°C and open at both ends, is used as a flute. The pipe is cooled to a low temperature but then is filled with air at 20.0°C as soon as you start to play it. After that, by how much does its fundamental frequency change as the metal rises in temperature from
A liquid has a density p. (a) Show that the fractional change in density for a change in temperature ΔT is Δp/ = -BΔT. What does the negative sign signify? (b) Fresh water has a maximum density of 1.000 0 g/cm3 at 4.0°C. At 10.0°C, its density is 0.999 7 g/cm3. What is ' for
Long-term space missions require reclamation of the oxygen in the carbon dioxide exhaled by the crew. In one method of reclamation, 1.00 mol of carbon dioxide produces 1.00 mol of oxygen and 1.00 mol of methane as a byproduct. The methane is stored in a tank under pressure and is available to
A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of mass m (Fig. P19.53) (a) If n moles of an ideal gas are in the cylinder at a temperature of T, what is the height h at which the piston is in equilibrium under its own weight? (b) What is the
A bimetallic strip is made of two ribbons of dissimilar metals bonded together. (a) First assume the strip is originally straight. As they are heated, the metal with the greater average coefficient of expansion expands more than the other, forcing the strip into an arc, with the outer radius
The Nova laser at Lawrence Livermore National Laboratory in California is used in studies of initiating controlled nuclear fusion (Section 45.4). It can deliver a power of 1.60 X 1013 W over a time interval of 2.50 ns. Compare its energy output in one such time interval to the energy required to
The rectangular plate shown in Figure P19.55 has an area Ai equal to If the temperature increases by ΔT, each dimension increases according to the equation ΔL = aLi ΔT, where & is the average coefficient of linear expansion. Show that the increase in area is ΔA = 2aAi ΔT.
A clock with a brass pendulum has a period of 1.000 s at 20.0°C. If the temperature increases to 30.0°C, (a) By how much does the period change, and (b) How much time does the clock gain or lose in one week?
(a) Derive an expression for the buoyant force on a spherical balloon, submerged in water, as a function of the depth below the surface, the volume of the balloon at the surface, the pressure at the surface, and the density of the water. (Assume water temperature does not change with depth) (b)
Consider an object with any one of the shapes displayed in Table 10.2. What is the percentage increase in the moment of inertia of the object when it is heated from 0°C to 100°C if it is composed of (a) copper or (b) aluminum? Assume that the average linear expansion coefficients shown in Table
A copper wire and a lead wire are joined together, end to end. The compound wire has an effective coefficient of linear expansion of 20.0 X 10-6 (°C)-1. What fraction of the length of the compound wire is copper?
Following a collision in outer space, a copper disk at 850°C is rotating about its axis with an angular speed of 25.0 rad/s. As the disk radiates infrared light, its temperature falls to 20.0°C. No external torque acts on the disk. (a) Does the angular speed change as the disk cools off?
Two concrete spans of a 250-m-long bridge are placed end to end so that no room is allowed for expansion (Fig. P19.61a). If a temperature increase of 20.0°C occurs, what is the height y to which the spans rise when they buckle (Fig P19.61b)?
Two concrete spans of a bridge of length L are placed end to end so that no room is allowed for expansion (Fig. P19.61a). If a temperature increase of ΔT occurs, what is the height y to which the spans rise when they buckle (Fig P19.61b)
A 1.50-kg iron horseshoe initially at 600°C is dropped into a bucket containing 20.0 kg of water at 25.0°C. What is the final temperature? (Ignore the heat capacity of the container, and assume that a negligible amount of water boils away.)
(a) Show that the density of an ideal gas occupying a volume V is given by p = PM/RT, where M is the molar mass. (b) Determine the density of oxygen gas at atmospheric pressure and 20.0°C
(a) Use the equation of state for an ideal gas and the definition of the coefficient of volume expansion, in the form β = (1/V) dV/dT, to show that the coefficient of volume expansion for an ideal gas at constant pressure is given by β = 1/T, where T is the absolute temperature. (b)
Starting with Equation 19.10, show that the total pressure P in a container filled with a mixture of several ideal gases is P = P1 + P2 + P3 + ., where P1, P2, . . . , are the pressures that each gas would exert if it alone filled the container (these individual pressures are called the partial
A sample of dry air that has a mass of 100.00 g, collected at sea level, is analyzed and found to consist of the following gases: Nitrogen (N2) = 75.52 g Oxygen (O2) = 23.15 g Argon (Ar) = 1.28 g Carbon dioxide (CO2) # 0.05 g Plus trace amounts of neon, helium, methane, and other gases. (a)
A 1.50-kg iron horseshoe initially at 600°C is dropped into a bucket containing 20.0 kg of water at 25.0°C. What is the final temperature? (Ignore the heat capacity of the container, and assume that a negligible amount of water boils away.
Helium gas is sold in steel tanks. If the helium is used to inflate a balloon, could the balloon lift the spherical tank the helium came in? Justify your answer. Steel will rupture if subjected to tensile stress greater than its yield strength of 5 X 108 N/m2. Suggestion: You may consider a steel
A cylinder that has a 40.0-cm radius and is 50.0 cm deep is filled with air at 20.0°C and 1.00 atm (Fig. P19.68a). A 20.0-kg piston is now lowered into the cylinder, compressing the air trapped inside (Fig. P19.68b). finally a 75.0-kg man stands on the piston, further compressing the air, which
An aluminum cup of mass 200 g contains 800 g of water in thermal equilibrium at 80.0°C. The combination of cup and water is cooled uniformly so that the temperature decreases by 1.50°C per minute. At what rate is energy being removed by heat? Express your answer in watts
The relationship Lf = Li (1 + αΔT) is an approximation that works when the average coefficient of expansion is small. If α is large, one must integrate the relationship dL/dT =αL to determine the final length. (a) Assuming that the coefficient of linear expansion is
A steel wire and a copper wire, each of diameter 2.000 mm, are joined end to end. At 40.0°C, each has an unscratched length of 2.000 m; they are connected between two fixed supports 4.000 m apart on a tabletop, so that the steel wire extends from x = -2.000 m to x = 0, the copper wire extends from
An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal equilibrium at 10.0°C. Two metallic blocks are placed into the water. One is a 50.0-g piece of copper at 80.0°C. The other block has a mass of 70.0 g and is originally at a temperature
A combination of 0.250 kg of water at 20.0°C, 0.400 kg of aluminum at 26.0°C, and 0.100 kg of copper at 100°C is mixed in an insulated container and allowed to come to thermal equilibrium. Ignore any energy transfer to or from the container and determine the final temperature of the mixture.
A steel guitar string with a diameter of 1.00 mm is stretched between supports 80.0 cm apart. The temperature is 0.0°C. (a) Find the mass per unit length of this string. (Use the value 7.86) 103 kg/m3 for the density.) (b) The fundamental frequency of transverse oscillations of the string is
In a chemical processing plant, a reaction chamber of fixed volume V0 is connected to a reservoir chamber of fixed volume 4V0 by a passage containing a thermally insulating porous plug. The plug permits the chambers to be at different temperatures. The plug allows gas to pass from either chamber to
A 1.00-km steel railroad rail is fastened securely at both ends when the temperature is 20.0°C. As the temperature increases, the rail begins to buckle. If its shape is an arc of a vertical circle, find the height h of the center of the rail when the temperature is 25.0°C. You will need to solve
A perfectly plane house roof makes an angle - with the horizontal. When its temperature changes, between Tc before dawn each day to Th in the middle of each afternoon, the roof expands and contracts uniformly with a coefficient of thermal expansion α1. Resting on the roof is a flat rectangular
Is it possible for two objects to be in thermal equilibrium if they are not in contact with each other? Explain
If water with a mass mh at temperature Th is poured into an aluminum cup of mass mAl containing mass mc of water at Tc, where Th > Tc , what is the equilibrium temperature of the system?
A water heater is operated by solar power. If the solar collector has an area of 6.00 m2 and the intensity delivered by sunlight is 550 W/m2, how long does it take to increase the temperature of 1.00 m3 of water from 20.0°C to 60.0°C?
Two thermally insulated vessels are connected by a narrow tube fitted with a valve that is initially closed. One vessel, of volume 16.8 L, contains oxygen at a temperature of 300 K and a pressure of 1.75 atm. The other vessel, of volume 22.4 L, contains oxygen at a temperature of 450 K and a
How much energy is required to change a 40.0-g ice cube from ice at -10.0°C to steam at 110°C?
A 50.0-g copper calorimeter contains 250 g of water at 20.0°C. How much steam must be condensed into the water if the final temperature of the system is to reach 50.0°C?
A 3.00-g lead bullet at 30.0°C is fired at a speed of 240 m/s into a large block of ice at 0°C, in which it becomes embedded. What quantity of ice melts?
Steam at 100°C is added to ice at 0°C. (a) Find the amount of ice melted and the final temperature when the mass of steam is 1.0 g and the mass of ice is 50.0 g. (b) What If? Repeat when the mass of steam is 1.00 g and the mass of ice is 50.0 g.
A 1.00-kg block of copper at 20.0°C is dropped into a large vessel of liquid nitrogen at 77.3 K. How many kilograms of nitrogen boil away by the time the copper reaches 77.3 K? (The specific heat of copper is 0.092 0 cal/g . °C. The latent heat of vaporization of nitrogen is 48.0 cal/g).
Assume that a hailstone at 0°C falls through air at a uniform temperature of 0°C and lands on a sidewalk also at this temperature. From what initial height must the hailstone fall in order to entirely melt on impact?
In an insulated vessel, 250 g of ice at 0°C is added to 600 g of water at 18.0°C. (a) What is the final temperature of the system? (b) How much ice remains when the system reaches equilibrium?
Two speeding lead bullets, each of mass 5.00 g, and at temperature 20.0°C, collide head-on at speeds of 500 m/s each. Assuming a perfectly inelastic collision and no loss of energy by heat to the atmosphere, describe the final state of the two-bullet system.
A sample of ideal gas is expanded to twice its original volume of 1.00 m3 in a quasi-static process for which P =αV 2, with α = 5.00 atm/m6, as shown in Figure P20.23. How much work is done on the expanding gas?
(a) Determine the work done on a fluid that expands from i to f as indicated in Figure P20.24. (b) What If? How much work is performed on the fluid if it is compressed from f to i along the same path?
An ideal gas is enclosed in a cylinder with a movable piston on top of it. The piston has a mass of 8 000 g and an area of 5.00 cm2 and is free to slide up and down, keeping the pressure of the gas constant. How much work is done on the gas as the temperature of 0.200 mol of the gas is raised from

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Physics 5th edition James S. Walker - Solutions

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