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physics
mechanics

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

What are the rms speeds of helium atoms, and nitrogen, hydrogen, and oxygen molecules at 25 °C?
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?
A sealed cylinder contains a sample of ideal gas at a pressure of 2.0 atm. The rms speed of the molecules is v0. If the rms speed is then reduced to 0.90 v0, what is the pressure of the gas?
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?
Show that the rms speed of a molecule in an ideal gas at absolute temperature T is given byWhere k is Boltzmann's constant and m is the mass of a molecule.
Show that the rms speed of a molecule in an ideal gas at absolute temperature T is given bywhere M is the molar mass -the mass of the gas per mole.
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. (13-24), what is the activation energy?
The reaction rate for the prepupal development of male Drosophila is temperature-dependent. Assuming that the reaction rate is exponential as in Eq. (13-24), the activation energy for this development is then 2.81 × 10−19 J. A Drosophila is originally at 10.00 ° C and its temperature is
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 chemical reactions that occur when the egg
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 that air is pure nitrogen gas. The
Steel railroad tracks of length 18.30 m are laid at 10.0 °C. How much space should be left between the track sections if they are to just touch when the temperature is 50.0 °C?
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.
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.
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 driver from Practice Problem 13.3 fills his 18.9-L steel gasoline can in the morning when the temperature of the can and the gasoline is 15.0 °C and the pressure is 1.0 atm, but this time he remembers to replace the tightly fitting cap after filling the can. Assume that the can is completely
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?
Consider the sphere and ring of Problem 17. What must the final temperature be if both the ring and the sphere are heated to the same final temperature?
Agnes Pockels (1862-1935) was able to determine Avogadro's number using only a few household chemicals, in particular oleic acid, whose formula is C18H34O2. (a) What is the molar mass of this acid? (b) The mass of one drop of oleic acid is 2.3 × 10−5 g and the volume is 2.6 × 10−5 cm 3 . How
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?
These data 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. Based on these data, estimate the value of absolute zero in
Given that our body temperature is 98.6 °F, (a) What is the average kinetic energy of the molecules in the air in our lungs? (b) If our temperature has increased to 100.0 °F, by what percentage has the kinetic energy of the molecules increased?
A highway is made of concrete slabs that are 15 m long at 20.0 °C. (a) If the temperature range at the location of the highway is from −20.0 °C to + 40.0 °C, what size expansion gap should be left (at 20.0 °C) to prevent buckling of the highway? (b) How large are the gaps at −20.0 °C?
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 takes in an average volume of 100 cm3 per
As a Boeing 747 gains altitude, the passenger cabin is pressurized. However, the cabin is not pressurized fully to atmospheric (1.01 × 105 Pa), as it would be at sea level, but rather pressurized to 7.62 × 104 Pa. Suppose a 747 takes off from sea level when the temperature in the airplane is 25.0
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 temperature is 30 °C?
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?
A hand pump is being used to inflate a bicycle tire that has a gauge pressure of 40.0 psi. 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?
An ideal gas in a constant-volume gas thermometer (Fig. 13.11) is held at a volume of 0.500 L. As the temperature of the gas is increased by 20.0 °C, the mercury level on the right side of the manometer must rise by 8.00 mm in order to keep the gas volume constant.(a) What is the slope of a
A cylinder with an interior cross-sectional area of 70.0 cm2 has a moveable piston of mass 5.40 kg at the top that can move up and down without friction. The cylinder contains 2.25 × 10−3 mol of an ideal gas at 23.0 °C. (a) What is the volume of the gas when the piston is in equilibrium? Assume
Estimate the average distance between air molecules at 0.0 °C and 1.00 atm.
If you wanted to make a scale model of air at 0.0 °C and 1.00 atm, using ping-pong balls (diameter, 3.75 cm) to represent the N2 molecules (diameter, 0.30 nm), (a) How far apart on average should the ping-pong balls be at any instant? (b) How far would a ping-pong ball travel on average before
For divers going to great depths, the composition of the air in the tank must be modified. The ideal composition is to have approximately the same number of O2 molecules per unit volume as in surface air (to avoid oxygen poisoning), and to use helium instead of nitrogen for the remainder of the gas
Explain the theory behind the pressure cooker. How does it speed up cooking times?
When you eat a pizza that has just come from the oven, why is it that you are apt to burn the roof of your mouth with the first bite although the crust of the pizza feels only warm to your hand?
Explain why the molar specific heat of a diatomic gas such as O2 is larger than that of a monatomic gas such as Ne.
At very low temperatures, the molar specific heat of hydrogen (H2) is CV = 1.5 R. At room temperature, CV = 2.5 R. Explain.
A cup of hot coffee has been poured, but the coffee drinker has a little more work to do at the computer before she picks up the cup. She intends to add some milk to the coffee. To keep the coffee hot as long as possible, should she add the milk at once, or wait until just before she takes her
Would heat loss be reduced or increased by increasing the usual air gap, 1 to 2 cm, between commercially made double-paned windows? Explain your reasoning.
A study of food preservation in Britain discovered that the temperature of meat that is kept in transparent plastic packages and stored in open and lighted freezers can be as much as 12°C above the temperature of the freezer. Why is this? How could this be prevented?
When an old movie has a scene of someone ironing, the person is often shown testing the heat of a hot flat iron with a moistened finger. Why is this safe to do?
Which possesses more total internal energy, the water within a large, partially ice-covered lake in winter or a 6-cup teapot filled with hot tea? Explain.
A room in which the air temperature is held constant may feel warm in the summer but cool in the winter. Explain.
Many homes are heated with "radiators," which are hollow metal devices filled with hot water or steam and located in each room of the house. They are sometimes painted with metallic, high-gloss silver paint so that they look well polished. Does this make them better radiators of heat? If not, what
The two objects must be in thermal equilibrium with each other and the walls of the evacuated chamber in which they reside. If an object were to absorb more heat energy than it emitted, its temperature would change and the system would no longer be in thermal equilibrium. Each body must therefore
Even though heat is not a fluid, Eq. (14-11) has a close analogy in Poiseuille's law, which describes the viscous flow of a fluid through a pipe.In Eq 14.11(a) Explain the analogy. (b) For two or more thermal Conductors in series, the total thermal resistance is just the sum of the thermal
Why do lakes and rivers freeze first at their surfaces?
Why are vineyards planted along lakeshores or riverbanks in cold climates?
A mass of 1.4 kg of water at 22°C is poured from a height of 2.5 m into a vessel containing 5.0 kg of water at 22°C. (a) How much does the internal energy of the 6.4 kg of water increase? (b) Is it likely that the water temperature increases? Explain.
What is the heat capacity of 20.0 kg of silver?
On a very hot summer day, Daphne is off to the park for a picnic. She puts 0.10 kg of ice at 0°C in a thermos and then adds a grape-flavored drink, which she has mixed from a powder using room temperature water (25°C). How much grape-flavored drink will just melt all the ice?
It requires 17.10 kJ to melt 1.00 × 102 g of urethane [CO2 (NH2)C2H5] at 48.7°C. What is the latent heat of fusion of urethane in kJ/mol?
A 20.0-g lead bullet leaves a rifle at a temperature of 47.0°C and travels at a velocity of 5.00 × 102 m/s until it hits a large block of ice at 0°C and comes to rest within it. How much ice will melt?
What is the heat capacity of a gold ring that has a mass of 5.00 g?
If 125.6 kJ of heat are supplied to 5.00 × 102 g of water at 22°C, what is the final temperature of the water?
It is a damp, chilly day in a New England seacoast town suffering from a power failure. To warm up the cold, clammy sheets, Jen decides to fill hot water bottles to tuck between the sheets at the foot of the beds. If she wishes to heat 2.0 L of water on the wood stove from 20.0°C to 80.0°C, how
An 83-kg man eats a banana of energy content 1.00 × 102 kcal. If all of the energy from the banana is converted into kinetic energy of the man, how fast is he moving, assuming he starts from rest?
A high jumper of mass 60.0 kg consumes a meal of 3.00 × 103 kcal prior to a jump. If 3.3% of the energy from the food could be converted to gravitational potential energy in a single jump, how high could the athlete jump?
What is the heat capacity of a 30.0-kg block of ice?
What is the heat capacity of 1.00 m 3 of(a) Aluminum?(b) Iron?See Table 9.1 for density values.
What is the heat capacity of a system consisting of (a) A 0.450-kg brass cup filled with 0.050 kg of water? (b) 7.5 kg of water in a 0.75-kg aluminum bucket?
A 0.400-kg aluminum teakettle contains 2.00 kg of water at 15.0°C. How much heat is required to raise the temperature of the water (and kettle) to 100.0°C?
The water passing over Victoria Falls, located along the Zambezi River on the border of Zimbabwe and Zambia, drops about 105 m. How much internal energy is produced per kilogram as a result of the fall?
How much heat is required to raise the body temperature of a 50.0-kg woman from 37.0°C to 38.4°C?
It takes 880 J to raise the temperature of 350 g of lead from 0 to 20.0°C. What is the specific heat of lead?
A mass of 1.00 kg of water at temperature T is poured from a height of 0.100 km into a vessel containing water of the same temperature T, and a temperature change of 0.100°C is measured. What mass of water was in the vessel? Ignore heat flow into the vessel, the thermometer, etc.
A thermometer containing 0.10 g of mercury is cooled from 15.0°C to 8.5°C. How much energy left the mercury in this process?
A heating coil inside an electric kettle delivers 2.1 kW of electric power to the water in the kettle. How long will it take to raise the temperature of 0.50 kg of water from 20.0°C to 100.0°C?
A cylinder contains 250 L of hydrogen gas (H2) at 0.0°C and a pressure of 10.0 atm. How much energy is required to raise the temperature of this gas to 25.0°C?
A container of nitrogen gas (N2) at 23°C contains 425 L at a pressure of 3.5 atm. If 26.6 kJ of heat are added to the container, what will be the new temperature of the gas?
Imagine that 501 people are present in a movie theater of volume 8.00 × 103 m3 that is sealed shut so no air can escape. Each person gives off heat at an average rate of 110 W. By how much will the temperature of the air have increased during a 2.0-h movie? The initial pressure is 1.01 × 105 Pa
A chamber with a fixed volume of 1.0 m3 contains a monatomic gas at 3.00 × 102 K. The chamber is heated to a temperature of 41.00 × 102 K. This operation requires 10.0 J of heat. (Assume all the energy is transferred to the gas.) How many gas molecules are in the chamber?
As heat flows into a substance, its temperature changes according to the graph in the diagram. For what sections of the graph is the substance undergoing a phase change? For the sections you identified, what kind of phase change is occurring?
How much internal energy is generated when a 20.0-g lead bullet, traveling at 7.00 × 102 m/s, comes to a stop as it strikes a metal plate?
Given these data, compute the heat of vaporization of water. The specific heat capacity of water is 4.186 J/(g ∙ K). Mass of calorimeter = 3.00 × 102 g Specific heat of calorimeter = 0.380 J/(g ∙ K) Mass of water = 2.00 × 102 g Initial temperature of water and calorimeter = 15.0°C Mass of
Given these data, compute the heat of fusion of water. The specific heat capacity of water is 4.186 J/(g·K). Mass of calorimeter = 3.00 × 102 g Specific heat of calorimeter = 0.380 J/(g·K) Mass of water = 2.00 × 102 g Initial temperature of water and calorimeter = 20.0°C Mass of ice = 30.0 g
In a physics lab, a student accidentally drops a 25.0-g brass washer into an open dewar of liquid nitrogen at 77.2 K. How much liquid nitrogen boils away as the washer cools from 293 K to 77.2 K? The latent heat of vaporization for nitrogen is 199.1 kJ/kg.
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?
How much heat is required to change 1.0 kg of ice, originally at − 20.0°C, into steam at 110.0°C? Assume 1.0 atm of pressure.
Ice at 0.0°C is mixed with 5.00 × 102 mL of water at 25.0°C. How much ice must melt to lower the water temperature to 0.0°C?
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 of the glass.
Repeat Problem 36 without neglecting 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 36? In Problem 36 Tina is going to make iced tea by first brewing
The graph shows the change in temperature as heat is supplied to a certain mass of ice initially at ˆ’ 80.0°C. What is the mass of the ice?
How many grams of aluminum at 80.0°C would have to be dropped into a hole in a block of ice at 0.0°C to melt 10.0 g of ice?
Nolan threw a baseball, of mass 147.5 g, at a speed of 162 km/h to a catcher. How much internal energy was generated when the ball struck the catcher's mitt?
Is it possible to heat the aluminum of Problem 39 to a high enough temperature so that it melts an equal mass of ice? If so, what temperature must the aluminum have? In Problem 39 How many grams of aluminum at 80.0°C would have to be dropped into a hole in a block of ice at 0.0°C to melt 10.0 g
If a leaf is to maintain a temperature of 40°C (reasonable for a leaf), it must lose 250 W/m 2 by transpiration (evaporative heat loss), That the leaf also loses heat by radiation, but we will neglect this. How much water is lost after 1 h through transpiration only? The area of the leaf is 0.005
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?
You are given 250 g of coffee (same specific heat as water) at 80.0°C (too hot to drink). In order to cool this to 60.0°C, how much ice (at 0.0°C) must be added? Ignore heat content of the cup and heat exchanges with the surroundings.
A phase diagram is shown. Starting at point A, follow the dashed line to point E and consider what happens to the substance represented by this diagram as its pressure and temperature are changed.(a) Explain what happens for each line segment, AB, BC, CD, and DE. (b) What is the significance of
Compute the heat of fusion of a substance from these data: 31.15 kJ will change 0.500 kg of the solid at 21°C to liquid at 327°C, the melting point. The specific heat of the solid is 0.129 kJ/(kg∙K).
A dog loses a lot of heat through panting. The air rushing over the upper respiratory tract causes evaporation and thus heat loss. A dog typically pants at a rate of 670 pants per minute. As a rough calculation, assume that one pant causes 0.010 g of water to be evaporated from the respiratory
(a) What thickness of cork would have the same R-factor as a 1.0-cm thick stagnant air pocket? (b) What thickness of tin would be required for the same R-factor?
A metal rod with a diameter of 2.30 cm and length of 1.10 m has one end immersed in ice at 32.0°F and the other end in boiling water at 212°F. If the ice melts at a rate of 1.32 g every 175 s, what is the thermal conductivity of this metal? Identify the metal. Assume there is no heat lost to the
2.0 × 10−2 m, (a) What is the thermal resistance if the material is asbestos? (b) What is the thermal resistance if the material is iron? (c) What is the thermal resistance if the material is copper?
A child of mass 15 kg climbs to the top of a slide that is 1.7 m above a horizontal run that extends for 0.50 m at the base of the slide. After sliding down, the child comes to rest just before reaching the very end of the horizontal portion of the slide. (a) How much internal energy was generated
A copper rod of length 0.50 m and cross-sectional area 6.0 Ã— 10ˆ’2 cm2 is connected to an iron rod with the same cross section and length 0.25 m. One end of the copper is immersed in boiling water and the other end is at the junction with the iron. If the far end of the iron
For a temperature difference Î” T = 20.0°C, one slab of material conducts 10.0 W/m2; another of the same shape conducts 20.0 W/m2. What is the rate of heat flow per m2 of surface area when the slabs are placed side by side with Î”T tot = 20.0 ° C?
A wall consists of a layer of wood and a layer of cork insulation of the same thickness. The temperature inside is 20.0°C and the temperature outside is 0.0°C.(a) What is the temperature at the interface between the wood and cork if the cork is on the inside and the wood on the outside?(b) What
The thermal conductivity of the fur (including the skin) of a male Husky dog is 0.026 W/(m ∙ K). The dog's heat output is measured to be 51 W, its internal temperature is 38°C, its surface area is 1.31 m2, and the thickness of the fur is 5.0 cm. How cold can the outside temperature be before the
The thermal resistance of a seal's fur and blubber combined is 0.33 K/W. If the seal's internal temperature is 37°C and the temperature of the sea is about 0°C, what must be the heat output of the seal in order for it to maintain its internal temperature?

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