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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

Analysis of the periodic sound wave produced by a violin's G string includes three frequencies: 392, 588, and 980 Hz. What is the fundamental frequency?
Your friend needs advice on her newest "acoustic sculpture." She attaches one end of a steel wire, of diameter 4.00 mm and density 7860 kg/m 3, to a wall. After passing over a pulley, located 1.00 m from the wall, the other end of the wire is attached to a hanging weight. Below the horizontal
A sound wave arriving at your ear is transferred to the fluid in the cochlea. If the intensity in the fluid is 0.80 times that in air and the frequency is the same as for the wave in air, what will be the ratio of the pressure amplitude of the wave in air to that in the fluid? Approximate the fluid
In this problem, you will estimate the smallest kinetic energy of vibration that the human ear can detect. Suppose that a harmonic sound wave at the threshold of hearing (I = 1.0 × 10−12 W/m 2) is incident on the eardrum. The speed of sound is 340 m/s and the density of air is 1.3 kg/m 3. (a)
During a rehearsal, all eight members of the first violin section of an orchestra play a very soft passage. The sound intensity level at a certain point in the concert hall is 38.0 dB. What is the sound intensity level at the same point if only one of the violinists plays the same passage?
Find the speed of sound in mercury, which has a bulk modulus of 2.8 ( 1010 Pa and a density of 1.36 ( 104 kg/m3.
Derive Eq. (12-4) as: (a) Starting with Eq. (12-3), substitute T = TC + 273.15. (b) Apply the binomial approximation to the square root (see Appendix A.5) and simplify.
(a) Show that since the bulk modulus has SI units N/m2 and mass density has SI units kg/m3, Eq. (12-1) gives the speed of sound in m/s. Thus, the equation is dimensionally consistent. (b) Show that no other combination of B and r can give dimensions of speed. Thus, Eq. (12- 1) must be correct
Explain why it would be impossible to uniquely define the temperature of an object if the zeroth law of thermodynamics were violated?
Suppose we have two tanks, one containing helium gas and the other nitrogen gas. The two gases are at the same temperature and pressure. Which has the higher number density (or are they equal)? Which has the higher mass density (or are they equal)?
Explain why there is almost no hydrogen (H2) or helium (He) in Earth's atmosphere, yet both are present in Jupiter's atmosphere. Escape velocity from Earth is 11.2 km/s and escape velocity from Jupiter is 60 km/s.
In air under ordinary conditions (room temperature and atmospheric pressure), the average intermolecular distance is about 4 nm and the mean free path is about 0.1 μm. The diameter of a nitrogen molecule is about 0.3 nm. Explain how the mean free path can be so much larger than the average
In air under ordinary conditions (room temperature and atmospheric pressure), the average intermolecular distance is about 4 nm and the mean free path is about 0.1 μm. The diameter of a nitrogen molecule is about 0.3 nm. Which two distances should we compare to decide that air is dilute and can be
In air under ordinary conditions (room temperature and atmospheric pressure), the average intermolecular distance is about 4 nm and the mean free path is about 0.1 μm. The diameter of a nitrogen molecule is about 0.3 nm. What would it mean if the intermolecular distance and the molecular diameter
Explain how an automobile airbag protects the passenger from injury. Why would the airbag be ineffective if the gas pressure inside is too low when the passenger comes into contact with it? What about if it is too high?
Why do we call the temperature 0 K "absolute zero"? How is 0 K fundamentally different from 0°C or 0°F?
It takes longer to hard-boil an egg in Mexico City (2200 m above sea level) than it does in Amsterdam (parts of which are below sea level). Why? At higher altitudes, water boils at less than 100°C.]
What happens to a hole in a flat metal plate when the plate expands on being heated? Does the hole get larger or smaller?
Why would silver and brass probably not be a good choice of metals for a bimetallic strip (leaving aside the question of the cost of silver)? (See Table 13.2 .) Material ......................................( (10−6 K−1) Glass (Vycor)
One way to loosen the lid on a glass jar is to run it under hot water. How does that work?
Why must we use absolute temperature (temperature in kelvins) in the ideal gas law (PV = NkT)? Explain how using the Celsius scale would give nonsensical results.
Natural gas is sold by volume. In the United States, the price charged is usually per cubic foot. Given the price per cubic foot, what other information would you need in order to calculate the price per mole?
What are the SI units of mass density and number density? If two different gases have the same number density, do they have the same mass density?
On a warm summer day, the air temperature is 84°F. Express this temperature in (a) °C and (b) kelvins.
A lead rod and a common glass rod both have the same length when at 20.0 °C. The lead rod is heated to 50.0 °C. To what temperature must the glass rod be heated so that they are again at the same length?
Show that, in two gases at the same temperature, the rms speeds are inversely proportional to the square root of the molecular masses:
The SR-71 Blackbird reconnaissance aircraft is primarily made of titanium and typically flies at speeds above Mach 3. In flight, the length of the SR-71 increases by about 0.20 m from its takeoff length of 32.70 m. The average coefficient of linear expansion for titanium over the temperature range
In plants, water diffuses out through small openings known as stomatal pores. If D = 2.4 × 10−5 m2/s for water vapor in air, and the length of the pores is 2.5 × 10−5 m, how long does it take for a water molecule to diffuse out through the pore?
The alveoli have an average radius of 0.125 mm and are approximately spherical. If the pressure in the sacs is 1.00 × 105 Pa, and the temperature is 310 K (average body temperature), how many air molecules are in an alveolus?
A 10.0-L vessel contains 12 g of N2 gas at 20 °C. (a) Estimate the nearest-neighbor distance. (b) Is the gas dilute? Compare the nearest-neighbor distance to the diameter of an N2 molecule, about 0.3 nm.
During hibernation, an animal's metabolism slows down, and its body temperature lowers. For example, a California ground squirrel's body temperature lowers from 40.0 °C to 10.0 °C during hibernation. If we assume that the air in the squirrel's lungs is 75.0% N2 and 25.0% O2, by how much will the
A steel ring of inner diameter 7.00000 cm at 20.0 °C is to be heated and placed over a brass shaft of outer diameter 7.00200 cm at 20.0 °C. (a) To what temperature must the ring be heated to fit over the shaft? The shaft remains at 20.0 °C. (b) Once the ring is on the shaft and has cooled to
The inner tube of a Pyrex glass mercury thermometer has a diameter of 0.120 mm. The bulb at the bottom of the thermometer contains 0.200 cm3 of mercury. How far will the thread of mercury move for a change of 1.00 °C? Remember to take into account the expansion of the glass.
A wine barrel has a diameter at its widest point of 134.460 cm at a temperature of 20.0 °C. A circular iron band, of diameter 134.448 cm, is to be placed around the barrel at the widest spot. The iron band is 5.00 cm wide and 0.500 cm thick. (a) To what temperature must the band be heated to be
A 12.0-cm cylindrical chamber has an 8.00-cmdiameter piston attached to one end. The piston is connected to an ideal spring as shown. Initially, the gas inside the chamber is at atmospheric pressure and 20.0 °C and the spring is not compressed. When a total of 6.50 Ã—
The coefficient of linear expansion of brass is 1.9 × 10-5 °C − 1. At 20.0 °C, a hole in a sheet of brass has an area of 1.00 mm 2. How much larger is the area of the hole at 30.0 °C?
A bimetallic strip is made from metals with expansion coefficients a1 and a2 (with a2 > a1). The thickness of each layer is s. At some temperature T0, the bimetallic strip is relaxed and straight.(a) Show that, at temperature T0 + Î”T, the radius of curvature of the strip isAt T0, the lengths
Aluminum rivets used in airplane construction are made slightly too large for the rivet holes to be sure of a tight fit. The rivets are cooled with dry ice (−78.5 °C) before they are driven into the holes. If the holes have a diameter of 0.6350 cm at 20.5 °C, what should be the diameter of the
A temperature change ΔT causes a volume change ΔV but has no effect on the mass of an object. (a) Show that the change in density Δ( is given by Δ ( = − ((ΔT. (b) Find the fractional change in density (Δ(/() of a brass sphere when the temperature changes from 32 °C to −10.0 °C.
A cylindrical brass container with a base of 75.0 cm2 and height of 20.0 cm is filled to the brim with water when the system is at 25.0 °C. How much water overflows when the temperature of the water and the container is raised to 95.0 °C?
An ordinary drinking glass is filled to the brim with water (268.4 mL) at 2.0 °C and placed on the sunny pool deck for a swimmer to enjoy. If the temperature of the water rises to 32.0 °C before the swimmer reaches for the glass, how much water will have spilled over the top of the glass? Assume
Consider the situation described in Problem 15.(a) Take into account the expansion of the glass and calculate how much water will spill out of the glass. Compare your answer with the case where the expansion of the glass was not considered.(b) By what percentage has the answer changed when the
A steel sphere with radius 1.0010 cm at 22.0 °C must slip through a brass ring that has an internal radius of 1.0000 cm at the same temperature. To what temperature must the brass ring be heated so that the sphere, still at 22.0 °C, can just slip through?
A long, narrow steel rod of length 2.5000 m at 25 °C is oscillating as a pendulum about a horizontal axis through one end. If the temperature changes to 0 °C, what will be the fractional change in its period?
The George Washington Bridge crosses the Hudson River between New York and New Jersey. The span of the steel bridge is about 1.6 km. If the temperature can vary from a low of −15 °F in winter to a high of 105 °F in summer, by how much might the length of the span change over an entire year?
The temperature at which liquid nitrogen boils (at atmospheric pressure) is 77 K. Express this temperature in (a) °C and (b) °F.
A square brass plate, 8.00 cm on a side, has a hole cut into its center of area 4.90874 cm2 (at 20.0 °C). The hole in the plate is to slide over a cylindrical steel shaft of cross-sectional area 4.91000 cm2 (also at 20.0 °C). To what temperature must the brass plate be heated so that it can
A copper washer is to be fit in place over a steel bolt. Both pieces of metal are at 20.0 °C. If the diameter of the bolt is 1.0000 cm and the inner diameter of the washer is 0.9980 cm, to what temperature must the washer be raised so it will fit over the bolt? Only the copper washer is heated.
Repeat Problem 21, but now the copper washer and the steel bolt are both raised to the same temperature. At what temperature will the washer fit on the bolt?A copper washer is to be fit in place over a steel bolt. Both pieces of metal are at 20.0 °C. If the diameter of the bolt is 1.0000 cm and
A steel rule is calibrated for measuring lengths at 20.00 °C. The rule is used to measure the length of a Vycor glass brick; when both are at 20.00 °C, the brick is found to be 25.00 cm long. If the rule and the brick are both at 80.00 °C, what would be the length of the brick as measured by the
The fuselage of an Airbus A340 has a circumference of 17.72 m on the ground. The circumference increases by 26 cm when it is in flight. Part of this increase is due to the pressure difference between the inside and outside of the plane and part is due to the increase in the temperature due to air
A flat square of side s0 at temperature T0 expands by Î”s in both length and width when the temperature increases by Î”T. The original area is s02 = A0 and the final area is (s0 + Î” s)2 = A. Show that if Î”s(Although we derive this relation for a square
The volume of a solid cube with side s0 at temperature T0 is V0 = s03. Show that if Î”sAnd therefore that ( = 3(. (Although we derive this relation for a cube, it applies to a solid of any shape.)
Use the definition that 1 mol of 12C (carbon-12) atoms has a mass of exactly 12 g, along with Avogadro's number, to derive the conversion between atomic mass units and kg.
Find the molar mass of ammonia (NH3).
Find the mass (in kg) of one molecule of CO2.
(a) At what temperature (if any) does the numerical value of Celsius degrees equal the numerical value of Fahrenheit degrees? (b) At what temperature (if any) does the numerical value of kelvins equal the numerical value of Fahrenheit degrees?
The mass of 1 mol of 13C (carbon-13) is 13.003 g. (a) What is the mass in u of one 13C atom? (b) What is the mass in kilograms of one 13C atom?
Estimate the number of H2O molecules in a human body of mass 80.2 kg. Assume that, on average, water makes up about 62% of the mass of a human body.
The mass density of diamond (a crystalline form of carbon) is 3500 kg/m3. How many carbon atoms per cm3 are there?
How many hydrogen atoms are present in 684.6 g of sucrose (C12H22O11)?
How many moles of He are in 13 g of He?
The principal component of natural gas is methane (CH4). How many moles of CH4 are present in 144.36 g of methane?
What is the mass of one gold atom in kilograms?
Air at room temperature and atmospheric pressure has a mass density of 1.2 kg/m3. The average molecular mass of air is 29.0 u. How many molecules are in 1.0 cm3 of air?
At 0.0 °C and 1.00 atm, 1.00 mol of a gas occupies a volume of 0.0224 m3. (a) What is the number density? (b) Estimate the average distance between the molecules. (c) If the gas is nitrogen (N2), the principal component of air, what is the total mass and mass density?
Sand is composed of SiO2. Find the order of magnitude of the number of silicon (Si) atoms in a grain of sand. Approximate the sand grain as a sphere of diameter 0.5 mm and an SiO2 molecule as a sphere of diameter 0.5 nm.
A room air conditioner causes a temperature change of −6.0 °C. (a) What is the temperature change in kelvins? (b) What is the temperature change in °F?
A flight attendant wants to change the temperature of the air in the cabin from 18 °C to 24 °C without changing the number of moles of air per m3. What fractional change in pressure would be required?
A cylinder in a car engine takes Vi = 4.50 × 10−2 m3 of air into the chamber at 30 ° C and at atmospheric pressure. The piston then compresses the air to one-ninth of the original volume (0.111 Vi) and to 20.0 times the original pressure (20.0 Pi). What is the new temperature of the air?
A tire with an inner volume of 0.0250 m 3 is filled with air at a gauge pressure of 36.0 psi. If the tire valve is opened to the atmosphere, what volume outside of the tire does the escaping air occupy? Some air remains within the tire occupying the original volume, but now that remaining air is at
Verify, using the ideal gas law, the assertion in Problem 38 that 1.00 mol of a gas at 0.0 °C and 1.00 atm occupies a volume of 0.0224 m3.
Incandescent light bulbs are filled with an inert gas to lengthen the filament life. With the current off (at T = 20.0 °C), the gas inside a light bulb has a pressure of 115 kPa. When the bulb is burning, the temperature rises to 70.0 °C. What is the pressure at the higher temperature?
What fraction of the air molecules in a house must be pushed outside while the furnace raises the inside temperature from 16.0 °C to 20.0 °C? The pressure does not change since the house is not 100% airtight.
What is the mass density of air at P = 1.0 atm and T = (a) − 10 °C and (b) 30 °C? The average molecular mass of air is approximately 29 u.
A constant volume gas thermometer containing helium is immersed in boiling ammonia (−33 °C) and the pressure is read once equilibrium is reached. The thermometer is then moved to a bath of boiling water (100.0 °C). After the manometer was adjusted to keep the volume of helium constant, by what
A hydrogen balloon at Earth's surface has a volume of 5.0 m3 on a day when the temperature is 27 ° C and the pressure is 1.00 × 105 N/m2. The balloon rises and expands as the pressure drops. What would the volume of the same number of moles of hydrogen be at an altitude of 40 km where the
Aliens from the planet Jeenkah have based their temperature scale on the boiling and freezing temperatures of ethyl alcohol. These temperatures are 78 °C and −114 °C, respectively. The people of Jeenkah have six digits on each hand, so they use a base-12 number system and have decided to have
An ideal gas that occupies 1.2 m3 at a pressure of 1.0 × 105 Pa and a temperature of 27 °C is compressed to a volume of 0.60 m3 and heated to a temperature of 227 °C. What is the new pressure?
A diver rises quickly to the surface from a 5.0-m depth. If she did not exhale the gas from her lungs before rising, by what factor would her lungs expand? Assume the temperature to be constant and the pressure in the lungs to match the pressure outside the diver's body. The density of seawater is
In intergalactic space, there is an average of about one hydrogen atom per cm3 and the temperature is 3 K. What is the absolute pressure?
A tank of compressed air of volume 1.0 m3 is pressurized to 20.0 atm at T = 273 K. A valve is opened and air is released until the pressure in the tank is 15.0 atm. How many air molecules were released?
A mass of 0.532 kg of molecular oxygen is contained in a cylinder at a pressure of 1.0 × 105 Pa and a temperature of 0.0 °C. What volume does the gas occupy?
A bubble rises from the bottom of a lake of depth 80.0 m, where the temperature is 4 °C. The water temperature at the surface is 18 °C. If the bubble's initial diameter is 1.00 mm, what is its diameter when it reaches the surface? (Ignore the surface tension of water. Assume the bubble warms as
A bubble with a volume of 1.00 cm3 forms at the bottom of a lake that is 20.0 m deep. The temperature at the bottom of the lake is 10.0°C. The bubble rises to the surface where the water temperature is 25.0°C. Assume that the bubble is small enough that its temperature always matches that of its
A scuba diver has an air tank with a volume of 0.010 m3. The air in the tank is initially at a pressure of 1.0 × 107 Pa. Assuming that the diver breathes 0.500 L/s of air, find how long the tank will last at depths of (a) 2.0 m and (b) 20.0 m. (Make the same assumptions as in Example 13.6.)
An emphysema patient is breathing pure O2 through a face mask. The cylinder of O2 contains 0.60 ft3 of O2 gas at a pressure of 2200 lb/in2. (a) What volume would the oxygen occupy at atmospheric pressure (and the same temperature)? (b) If the patient takes in 8 L/min of O2 at atmospheric pressure,
Consider the expansion of an ideal gas at constant pressure. The initial temperature is T0 and the initial volume is V0.(a) Show that ΔV/V0 = (ΔT, where ( = 1/ T0.(b) Compare the coefficient of volume expansion b for an ideal gas at 20 °C to the values for liquids and gases listed in Table
A 2.4-m length of copper pipe extends directly from a hot-water heater in a basement to a faucet on the first floor of a house. If the faucet isn't fixed in place, how much will it rise when the pipe is heated from 20.0 °C to 90.0 °C. Ignore any increase in the size of the faucet itself or of the
What is the temperature of an ideal gas whose molecules have an average translational kinetic energy of 3.20 × 10−20 J?
What is the total translational kinetic energy of the gas molecules of 0.420 mol of air at atmospheric pressure that occupies a volume of 1.00 L (0.00100 m3)?
What is the kinetic energy per unit volume in an ideal gas at (a) P = 1.00 atm and (b) P = 300.0 atm?
Show that, for an ideal gas,Where P is the pressure, r is the mass density, and vrms is the rms speed of the gas molecules.
Estimate the percentage of the O2 molecules in air at 0.0 °C and 1.00 atm that are moving faster than the speed of sound in air at that temperature (see Fig. 13.13 ). Material................................................ ( (10−6
What is the total internal kinetic energy of 1.0 mol of an ideal gas at 0.0 °C and 1.00 atm?
If 2.0 mol of nitrogen gas (N2) are placed in a cubic box, 25 cm on each side, at 1.6 atm of pressure, what is the rms speed of the nitrogen molecules?
There are two identical containers of gas at the same temperature and pressure, one containing argon and the other neon. What is the ratio of the rms speed of the argon atoms to that of the neon atoms? The atomic mass of argon is twice that of neon.
A smoke particle has a mass of 1.38 × 10−17 kg and it is randomly moving about in thermal equilibrium with room temperature air at 27 °C. What is the rms speed of the particle?
Find the rms speed in air at 0.0 °C and 1.00 atm of (a) The N2 molecules, (b) The O2 molecules, and (c) The CO2 molecules.
Two 35.0-cm metal rods, one made of copper and one made of aluminum, are placed end to end, touching each other. One end is fixed, so that it cannot move. The rods are heated from 0.0 °C to 150 °C. How far does the other end of the system of rods move?

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