Solved: Multiple-Concept Example 4 and Conceptual Example

Figure 14.2a shows the Hope diamond (44.5 carats), which is almost pure carbon. Figure 14.2b shows the Rosser Reeves ruby (138 carats), which is primarily aluminum oxide (Al2O3). One carat is equivalent to a mass of 0.200 g. Determine (a) the number of carbon atoms in the diamond and (b) the number of Al2O3 molecules in the ruby.

Consider one mole of hydrogen (H2) and one mole of oxygen (O2). Which, if either, has the greater number of molecules and which, if either, has the greater mass?

The molecules of substances A and B are composed of different atoms. However, the two substances have the same mass densities. Consider the possibilities for the molecular masses of the two types of molecules and decide whether 1 m3 of substance A contains the same number of molecules as 1 m3 of substance B.

A gas mixture contains equal masses of the monatomic gases argon (atomic mass 39.948 u) and neon (atomic mass 20.179 u). These two are the only gases present. Of the total number of atoms in the mixture, what percentage is neon?

In the lungs, a thin respiratory membrane separates tiny sacs of air (absolute pressure 1.00 105 Pa) from the blood in the capillaries. These sacs are called alveoli, and it is from them that oxygen enters the blood. The average radius of the alveoli is 0.125 mm, and the air inside contains 14% oxygen. Assuming that the air behaves as an ideal gas at body temperature (310 K), find the number of oxygen molecules in one of the sacs. R

If you look carefully at the bubbles rising in a glass of beer (see Figure 14.5), youll see them grow in size as they move upward, often doubling in volume by the time they reach the surface. Beer bubbles contain mostly carbon dioxide (CO2), a gas that is dissolved in the beer because of the fermentation process. Which variable describing the gas is responsible for the growth of the rising bubbles? (a) The Kelvin temperature T (b) The absolute pressure P (c) The number of moles n

When a scuba diver descends to greater depths, the water pressure increases. The air pressure inside the body cavities (e.g., lungs, sinuses) must be maintained at the same pressure as that of the surrounding water; otherwise the cavities would collapse. A special valve automatically adjusts the pressure of the air coming from the scuba tank to ensure that the air pressure equals the water pressure at all times. The scuba gear in Figure 14.7a consists of a 0.0150-m3 tank filled with compressed air at an absolute pressure of 2.02 107 Pa. Assume that the diver consumes air at the rate of 0.0300 m3 per minute and that the temperature of the air does not change as the diver goes deeper into the water. How long (in minutes) can a diver stay under water at a depth of 10.0 m? Take the density of seawater to be 1025 kg/m3 .

A tightly sealed house has a large ceiling fan that blows air out of the house and into the attic. The owners turn the fan on and forget to open any windows or doors. What happens to the air pressure in the house after the fan has been on for a while, and does it become easier or harder for the fan to do its job?

Above the liquid in a can of hair spray is a gas at a relatively high pressure. The label on the can includes the warning DO NOT STORE AT HIGH TEMPERATURES. Why is the warning given?

What happens to the pressure in a tightly sealed house when the electric furnace turns on and runs for a while?

When you climb a mountain, your eardrums pop outward as the air pressure decreases. When you come down, they pop inward as the pressure increases. At the sea coast, you swim through a completely submerged passage and emerge into a pocket of air trapped within a cave. As the tide comes in, the water level in the cave rises, and your eardrums pop. Is this popping analogous to what happens as you climb up or climb down a mountain?

Atmospheric pressure decreases with increasing altitude. Given this fact, explain why helium-filled weather balloons are underinflated when they are launched from the ground. Assume that the temperature does not change much as the balloon rises.

A slippery cork is being pressed into an almost full (but not 100% full) bottle of wine. When released, the cork slowly slides back out. However, if half the wine is removed from the bottle before the cork is inserted, the cork does not slide out. Explain.

Consider equal masses of three monatomic gases: argon (atomic mass 39.948 u), krypton (atomic mass 83.80 u), and xenon (atomic mass 131.29 u). The pressure and volume of each gas is the same. Which gas has the greatest and which the smallest temperature? Ki

Each particle in a gas has kinetic energy. Furthermore, the equation establishes the relationship between the average kinetic energy per particle and the temperature of an ideal gas. Is it valid, then, to conclude that a single particle has a temperature?

Air is primarily a mixture of nitrogen N2 (molecular mass 28.0 u) and oxygen O2 (molecular mass 32.0 u). Assume that each behaves like an ideal gas and determine the rms speed of the nitrogen and oxygen molecules when the air temperature is 293 K. R

The kinetic theory of gases assumes that, for a given collision time, a gas molecule rebounds with the same speed after colliding with the wall of a container. If the speed after the collision were less than the speed before the collision, the duration of the collision remaining the same, would the pressure of the gas be greater than, equal to, or less than the pressure predicted by kinetic theory?

If the temperature of an ideal gas were doubled from 50 to 100 C, would the average translational kinetic energy of the gas particles also double?

The pressure of a monatomic ideal gas doubles, while the volume decreases to one-half its initial value. Does the internal energy of the gas increase, decrease, or remain unchanged?

The atoms in a container of helium (He) have the same translational rms speed as the atoms in a container of argon (Ar). Treating each gas as an ideal gas, decide which, if either, has the greater temperature.

The pressure of a monatomic ideal gas is doubled, while its volume is reduced by a factor of four. What is the ratio of the new rms speed of the atoms to the initial rms speed?

The fragrance from an open bottle of perfume takes several seconds or sometimes even minutes to reach the other side of a room by the process of diffusion. Which of the following accounts for the fact that diffusion is relatively slow? (a) The nature of Brownian motion (b) The relatively slow translational rms speeds that characterize gas molecules at room temperature

Large amounts of water can be given off by plants. It has been estimated, for instance, that a single sunflower plant can lose up to a pint of water a day during the growing season. Figure 14.16 shows a cross-sectional view of a leaf. Inside the leaf, water passes from the liquid phase to the vapor phase at the walls of the mesophyll cells. The water vapor then diffuses through the intercellular air spaces and eventually exits the leaf through small openings, called stomatal pores. The diffusion constant for water vapor in air is D 2.4 105 m2 /s. A stomatal pore has a cross-sectional area of about A 8.0 1011 m2 and a length of about L 2.5 105 m. The concentration of water vapor on the interior side of a pore is roughly C2 0.022 kg/m3 , whereas the concentration on the outside is approximately C1 0.011 kg/m3 . Determine the mass of water vapor that passes through a stomatal pore in one hour. Reason

In the lungs, oxygen in very small sacs called alveoli diffuses into the blood. The diffusion occurs directly through the walls of the sacs, which have a thickness L. The total effective area A across which diffusion occurs is the sum of the individual areas (each quite small) of the various sac walls. Considering the fact that the mass m of oxygen that enters the blood per second needs to be large and referring to Ficks law of diffusion, what can you deduce about L and about the total number of sacs present in the lungs?

The same solute is diffusing through the same solvent in each of three cases. For each case, the table gives the length and cross-sectional area of the diffusion channel. The concentration difference between the ends of the diffusion channel is the same in each case. Rank the diffusion rates (in kg/s) in descending order (largest first).

Figure 14.17 shows three identical chambers containing a piston and a spring whose spring constant is k 5.8 104 N/m. The chamber in part a is completely evacuated, and the piston just touches its left end. In this position, the spring is unstrained. In part b of the drawing, 0.75 mol of ideal gas 1 is introduced into the chamber, and the spring compresses by x1 15 cm. In part c, 0.75 mol of ideal gas 2 is introduced into the chamber, and the spring compresses by x2 24 cm. Find the temperature of each gas. Co

Which gas exerts the greater force on the piston?

How is the force required to compress a spring related to the displacement of the spring from its unstrained position?

Which gas exerts the greater pressure on the piston?

Which gas has the greater temperature?

In outer space the density of matter is extremely low, about one atom per cm3 . The matter is mainly hydrogen atoms (m 1.67 1027 kg) whose rms speed is 260 m/s. A cubical box, 2.0 m on a side, is placed in outer space, and the hydrogen atoms are allowed to enter. (a) What is the magnitude of the force that the atoms exert on one wall of the box? (b) Determine the pressure that the atoms exert. (c) Does outer space have a temperature, and, if so, what is it?

Why do hydrogen atoms exert a force on the walls of the box?

Do the atoms generate a pressure on the walls of the box?

Do hydrogen atoms in outer space have a temperature? If so, how is the temperature related to the microscopic properties of the atoms?

Hemoglobin has a molecular mass of 64 500 u. Find the mass (in kg) of one molecule of hemoglobin. 2. Manufacturers of headache remedies routinely claim that their own brands are more potent pain relievers than the competing brands. Their way of making the comparison is to compare the number of molecules in the standard dosage. Tylenol uses 325 mg of acetaminophen (C8H9NO2) as the standard dose, whereas Advil uses 2.00 102 mg of ibuprofen (C13H18O2). Find the number of molecules of pain reliever in the standard doses of (a) Tylenol and (b) Advil.

Manufacturers of headache remedies routinely claim that their own brands are more potent pain relievers than the competing brands. Their way of making the comparison is to compare the number of molecules in the standard dosage. Tylenol uses 325 mg of acetaminophen (C8H9NO2) as the standard dose, whereas Advil uses 2.00 102 mg of ibuprofen (C13H18O2). Find the number of molecules of pain reliever in the standard doses of (a) Tylenol and (b) Advil. c

A mass of 135 g of a certain element is known to contain 30.1 1023 atoms. What is the element?

A certain element has a mass per mole of 196.967 g/mol. What is the mass of a single atom in (a) atomic mass units and (b) kilograms? (c) How many moles of atoms are in a 285-g sample?

The active ingredient in the allergy medication Claritin contains carbon (C), hydrogen (H), chlorine (Cl), nitrogen (N), and oxygen (O). Its molecular formula is C22H23ClN2O2. The standard adult dosage utilizes 1.572 1019 molecules of this species. Determine the mass (in grams) of the active ingredient in the standard dosage.

The chlorophyll-a molecule (C55H72MgN4O5) is important in photosynthesis. (a) Determine its molecular mass (in atomic mass units). (b) What is the mass (in grams) of 3.00 moles of chlorophyll-a molecules?

A runner weighs 580 N (about 130 lb), and 71% of this weight is water. (a) How many moles of water are in the runners body? (b) How many water molecules (H2O) are there?

Consider a mixture of three different gases: 1.20 g of argon (molecular mass 39.948 g/mol), 2.60 g of neon (molecular mass 20.180 g/mol), and 3.20 g of helium (molecular mass 4.0026 g/mol). For this mixture, determine the percentage of the total number of atoms that corresponds to each of the components. *

The preparation of homeopathic remedies involves the repeated dilution of solutions containing an active ingredient such as arsenic trioxide (As2O3). Suppose one begins with 18.0 g of arsenic trioxide dissolved in water, and repeatedly dilutes the solution with pure water, each dilution reducing the amount of arsenic trioxide remaining in the solution by a factor of 100. Assuming perfect mixing at each dilution, what is the maximum number of dilutions one may perform so that at least one molecule of arsenic trioxide remains in the diluted solution? For comparison, homeopathic remedies are commonly diluted 15 or even 30 times.

A cylindrical glass of water (H2O) has a radius of 4.50 cm and a height of 12.0 cm. The density of water is 1.00 g/cm3 . How many moles of water molecules are contained in the glass?

It takes 0.16 g of helium (He) to fill a balloon. How many grams of nitrogen (N2) would be required to fill the balloon to the same pressure, volume, and temperature?

A 0.030-m3 container is initially evacuated. Then, 4.0 g of water is placed in the container, and, after some time, all the water evaporates. If the temperature of the water vapor is 388 K, what is its pressure?

An ideal gas at 15.5 C and a pressure of 1.72 105 Pa occupies a volume of 2.81 m3 . (a) How many moles of gas are present? (b) If the volume is raised to 4.16 m3 and the temperature raised to 28.2 C, what will be the pressure of the gas?

Four closed tanks, A, B, C, and D, each contain an ideal gas. The table gives the absolute pressure and volume of the gas in each tank. In each case, there is 0.10 mol of gas. Using this number and the data in the table, compute the temperature of the gas in each tank.

A young male adult takes in about 5.0 104 m3 of fresh air during a normal breath. Fresh air contains approximately 21% oxygen. Assuming that the pressure in the lungs is 1.0 105 Pa and that air is an ideal gas at a temperature of 310 K, find the number of oxygen molecules in a normal breath. P

A Goodyear blimp typically contains 5400 m3 of helium (He) at an absolute pressure of 1.1 105 Pa. The temperature of the helium is 280 K. What is the mass (in kg) of the helium in the blimp?

A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.034 m3 of helium at an absolute pressure of 1.2 105 Pa. The cylinder contains helium at an absolute pressure of 1.6 107 Pa and has a volume of 0.0031 m3 . The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of balloons that can be filled? 1

The volume of an ideal gas is held constant. Determine the ratio P2/P1 of the final pressure to the initial pressure when the temperature of the gas rises (a) from 35.0 to 70.0 K and (b) from 35.0 to 70.0 C.

What is the density (in kg/m3 ) of nitrogen gas (molecular mass 28 u) at a pressure of 2.0 atmospheres and a temperature of 310 K?

Two ideal gases have the same mass density and the same absolute pressure. One of the gases is helium (He), and its temperature is 175 K. The other gas is neon (Ne). What is the temperature of the neon?

On the sunlit surface of Venus, the atmospheric pressure is 9.0 106 Pa, and the temperature is 740 K. On the earths surface the atmospheric pressure is 1.0 105 Pa, while the surface temperature can reach 320 K. These data imply that Venus has a thicker atmosphere at its surface than does the earth, which means that the number of molecules per unit volume (N/V) is greater on the surface of Venus than on the earth. Find the ratio (N/V)Venus/(N/V)Earth. 2

A tank contains 0.85 mol of molecular nitrogen (N2). Determine the mass (in grams) of nitrogen that must be removed from the tank in order to lower the pressure from 38 to 25 atm. Assume that the volume and temperature of the nitrogen in the tank do not change.

Multiple-Concept Example 4 reviews the principles that play roles in this problem. A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature remains constant during the descent. The tank is brought to a halt when the distance between the surface of the water in the tank and the surface of the lake is 40.0 m. Atmospheric pressure at the surface of the lake is 1.01 105 Pa. Find the fraction of the tanks volume that is filled with air.

A tank contains 11.0 g of chlorine gas (Cl 2) at a temperature of 82 C and an absolute pressure of 5.60 105 Pa. The mass per mole of Cl 2 is 70.9 g/mol. (a) Determine the volume of the tank. (b) Later, the temperature of the tank has dropped to 31 C and, due to a leak, the pressure has dropped to 3.80 105 Pa. How many grams of chlorine gas have leaked out of the tank? *

The dimensions of a room are 2.5 m 4.0 m 5.0 m. Assume that the air in the room is composed of 79% nitrogen (N2) and 21% oxygen (O2). At a temperature of 22 C and a pressure of 1.01105 Pa, what is the mass (in grams) of the air? *

The drawing shows an ideal gas confined to a cylinder by a massless piston that is attached to an ideal spring. Outside the cylinder is a vacuum. The cross-sectional area of the piston is A 2.50 103 m2 . The initial pressure, volume, and temperature of the gas are, respectively, P0, V0 6.00 104 m3 , and T0 273 K, and the spring is initially stretched by an amount x 0 0.0800 m with respect to its unstrained length. The gas is heated, so that its final pressure, volume, and temperature are Pf, Vf, and Tf, and the spring is stretched by an amount xf 0.1000 m with respect to its unstrained length. What is the final temperature of the gas? Piston

Multiple-Concept Example 4 and Conceptual Example 3 are pertinent to this problem. A bubble, located 0.200 m beneath the surface in a glass of beer, rises to the top. The air pressure at the top is 1.01 105 Pa. Assume that the density of beer is the same as that of fresh water. If the temperature and number of moles of CO2 in the bubble remain constant as the bubble rises, find the ratio of the bubbles volume at the top to its volume at the bottom.

The relative humidity is 55% on a day when the temperature is 30.0 C. Using the graph that accompanies Problem 75 in Chapter 12, determine the number of moles of water vapor per cubic meter of air.

One assumption of the ideal gas law is that the atoms or molecules themselves occupy a negligible volume. Verify that this assumption is reasonable by considering gaseous xenon (Xe). Xenon has an atomic radius of 2.0 1010 m. For STP conditions, calculate the percentage of the total volume occupied by the atoms.

A spherical balloon is made from an amount of material whose mass is 3.00 kg. The thickness of the material is negligible compared to the 1.50-m radius of the balloon. The balloon is filled with helium (He) at a temperature of 305 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3 . Find the absolute pressure of the helium gas.

A cylindrical glass beaker of height 1.520 m rests on a table. The bottom half of the beaker is filled with a gas, and the top half is filled with liquid mercury that is exposed to the atmosphere. The gas and mercury do not mix because they are separated by a frictionless movable piston of negligible mass and thickness. The initial temperature is 273 K. The temperature is increased until a value is reached when one-half of the mercury has spilled out. Ignore the thermal expansion of the glass and the mercury, and find this temperature.

The mass of a hot-air balloon and its occupants is 320 kg (excluding the hot air inside the balloon). The air outside the balloon has a pressure of 1.01 105 Pa and a density of 1.29 kg/m3 . To lift off, the air inside the balloon is heated. The volume of the heated balloon is 650 m3 . The pressure of the heated air remains the same as the pressure of the outside air. To what temperature (in kelvins) must the air be heated so that the balloon just lifts off? The molecular mass of air is 29 u.

Very fine smoke particles are suspended in air. The translational rms speed of a smoke particle is 2.8 103 m/s, and the temperature is 301 K. Find the mass of a particle.

Four tanks A, B, C, and D are filled with monatomic ideal gases. For each tank, the mass of an individual atom and the rms speed of the atoms are expressed in terms of m and vrms, respectively (see the table). Suppose that m 3.32 1026 kg, and vrms 1223 m/s. Find the temperature of the gas in each tank. ABC D Mass m m 2m 2m Rms speed vrms 2vrms vrms 2vrms 35.

Suppose a tank contains 680 m3 of neon (Ne) at an absolute pressure of 1.01 105 Pa. The temperature is changed from 293.2 to 294.3 K. What is the increase in the internal energy of the neon?

Two moles of an ideal gas are placed in a container whose volume is 8.5 103 m3 . The absolute pressure of the gas is 4.5 105 Pa. What is the average translational kinetic energy of a molecule of the gas? 3

The average value of the squared speed does not equal the square of the average speed To verify this fact, consider three particles with the following speeds: v1 3.0 m/s, v2 7.0 m/s, and v3 9.0 m/s. Calculate (a) and (b)

Two gas cylinders are identical. One contains the monatomic gas argon (Ar), and the other contains an equal mass of the monatomic gas krypton (Kr). The pressures in the cylinders are the same, but the temperatures are different. Determine the ratio of the average kinetic energy of a krypton atom to the average kinetic energy of an argon atom.

Refer to Multiple-Concept Example 6 for insight into the concepts used in this problem. An oxygen molecule is moving near the earths surface. Another oxygen molecule is moving in the ionosphere (the uppermost part of the earths atmosphere) where the Kelvin temperature is three times greater. Determine the ratio of the translational rms speed in the ionosphere to the translational rms speed near the earths surface.

A container holds 2.0 mol of gas. The total average kinetic energy of the gas molecules in the container is equal to the kinetic energy of an 8.0 103 -kg bullet with a speed of 770 m/s. What is the Kelvin temperature of the gas?

The temperature near the surface of the earth is 291 K. A xenon atom (atomic mass 131.29 u) has a kinetic energy equal to the average translational kinetic energy and is moving straight up. If the atom does not collide with any other atoms or molecules, how high up will it go before coming to rest? Assume that the acceleration due to gravity is constant throughout the ascent.

Compressed air can be pumped underground into huge caverns as a form of energy storage. The volume of a cavern is 5.6 105 m3 , and the pressure of the air in it is 7.7 106 Pa. Assume that air is a diatomic ideal gas whose internal energy U is given by If one home uses 30.0 kW h of energy per day, how many homes could this internal energy serve for one day? *

In 10.0 s, 200 bullets strike and embed themselves in a wall. The bullets strike the wall perpendicularly. Each bullet has a mass of 5.0 103 kg and a speed of 1200 m/s. (a) What is the average change in momentum per second for the bullets? (b) Determine the average force exerted on the wall. (c) Assuming the bullets are spread out over an area of 3.0 104 m2 , obtain the average pressure they exert on this region of the wall. *

A cubical box with each side of length 0.300 m contains 1.000 moles of neon gas at room temperature (293 K). What is the average rate (in atoms/s) at which neon atoms collide with one side of the container? The mass of a single neon atom is 3.35 1026 kg.

Insects do not have lungs as we do, nor do they breathe through their mouths. Instead, they have a system of tiny tubes, called tracheae, through which oxygen diffuses into their bodies. The tracheae begin at the surface of an insects body and penetrate into the interior. Suppose that a trachea is 1.9 mm long with a crosssectional area of 2.1 109 m2 . The concentration of oxygen in the air outside the insect is 0.28 kg/m3 , and the diffusion constant is 1.1 105 m2 /s. If the mass per second of oxygen diffusing through a trachea is 1.7 1012 kg/s, find the oxygen concentration at the interior end of the tube. 4

A tube has a length of 0.015 m and a cross-sectional area of 7.0 104 m2 . The tube is filled with a solution of sucrose in water. The diffusion constant of sucrose in water is 5.0 1010 m2 /s. A difference in concentration of 3.0 103 kg/m3 is maintained between the ends of the tube. How much time is required for 8.0 1013 kg of sucrose to be transported through the tube? 47.

Review Conceptual Example 7 before working this problem. For water vapor in air at 293 K, the diffusion constant is D 2.4 105 m2 /s. As outlined in Problem 51(a), the time required for the first solute molecules to traverse a channel of length L is t L2 /(2D), according to Ficks law. (a) Find the time t for L 0.010 m. (b) For comparison, how long would a water molecule take to travel L 0.010 m at the translational rms speed of water molecules (assumed to be an ideal gas) at a temperature of 293 K? (c) Explain why the answer to part (a) is so much longer than the answer to part (b). 48.

The diffusion constant for the amino acid glycine in water has a value of 1.06 109 m2 /s. In a 2.0-cm-long tube with a cross-sectional area of 1.5 104 m2 , the mass rate of diffusion is m/t 4.2 1014 kg/s, because the glycine concentration is maintained at a value of 8.3 103 kg/m3 at one end of the tube and at a lower value at the other end. What is the lower concentration? 49. s

A large tank is filled with methane gas at a concentration of 0.650 kg/m3 . The valve of a 1.50-m pipe connecting the tank to the atmosphere is inadvertently left open for twelve hours. During this time, 9.00 104 kg of methane diffuses out of the tank, leaving the concentration of methane in the tank essentially unchanged. The diffusion constant for methane in air is 2.10 105 m2 /s. What is the crosssectional area of the pipe? Assume that the concentration of methane in the atmosphere is zero. *

Carbon tetrachloride (CCl 4) is diffusing through benzene (C6H6), as the drawing illustrates. The concentration of CCl 4 at the left end of the tube is maintained at 1.00 102 kg/m3 , and the diffusion constant is 20.0 1010 m2 /s. The CCl 4 enters the tube at a mass rate of 5.00 1013 kg/s. Using these data and those shown in the drawing, A find (a) the mass of CCl 4 per second that passes point A and (b) the concentration of CCl 4 at point A.

Review Conceptual Example 7 as background for this problem. It is possible to convert Ficks law into a form that is useful when the concentration is zero at one end of the diffusion channel (C1 0 in Figure 14.15a). (a) Noting that AL is the volume V of the channel and that m/V is the average concentration of solute in the channel, show that Ficks law becomes t L2 /(2D). This form of Ficks law can be used to estimate the time required for the first solute molecules to traverse the channel. (b) A bottle of perfume is opened in a room where convection currents are absent. Assuming that the diffusion constant for perfume in air is 1.0 105 m2 /s, estimate the minimum time required for the perfume to be smelled 2.5 cm away. **

The drawing shows a container that is partially filled with 2.0 grams of water. The temperature is maintained at a constant 20 C. The space above the liquid contains air that is completely saturated with water vapor. A tube of length 0.15 m and cross-sectional area 3.0 104 m2 connects the water vapor at one end to air that remains completely dry at the other end. The diffusion constant for water vapor in air is 2.4 105 m2 /s. How long does it take for the water in the container to evaporate completely? (H

At the start of a trip, a driver adjusts the absolute pressure in her tires to be 2.81 105 Pa when the outdoor temperature is 284 K. At the end of the trip she measures the pressure to be 3.01 105 Pa. Ignoring the expansion of the tires, find the air temperature inside the tires at the end of the trip. 54

When you push down on the handle of a bicycle pump, a piston in the pump cylinder compresses the air inside the cylinder. When the pressure in the cylinder is greater than the pressure inside the inner tube to which the pump is attached, air begins to flow from the pump to the inner tube. As a biker slowly begins to push down the handle of a bicycle pump, the pressure inside the cylinder is 1.0 105 Pa, and the piston in the pump is 0.55 m above the bottom of the cylinder. The pressure inside the inner tube is 2.4 105 Pa. How far down must the biker push the handle before air begins to flow from the pump to the inner tube? Ignore the air in the hose connecting the pump to the inner tube, and assume that the temperature of the air in the pump cylinder does not change.

In a diesel engine, the piston compresses air at 305 K to a volume that is one-sixteenth of the original volume and a pressure that is 48.5 times the original pressure. What is the temperature of the air after the compression?

When a gas is diffusing through air in a diffusion channel, the diffusion rate is the number of gas atoms per second diffusing from one end of the channel to the other end. The faster the atoms move, the greater is the diffusion rate, so the diffusion rate is proportional to the rms speed of the atoms. The atomic mass of ideal gas A is 1.0 u, and that of ideal gas B is 2.0 u. For diffusion through the same channel under the same conditions, find the ratio of the diffusion rate of gas A to the diffusion rate of gas B

Initially, the translational rms speed of a molecule of an ideal gas is 463 m/s. The pressure and volume of this gas are kept constant, while the number of molecules is doubled. What is the final translational rms speed of the molecules?

Consult Multiple-Concept Example 6 to review the principles involved in this problem. Near the surface of Venus, the rms speed of carbon dioxide molecules (CO2) is 650 m/s. What is the temperature (in kelvins) of the atmosphere at that point?

Oxygen for hospital patients is kept in special tanks, where the oxygen has a pressure of 65.0 atmospheres and a temperature of 288 K. The tanks are stored in a separate room, and the oxygen is pumped to the patients room, where it is administered at a pressure of 1.00 atmosphere and a temperature of 297 K. What volume does 1.00 m3 of oxygen in the tanks occupy at the conditions in the patients room?

At the normal boiling point of a material, the liquid phase has a density of 958 kg/m3 , and the vapor phase has a density of 0.598 kg/m3 . The average distance between neighboring molecules in the vapor phase is dvapor. The average distance between neighboring molecules in the liquid phase is dliquid. Determine the ratio dvapor/dliquid. (Hint: Assume that

Helium (He), a monatomic gas, fills a 0.010-m3 container. The pressure of the gas is 6.2 105 Pa. How long would a 0.25-hp engine have to run (1 hp 746 W) to produce an amount of energy equal to the internal energy of this gas? *

When perspiration on the human body absorbs heat, some of the perspiration turns into water vapor. The latent heat of vaporization at body temperature (37 C) is 2.42 106 J/kg. The heat absorbed is approximately equal to the average energy given to a single water molecule (H2O) times the number of water molecules that are vaporized. What is ?

A gas fills the right portion of a horizontal cylinder whose radius is 5.00 cm. The initial pressure of the gas is 1.01 105 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the drawing shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 20.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

The pressure of sulfur dioxide (SO2 ) is 2.12 104 Pa. There are 421 moles of this gas in a volume of 50.0 m3 . Find the translational rms speed of the sulfur dioxide molecules.