Question: The driver from Practice Problem 13.3

> A 2.0 kg block of copper at 100.0°C is placed into 1.0 kg of water in a 2.0 kg iron pot. The water and the iron pot are at 25.0°C just before the copper block is placed into the pot. What is the final temperature of the water, assuming negligible heat fl

> A 75 g cube of ice at −10.0°C is placed in 0.500 kg of water at 50.0°C in an insulating container so that no heat is lost to the environment. Will the ice melt completely? What will be the final temperature of this system?

> The student from Problem 79 realizes that standing naked in a cold room will not give him the desired weight loss results since it is much less efficient than simply exercising. So he decides to “burn” calories through conduction. He fills the bathtub wi

> (a) How much ice at −10.0°C must be placed in 0.250 kg of water at 25.0°C to cool the water to 0°C and melt all of the ice? (b) If half that amount of ice is placed in the water, what is the final temperature of the water?

> Before the discovery of the neutron, one theory of the nucleus proposed that the nucleus contains protons and electrons. For example, the helium-4 nucleus would contain 4 protons and 2 electrons instead of—as we now know to be true—2 protons and 2 neutro

> A blacksmith heats a 0.38 kg piece of iron to 498°C in his forge. After shaping it into a decorative design, he places it into a bucket of water to cool. If the available water is at 20.0°C, what minimum amount of water must be in the bucket to cool the

> In the human nervous system, signals are transmitted along neurons as action potentials that travel at speeds of up to 100 m/s. (An action potential is a traveling influx of sodium ions through the membrane of a neuron.) The signal is passed from one neu

> A birch tree loses 618 mg of water per minute through transpiration (evaporation of water through stomatal pores). What is the rate of heat lost through transpiration?

> A container has a large cylindrical lower part with a long thin cylindrical neck open at the top. The lower part of the container holds 12.5 m3 of water and the surface area of the bottom of the container is 5.00 m2. The height of the lower part of the c

> An x-ray photon with wavelength 6.00 pm collides with a free electron initially at rest. What is the maximum possible kinetic energy acquired by the electron?

> One end of a cylindrical iron rod of length 1.00 m and of radius 1.30 cm is placed in the blacksmith's fire and reaches a temperature of 327°C. If the other end of the rod is being held in your hand (37°C), what is the rate of heat flow along the rod? Th

> If a leaf is to maintain a temperature of 40°C (reasonable for a leaf), it must lose 250 W/m2 by transpiration (evaporative heat loss). Note that the leaf also loses heat by radiation, but we will ignore this. How much water is lost after 1 h through tra

> A spring of force constant k = 8.4 × 103 N/m is compressed by 0.10 m. It is placed into a vessel containing 1.0 kg of water and then released. Assuming all the energy from the spring goes into heating the water, find the change in temperature of the wate

> The graph shows the change in temperature as heat is supplied to a certain mass of ice initially at −80.0°C. What is the mass of the ice?

> A 0.500 kg slab of granite is heated so that its temperature increases by 7.40°C. The amount of heat supplied to the granite is 2.93 kJ. Based on this information, what is the specific heat of granite?

> Repeat Problem 41 without ignoring the temperature change of the glass. The glass has a mass of 350 g and the specific heat of the glass is 0.837 kJ/(kg·K). By what percentage does the answer change from the answer for Problem 41?

> Two 62 g ice cubes are dropped into 186 g of water in a glass. If the water is initially at a temperature of 24°C and the ice is at −15°C, what is the final temperature of the drink?

> Tina is going to make iced tea by first brewing hot tea, then adding ice until the tea cools. How much ice, at a temperature of −10.0°C, should be added to a 2.00 × 10−4 m3 glass of tea at 95.0°C to cool the tea to 10.0°C? Ignore the temperature change o

> A flywheel (a massive disk) rotates with constant angular acceleration. For a point on the rim of the flywheel, is the tangential acceleration component constant? Is the radial acceleration component constant?

> Imagine a trip where you drive along an east-west highway at 80.0 km/h for 45.0 min and then you turn onto a highway that runs 38.0° north of east and travel at 60.0 km/h for 30.0 min. (a) What is your average velocity for the trip? (b) What is your av

> A sperm whale can reach depths of 2500 m below the surface of the ocean. What is the pressure on the whale’s skin at that depth, assuming that the density of seawater is constant from the surface to that depth?

> A wall consists of a layer of wood outside and a layer of insulation inside. The temperatures inside and outside the wall are +22°C and −18°C; the temperature at the wood/insulation boundary is −8.0°C. By what factor would the heat loss through the wall

> What mass of water at 25.0°C added to a Styrofoam cup containing two 50.0 g ice cubes from a freezer at −15.0°C will result in a final temperature of 5.0°C for the drink?

> A hand pump is being used to inflate a bicycle tire that has a gauge pressure of 40.0 lb/in2. If the pump is a cylinder of length 18.0 in. with a cross-sectional area of 3.00 in.2, how far down must the piston be pushed before air will flow into the tire

> 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?

> Ten students take a test and get the following scores: 83, 62, 81, 77, 68, 92, 88, 83, 72, and 75. What are the average value, the rms value, and the most probable value, respectively, of these test scores?

> Platelet cells in blood play an essential role in the formation of clots and exist in normal human blood at the level of about 200 000 per cubic millimeter. In order to illustrate that diffusion alone is not responsible for transporting platelets, consid

> An iron cannonball of radius 0.08 m has a cavity of radius 0.05 m that is to be filled with gunpowder. If the measurements were made at a temperature of 22°C, how much extra volume of gunpowder, if any, will be required to fill 500 cannonballs when the t

> Your friend is 3.0 m away from you in a room. There are no significant air currents. She opens a bottle of perfume, and you first smell it 20 s later. How long would it have taken for you to smell it if she had been 6.0 m away instead?

> The volume of air taken in by a warm-blooded vertebrate in the Andes Mountains is 210 L/day at standard temperature and pressure (i.e., 0°C and 1 atm). If the air in the lungs is at 39°C, under a pressure of 450 mm Hg, and we assume that the vertebrate t

> Estimate the time it takes a sucrose molecule to move 5.00 mm in one direction by diffusion in water. Assume there are no currents in the water.

> A beam of electrons of mass me is deflected vertically by the uniform electric field between two oppositely charged, parallel metal plates. The plates are a distance d apart, and the potential difference between the plates is ΔV. (a) What is

> A toy cart of mass m1 moves on frictionless wheels as it is pulled by a string under tension T. A block of mass m2 rests on top of the cart. The coefficient of static friction between the cart and the block is μs. Find the maximum tension T that will not

> A marble of mass 10 g is confined to a box 10 cm long and moves at a speed of 2 cmis. (a) What is the marble's quantum number n? (b) Why can we not observe the quantization of the marble's energy? [Hint: Calculate the energy difference between states n

> At a normal body temperature of 37.0°C, (a) what is the average kinetic energy of the gas molecules in the lungs? (b) If a fever increases the temperature to 37.8°C, by what percentage does the average kinetic energy of the molecules increase?

> About how long will it take a perfume molecule to diffuse a distance of 5.00 m in one direction in a room if the diffusion constant is 1.00 × 10−5 m2/s? Assume that the air is perfectly still—there are no air currents.

> The data in the following table are from a constant-volume gas thermometer experiment. The volume of the gas was kept constant, while the temperature was changed. The resulting pressure was measured. Plot the data on a pressure versus temperature diagram

> Estimate the mean free path of a N2 molecule in air at (a) sea level (P ≈ 100 kPa and T ≈ 290 K), (b) the top of Mt. Everest (altitude = 8.8 km, P ≈ 50 kPa, and T ≈ 230 K), and (c) an altitude of 30 km (P ≈ 1 kPa and T ≈ 230 K). For simplicity, assume

> A certain acid has a molecular mass of 63 u. By mass, it consists of 1.6% hydrogen, 22.2% nitrogen, and 76.2% oxygen. What is the chemical formula for this acid?

> At high altitudes, water boils at a temperature lower than 100.0°C due to the lower air pressure. A rule of thumb states that the time to hard-boil an egg doubles for every 10.0°C drop in temperature. What activation energy does this rule imply for the c

> Suppose due to a bad break of your femur, you require the insertion of a titanium rod to help the fracture heal. The coefficient of linear expansion for titanium is α = 8.6 × 10−6 K−1, and the length of the rod when it is in equilibrium with the leg bone

> The reaction rate for the hydrolysis of benzoyl-L-arginine amide by trypsin at 10.0°C is 1.878 times faster than that at 5.0°C. Assuming that the reaction rate is exponential as in Eq. (13-41), what is the activation energy?

> How high can you suck water up a straw? The pressure in the lungs can be reduced to about 10 kPa below atmospheric pressure.

> Consider the sphere and ring of Problem 20. What must the final temperature be if both the ring and the sphere are heated to the same final temperature?

> A crate of books is to be put on a truck by rolling it up an incline of angle θ using a dolly. The total mass of the crate and the dolly is m. Assume that rolling the dolly up the incline is the same as sliding it up a frictionless surface. (a) What is

> The reaction rate for the prepupal development of male Drosophila is temperature-dependent. Assuming that the reaction rate is exponential as in Eq. (13-41), the activation energy for this development is 2.81 × 10−19 J. A Drosophila is originally at 10.0

> The speed of a satellite in circular orbit around a planet does not depend on the mass of the satellite. Does it depend on the mass of the planet? Explain.

> An iron bridge girder (Y = 2.0 × 1011 N/m2) is constrained between two rock faces whose spacing doesn't change. At 20.0°C the girder is relaxed. How large a stress develops in the iron if the sun heats the girder to 40.0°C?

> Show that the rms speed of a molecule in an ideal gas at absolute temperature T is given by where M is the molar mass—the mass of the gas per mole.

> Show that the rms speed of a molecule in an ideal gas at absolute temperature T is given by where m is the mass of a molecule.

> In a certain bimetallic strip (see Fig. 13.7) the brass strip is 0.100% longer than the steel strip at a temperature of 275°C. At what temperature do the two strips have the same length?

> On a cold day, you take a breath, inhaling 0.50 L of air whose initial temperature is −10°C. In your lungs, its temperature is raised to 37°C. Assume that the pressure is 101 kPa and that the air may be treated as an ideal gas. What is the total change i

> A giraffe’s brain is approximately 3.4 m above its heart. Estimate the minimum gauge pressure that its heart must produce to move the blood to his brain. Ignore any effects from the blood flow through arteries of different area, and assume that giraffe b

> A hot air balloon with a volume of 12.0 m3 is initially filled with air at a pressure of 1.00 atm and a temperature of 19.0°C. When the balloon air is heated, the volume and the pressure of the balloon remain constant because the balloon is open to the a

> What is the temperature of an ideal gas whose molecules in random motion have an average translational kinetic energy of 4.60 × 10−20 J?

> A mass-spring system oscillates so that the position of the mass is described by x = (−10 cm) cos [(1.57 rad/s)t]. Make a motion diagram that has a dot for the position of the mass at t = 0, t = 0.2 s, t = 0.4 s, …, t = 4 s. The time interval between con

> A Pyrex container is filled to the very top with 4.00 L of water. Both the container and the water are at a temperature of 90.0°C. When the temperature has cooled to 20.0°C, how much additional water can be added to the container?

> If the upper atmosphere of Jupiter has a temperature of 160 K and the escape speed is 60 km/s, would an astronaut expect to find much hydrogen there?

> At the beginning of a 3.0 h plane trip, you are traveling due north at 192 km/h. At the end, you are traveling 240 km/h in the northwest direction (45° west of north). (a) Draw your initial and final velocity vectors. (b) Find the change in your veloci

> Which fundamental force is responsible for each of the decays shown here? [Hint: In each case, one of the decay products reveals the interaction force.] (a)

> A 12.0 cm cylindrical chamber has an 8.00 cm diameter 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

> What are the rms speeds of helium atoms, and nitrogen, hydrogen, and oxygen molecules at 25°C?

> The diameter of an oxygen (O2) molecule is approximately 0.3 nm. For an oxygen molecule in air at atmospheric pressure and 20°C, estimate the average magnitudes of these quantities during a 1.0 s time interval: (a) the distance traveled between collisio

> Each of six barrels is filled to a height h above the bottom with a liquid of density ρ. Each barrel has a hole of radius r in its side. The center of each hole is 20 cm above the barrel bottom. A plug in the hole keeps the liquid from escaping. Rank the

> 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.

> Estimate the percentage of the O2 molecules in air at 30°C that are moving faster than the speed of sound in air at that temperature (see Fig. 13.13).

> 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?

> How far does the object move from t = 0 to t = 3 s?

> A sealed cylinder contains a sample of ideal gas at a pressure of 2.0 atm. The rms speed of the molecules is v0. (a) If the rms speed is then reduced to 0.90v0, what is the pressure of the gas? (b) By what percentage does the speed of sound in the gas

> 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 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 th

> 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?

> In uniform circular motion, the net force is perpendicular to the velocity and changes the direction of the velocity but not the speed. If a projectile is launched horizontally, the net force (ignoring air resistance) is perpendicular to the initial velo

> 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 output power of a laser pointer is about 1 mW. (a) What are the energy and momentum of one laser photon if the laser wavelength is 670 nm? (b) How many photons per second are emitted by the laser? (c) What is the average force on the laser due to t

> What is the total internal kinetic energy of 1.0 mol of an ideal gas at 0.0°C and 1.00 atm?

> 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 Δρ is given by Δρ = −βρ ΔT. (b) Find the fractional change in density (Δρ/ρ) of a brass sphere when the temperature changes

> Rank the six gases of Problem 43 in order of the total translational kinetic energy, greatest to least.

> 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?

> Rank the time intervals in order of decreasing velocity vx, from largest positive to largest negative.

> Show that, for an ideal gas, where P is the pressure, ρ is the mass density, and vrms is the rms speed of the gas molecules.

> (a) Calculate Earth's escape speed—the minimum speed needed for an object near the surface to escape Earth's gravitational pull. [Hint: Use conservation of energy and ignore air resistance.] (b) Calculate the average speed of a hydrogen molecule (H2) at

> What is the kinetic energy per unit volume in an ideal gas at (a) P = 1.00 atm and (b) P = 300.0 atm?

> Michael has set the gauge pressure of the tires on his car to 36.0 lb/in2. He draws chalk lines around the edges of the tires where they touch the driveway surface to measure the area of contact between the tires and the ground. Each front tire has a con

> What is the total translational kinetic energy of the gas molecules of air at atmospheric pressure that occupies a volume of 1.00 L?

> Each of five cylindrical drums with radius R is filled to a height h above the bottom with a liquid of density ρ. Rank the drums in order of the pressure at the bottom of the drum, largest to smallest. (a) R = 40 cm, h = 80 cm, ρ = 1000 kg/m3 (b) R = 40

> John drives 16 km directly west from Orion to Chester at a speed of 90 km/h, then directly south for 8.0 km to Seiling at a speed of 80 km/h, then finally 34 km southeast to Oakwood at a speed of 100 km/h. (a) What was the change in velocity during this

> A bimetallic strip is made from metals with expansion coefficients α1 and α2 (with α2 > α1). The thickness of each layer is s. At some temperature T0, the bimetallic strip is relaxed and straight

> What is the temperature of an ideal gas whose molecules have an average translational kinetic energy of 3.20 × 10−20 J?

> 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

> 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 = β ΔT, where β = 1/T0. (b) Compare the coefficient of volume expansion β for an ideal gas at 20°C to the value

> Rank the time intervals in order of increasing speed.

> Two slits separated by 20.0 µm are illuminated by light of wavelength 0.50 µm. If the screen is 8.0 m from the slits, what is the distance between the m = 0 and m = 1 bright fringes?

> 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 acco

> 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 tensi

> A steel ring of inner diameter 7.000 00 cm at 20.0°C is to be heated and placed over a brass shaft of outer diameter 7.002 00 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

> In the Netherlands, a dike holds back the sea from a town below sea level. The dike springs a leak 3.0 m below the water surface. If the area of the hole in the dike is 1.0 cm2, what force must the Dutch boy exert to save the town?

> 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.

> 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.

> 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?