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physics
college physics 2nd

College Physics 2nd Edition OpenStax - Solutions

How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is.Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0°C and
One method of getting a tight fit, say of a metal peg in a hole in a metal block, is to manufacture the peg slightly larger than the hole. The peg is then inserted when at a different temperature than the block. Should the block be hotter or colder than the peg during insertion? Explain your answer.
Is energy transfer involved in a phase change? If so, will energy have to be supplied to change phase from solid to liquid and liquid to gas? What about gas to liquid and liquid to solid? Why do they spray the orange trees with water in Florida when the temperatures are near or just below freezing?
(a) At what temperature do the Fahrenheit and Celsius scales have the same numerical value?(b) At what temperature do the Fahrenheit and Kelvin scales have the same numerical value?
Does it really help to run hot water over a tight metal lid on a glass jar before trying to open it? Explain your answer.
How many moles of gas are in a bike tire with a volume of 2.00 x 10-3 m (2.00 L), a pressure of 7.00 x 105 Pa (a gauge pressure of just under 90.0 lb/in2), and at a temperature of 18.0°C?StrategyIdentify the knowns and unknowns, and choose an equation to solve for the unknown. In this case, we
Freeze drying is a process in which substances, such as foods, are dried by placing them in a vacuum chamber and lowering the atmospheric pressure around them. How does the lowered atmospheric pressure speed the drying process, and why does it cause the temperature of the food to drop?
The height of the Washington Monument is measured to be 170 m on a day when the temperature is 35.0°C. What will its height be on a day when the temperature falls to -10.0°C? Although the monument is made of limestone, assume that its thermal coefficient of expansion is the same as marble's.
(a) What is the average kinetic energy of a gas molecule at 20.0°C (room temperature)?(b) Find the rms speed of a nitrogen molecule (N2) at this temperature.Strategy for (a)The known in the equation for the average kinetic energy is the temperature.Before substituting values into this equation, we
How much taller does the Eiffel Tower become at the end of a day when the temperature has increased by 15°C? Its original height is 321 m and you can assume it is made of steel.
What is the change in length of a 3.00-cm-long column of mercury if its temperature changes from 37.0°C to 40.0°C, assuming the mercury is unconstrained?
In order to escape Earth’s gravity, an object near the top of the atmosphere (at an altitude of 100 km) must travel away from Earth at 11.1 km/s. This speed is called the escape velocity. At what temperature would helium atoms have an rms speed equal to the escape velocity?StrategyIdentify the
Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?
How large an expansion gap should be left between steel railroad rails if they may reach a maximum temperature 35.0°C greater than when they were laid? Their original length is 10.0 m.
A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?
(a) Calculate the percent relative humidity on a day when the temperature is 25.0°C and the air contains 9.40 g of water vapor per m3.(b) At what temperature will this air reach 100% relative humidity (the saturation density)? This temperature is the dew point.(c) What is the humidity when the air
You are looking to purchase a small piece of land in Hong Kong. The price is "only" $60,000 per square meter! The land title says the dimensions are 20 m x 30 m. By how much would the total price change if you measured the parcel with a steel tape measure on a day when the temperature was 20°C
How is momentum related to the pressure exerted by a gas? Explain on the atomic and molecular level, considering the behavior of atoms and molecules.
Global warming will produce rising sea levels partly due to melting ice caps but also due to the expansion of water as average ocean temperatures rise. To get some idea of the size of this effect, calculate the change in length of a column of water 1.00 km high for a temperature increase of
A pressure cooker contains water and steam in equilibrium at a pressure greater than atmospheric pressure. How does this greater pressure increase cooking speed?
Why does condensation form most rapidly on the coldest object in a room—for example, on a glass of ice water?
(a) Suppose a meter stick made of steel and one made of invar (an alloy of iron and nickel) are the same length at 0°C. What is their difference in length at 22.0°C?(b) Repeat the calculation for two 30.0-m-long surveyor's tapes.
What is the vapor pressure of solid carbon dioxide (dry ice) at -78.5°C?
Can carbon dioxide be liquefied at room temperature (20°C)? If so, how? If not, why not? (See Figure 13.33.) Pressure, P(atm) 73 56 5.11 S CO₂ Triple point -78.5 -56.6 1 Critical point 20 31 Temperature, T(°C)
(a) If a 500-mL glass beaker is filled to the brim with ethyl alcohol at a temperature of 5.00°C, how much will overflow when its temperature reaches 22.0°C?(b) How much less water would overflow under the same conditions?
Most automobiles have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at 10.0°C. What volume of radiator fluid will overflow when the radiator and fluid reach their 95.0°C operating
Oxygen cannot be liquefied at room temperature by placing it under a large enough pressure to force its molecules together. Explain why this is.
A physicist makes a cup of instant coffee and notices that, as the coffee cools, its level drops 3.00 mm in the glass cup. Show that this decrease cannot be due to thermal contraction by calculating the decrease in level if the 350 cm3 of coffee is in a 7.00-cm-diameter cup and decreases in
What is the distinction between gas and vapor?
Because humidity depends only on water's vapor pressure and temperature, are the saturation vapor densities listed in Table 13.5 valid in an atmosphere of helium at a pressure of 1.01 x 105 N/m2, rather than air? Are those values affected by altitude on Earth?Data given in Table 13.5 Temperature
(a) The density of water at 0°C is very nearly 1000 kg/m3 (it is actually 999.84 kg/m3), whereas the density of ice at 0°C is 917 kg/m3. Calculate the pressure necessary to keep ice from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature.
Why does a beaker of 40.0°C water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker?
Convert an absolute pressure of 7.00 × 105 N/m2 to gauge pressure in lb/in2. (This value was stated to be just less than 90.0 lb/in2 in Example 13.9. Is it?)Data given in Example 13.9How many moles of gas are in a bike tire with a volume of 2.00 x 10-3 m3 (2.00 L), a pressure of 7.00 x 105 Pa (a
Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)?
The gauge pressure in your car tires is 2.50 x 105 N/m2 at a temperature of 35.0°C when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to -40.0°C ?
Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0°C.(a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60.0°C (an approximation) and
To test a balloon, it is placed in a lab and filled with helium. The temperature of the helium is 10.0°C and the pressure is 1.00 atmosphere. The pressure in the lab is maintained. Assume the membrane of the balloon provides a negligible inward pressure, so it is not considered significant.(a)
Confirm that the units of nRT are those of energy for each value of R: (a) 8.31 J/mol. K, (b) 1.99 cal/mol K, and(c) 0.0821 L. atm/mol. K.
Calculate the number of moles in the 2.00-L volume of air in the lungs of the average person. Note that the air is at 37.0°C (body temperature).
(a) What is the volume (in km3) of Avogadro's number of sand grains if each grain is a cube and has sides that are 1.0 mm long?(b) How many kilometers of beaches in length would this cover if the beach averages 100 m in width and 10.0 m in depth? Neglect air spaces between grains.
An airplane passenger has 100 cm3 of air in his stomach just before the plane takes off from a sea-level airport. What volume will the air have at cruising altitude if cabin pressure drops to 7.50 x 104 N/m2?
An expensive vacuum system can achieve a pressure as low as 1.00 x 10-7 N/m2 at 20°C. How many atoms are there in a cubic centimeter at this pressure and temperature?
The number density of gas atoms at a certain location in the space above our planet is about 1.00 x 1011 m-3, and the pressure is 2.75 x 10-10 N/m2 in this space. What is the temperature there?
A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1.40 x 107 N/m2 and a temperature of 25.0°C. Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature (-78.5°C) to reduce the leak rate and pressure so that it can be safely repaired.(a)
Find the number of moles in 2.00 L of gas at 35.0°C and under 7.41 x 107 N/m2 of pressure.
Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra 25.0% to their volume and assume they are not crushed by their own weight.
(a) What is the gauge pressure in a 25.0°C car tire containing 3.60 mol of gas in a 30.0 L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and 25.0°C? Assume the temperature returns to 25.0°C and the volume remains constant.
(a) In the deep space between galaxies, the density of atoms is as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. What is the pressure?(b) What volume (in m3) is occupied by 1 mol of gas?(c) If this volume is a cube, what is the length of its sides in kilometers?
Average atomic and molecular speeds (Vrms) are large, even at low temperatures. What is Vrms for helium atoms at 5.00 K, just one degree above helium's liquefaction temperature?
Some incandescent light bulbs are filled with argon gas. What is vrms for argon atoms near the filament, assuming their temperature is 2500 K?
(a) What is the average kinetic energy in joules of hydrogen atoms on the 5500°C surface of the Sun?(b) What is the average kinetic energy of helium atoms in a region of the solar corona where the temperature is 6.00 × 105 K?
The escape velocity of any object from Earth is 11.2 km/s.(a) Express this speed in m/s and km/ h. (b) At what temperature would oxygen molecules (molecular mass is equal to 32.0 g/ mol) have an average velocity vrms equal to Earth's escape velocity of 11.1 km/s?
The escape velocity from the Moon is much smaller than from Earth and is only 2.38 km/s. At what temperature would hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity vrms equal to the Moon's escape velocity?
Suppose that the average velocity (vrms) of carbon dioxide molecules (molecular mass is equal to 44.0 g/mol) in a flame is found to be 1.05 x 105 m/s. What temperature does this represent?
Hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity vrms equal to 193 m/s. What is the temperature?
Much of the gas near the Sun is atomic hydrogen. Its temperature would have to be 1.5 x 107 K for the average velocity vrms to equal the escape velocity from the Sun. What is that velocity?
There are two important isotopes of uranium- 235U and 238U; these isotopes are nearly identical chemically but have different atomic masses. Only 235U is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities vrms of
Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when the atmospheric pressure is 1.01 × 105 N/m2?
(a) What is the vapor pressure of water at 20.0°C?(b) What percentage of atmospheric pressure does this correspond to?(c) What percent of 20.0°C air is water vapor if it has 100% relative humidity? (The density of dry air at 20.0°C is 1.20 kg/m3.)
Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure.(a) What pressure is necessary to raise the boiling point to 120.0°C? (b) What gauge pressure does this correspond to?
(a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is 8.59 x 104 N/m2?(b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is 7.00 x 104 N/m2?
What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature of 70.0°C?
At a spot in the high Andes, water boils at 80.0°C, greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location?
What is the relative humidity on a 25.0°C day when the air contains 18.0 g/m3 of water vapor?
A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of 1.01 x 105 N/m2.(a) What is the partial pressure of oxygen at sea level?(b) If the diver breathes a gas mixture at a pressure of
Air in human lungs has a temperature of 37.0°C and a saturation vapor density of 44.0 g/m3.(a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss of water vapor by the person? (b) Calculate the partial pressure of water vapor having this density, and compare it with
If the relative humidity is 90.0% on a muggy summer morning when the temperature is 20.0°C, what will it be later in the day when the temperature is 30.0°C, assuming the water vapor density remains constant?
Late on an autumn day, the relative humidity is 45.0% and the temperature is 20.0°C. What will the relative humidity be that evening when the temperature has dropped to 10.0°C, assuming constant water vapor density?
What is the dew point (the temperature at which 100% relative humidity would occur) on a day when relative humidity is 39.0% at a temperature of 20.0°C?
On a certain day, the temperature is 25.0°C and the relative humidity is 90.0%. How many grams of water must condense out of each cubic meter of air if the temperature falls to 15.0°C? Such a drop in temperature can, thus, produce heavy dew or fog.
The boiling point of water increases with depth because pressure increases with depth. At what depth will fresh water have a boiling point of 150°C, if the surface of the water is at sea level?
(a) At what depth in fresh water is the critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth?
To get an idea of the small effect that temperature has on Archimedes' principle, calculate the fraction of a copper block's weight that is supported by the buoyant force in 0°C water and compare this fraction with the fraction supported in 95.0°C water.
(a) How many moles per cubic meter of an ideal gas are there at a pressure of 1.00 x 1014 N/m2 and at 0°C?(b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
(a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If the hole is 10.0% bigger in diameter than the 22.0°C rod, at what temperature will the rod be the same size as the hole? (b) What is
The temperature inside a supernova explosion is said to be 2.00 × 1013 K.(a) What would the average velocity vrms of hydrogen atoms be? (b) What is unreasonable about this velocity?(c) Which premise or assumption is responsible?
Suppose the relative humidity is 80% on a day when the temperature is 30.0°C.(a) What will the relative humidity be if the air cools to 25.0°C and the vapor density remains constant? (b) What is unreasonable about this result?(c) Which premise is responsible?
The outward force on one end of an air tank was calculated in Example 11.2. How is this force balanced? (The tank does not accelerate, so the force must be balanced.)Data given in Example 11.2An astronaut is working outside the International Space Station where the atmospheric pressure is
Give an example of entrainment not mentioned in the text.
An oil gusher shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. Neglecting air resistance but not the resistance of the pipe, and assuming laminar flow, calculate the gauge pressure at the entrance of the 50.0-m-long vertical pipe. Take the density of the oil to be 900
How do you convert pressure units like millimeters of mercury, centimeters of water, and inches of mercury into units like newtons per meter squared without resorting to a table of pressure conversion factors?
Verify that the SI unit of hρg is N/m2.
Atmospheric pressure exerts a large force (equal to the weight of the atmosphere above your body—about 10 tons) on the top of your body when you are lying on the beach sunbathing. Why are you able to get up?
A crass host pours the remnants of several bottles of wine into a jug after a party. He then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. He is amazed when he pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks
The mass of an ancient Greek coin is determined in air to be 8.630 g. When the coin is submerged in water as shown in Figure 11.23, its apparent mass is 7.800 g. Calculate its density, given that water has a density of 1.000 g/cm3 and that effects caused by the wire suspending the coin are
What is the density of 18.0-karat gold that is a mixture of 18 parts gold, 5 parts silver, and 1 part copper? (These values are parts by mass, not volume.) Assume that this is a simple mixture having an average density equal to the weighted densities of its constituents.
Calculate the gauge pressure inside a soap bubble 2.00 x 10-4 m in radius using the surface tension for soapy water in Table 11.3. Convert this pressure to mm Hg.StrategyData given in Table 11.3 The radius is given and the surface tension can be found in Table 11.3, and so P can be found directly
There is relatively little empty space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale-approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 that of the atom and contains nearly all the mass of the
Why is force exerted by static fluids always perpendicular to a surface?
Can capillary action be solely responsible for sap rising in trees? To answer this question, calculate the radius of a capillary tube that would raise sap 100 m to the top of a giant redwood, assuming that sap's density is 1050 kg/m3, its contact angle is zero, and its surface tension is the same
As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of 1.50cm2 and the woman’s mass is 55.0 kg. Express the pressure in Pa. (In the early days of commercial flight, women were
In a remote location near the North Pole, an iceberg floats in a lake. Next to the lake (assume it is not frozen) sits a comparably sized glacier sitting on land. If both chunks of ice should melt due to rising global temperatures (and the melted ice all goes into the lake), which ice chunk would
Suppose a 3.00-N force can rupture an eardrum.(a) If the eardrum has an area of 1.00 cm2, calculate the maximum tolerable gauge pressure on the eardrum in newtons per meter squared and convert it to millimeters of mercury.(b) At what depth in freshwater would this person's eardrum rupture, assuming
How do jogging on soft ground and wearing padded shoes reduce the pressures to which the feet and legs are subjected?
Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of 3.00 x 109 N/m2? (This high pressure is possible because the hammer striking the
Toe dancing (as in ballet) is much harder on toes than normal dancing or walking. Explain in terms of pressure.
What depth of mercury creates a pressure of 1.00 atm?
The greatest ocean depths on the Earth are found in the Marianas Trench near the Philippines. Calculate the pressure due to the ocean at the bottom of this trench, given its depth is 11.0 km and assuming the density of seawater is constant all the way down.
(a) Calculate the buoyant force on 10,000 metric tons (1.00 x 107 kg) of solid steel completely submerged in water, and compare this with the steel's weight.(b) What is the maximum buoyant force that water could exert on this same steel if it were shaped into a boat that could displace 1.00 x 105
A reservoir has a surface area of 50.0 km2 and an average depth of 40.0 m. What mass of water is held behind the dam? (See Figure 11.4 for a view of a large reservoir—the Three Gorges Dam site on the Yangtze River in central China.)StrategyWe can calculate the volume of the reservoir from its

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