Answer: What is an ideal gas?

What are the phases of matter?

What is temperature?

What is an ideal gas?

What is an ideal-gas process?

Why are macroscopic properties important?

A project on which you are working uses a cylindrical lead pipe with outer and inner diameters of 4.0 cm and 3.5 cm, respectively, and a length of 50 cm. What is its mass?

The pressure in a system is measured to be 60 kPa. At a later time the pressure is 40 kPa. The value of p is a. 60 kPa b. 40 kPa c. 20 kPa d. -20 kPa

100 g of oxygen gas is how many moles of oxygen?

Which system contains more atoms: 5 mol of helium 1A = 42 or 1 mol of neon 1A = 202? a. Helium. b. Neon. Thermal expansion of the liquid in the thermometer tube pushes it higher in the hot water than in the ice water. c. They have the same number of atoms

The temperature of a glass of water increases from 20C to 30C. What is T? a. 10 K b. 283 K c. 293 K d. 303 K

A 55-m-long steel pipe runs from one side of a refinery to the other. By how much does the pipe expand on a 5C winter day when 155C oil is pumped through it?

A steel plate has a 2.000-cm-diameter hole through it. If the plate is heated, does the diameter of the hole increase or decrease?

100 g of oxygen gas is distilled into an evacuated 600 cm3 container. What is the gas pressure at a temperature of 150C?

For which is there a sublimation temperature that is higher than a melting temperature? a. Water b. Carbon dioxide c. Both d. Neither

A cylinder of gas is at 0C. A piston compresses the gas to half its original volume and three times its original pressure. What is the final gas temperature?

Standard temperature and pressure, abbreviated STP, are T = 0C and p = 1 atm. Estimate the average distance between gas molecules at STP

You have two containers of equal volume. One is full of helium gas. The other holds an equal mass of nitrogen gas. Both gases have the same pressure. How does the temperature of the helium compare to the temperature of the nitrogen? a. Thelium 7 Tnitrogen b. Thelium = Tnitrogen c. Thelium 6 Tnitrogen

A constant-volume gas thermometer A constant-volume gas thermometer is placed in contact with a reference cell containing water at the triple point. After reaching equilibrium, the gas pressure is recorded as 55.78 kPa. The thermometer is then placed in contact with a sample of unknown temperature. After the thermometer reaches a new equilibrium, the gas pressure is 65.12 kPa. What is the temperature of this sample?

Two cylinders of equal diameter contain the same number of moles of the same ideal gas. Each cylinder is sealed by a frictionless piston. To have the same pressure in both cylinders, which piston would you use in cylinder 2?

The two cylinders in FIGURE 18.12 contain ideal gases at 20C. Each cylinder is sealed by a frictionless piston of mass M. a. How does the pressure of gas 2 compare to that of gas 1? Is it larger, smaller, or the same? b. Suppose gas 2 is warmed to 80C. Describe what happens to the pressure and volume.

What is the ratio T2 /T1 for this process? a. 1 4 b. 1 2 c. 1 (no change) d. 2 e. 4 f. Theres not enough information to tell.

Your lab assistant distilled 50 g of a gas into a cylinder, but he left without writing down what kind of gas it is. The cylinder has a pressure regulator that adjusts a piston to keep the pressure at a constant 2.00 atm. To identify the gas, you measure the cylinder volume at several different temperatures, acquiring the data shown at the right. What is the gas?

An ocean snorkeler takes a deep breath at the surface, filling his lungs with 4.0 L of air. He then descends to a depth of 5.0 m. At this depth, what is the volume of air in the snorkelers lungs?

A gas at 2.0 atm pressure and a temperature of 200C is first expanded isothermally until its volume has doubled. It then undergoes an isobaric compression until it returns to its original volume. First show this process on a pV diagram. Then find the final temperature (in C) and pressure

A large, 50.0-cm-diameter metal cylinder filled with air supports a 20.0 kg piston that can slide up and down without friction. The piston is 100.0 cm above the bottom when the temperature is 20C. An 80.0 kg student then stands on the piston. After several minutes have elapsed, by how much has the piston been depressed

Rank in order, from highest to lowest, the temperatures T1 = 0 K, T2 = 0C, and T3 = 0F.

The sample in an experiment is initially at 10C. If the samples temperature is doubled, what is the new temperature in C?

a. Is there a highest temperature at which ice can exist? If so, what is it? If not, why not? b. Is there a lowest temperature at which water vapor can exist? If so, what is it? If not, why not?

The cylinder in FIGURE Q18.4 is divided into two compartments by a frictionless piston that can slide back and forth. If the piston is in equilibrium, is the pressure on the left side greater than, less than, or equal to the pressure on the right? Explain.

A gas is in a sealed container. By what factor does the gas temperature change if: a. The volume is doubled and the pressure is tripled? b. The volume is halved and the pressure is tripled

A gas is in a sealed container. The gas pressure is tripled and the temperature is doubled. a. Does the number of moles of gas in the container increase, decrease, or stay the same? b. By what factor does the number density of the gas increase?

An aquanaut lives in an underwater apartment 100 m beneath the surface of the ocean. Compare the freezing and boiling points of water in the aquanauts apartment to their values at the surface. Are they higher, lower, or the same? Explain.

a. A sample of water vapor in an enclosed cylinder has an initial pressure of 500 Pa at an initial temperature of -0.01C. A piston squeezes the sample smaller and smaller, without limit. Describe what happens to the water as the squeezing progresses. b. Repeat part a if the initial temperature is 0.03C warmer.

A gas is in a sealed container. By what factor does the gas pressure change if: a. The volume is doubled and the temperature is tripled? b. The volume is halved and the temperature is tripled?

A gas undergoes the process shown in FIGURE Q18.10. By what factor does the temperature change?

The temperature increases from 300 K to 1200 K as a gas undergoes the process shown in FIGURE Q18.11. What is the final pressure?

A student is asked to sketch a pV diagram for a gas that goes through a cycle consisting of (a) an isobaric expansion, (b) a constant-volume reduction in temperature, and (c) an isothermal process that returns the gas to its initial state. The student draws the diagram shown in FIGURE Q18.12. What, if anything, is wrong with the students diagram?

What volume of water has the same mass as 100 cm3 of gold?

The nucleus of a uranium atom has a diameter of 1.5 * 10-14 m and a mass of 4.0 * 10-25 kg. What is the density of the nucleus?

What is the diameter of a copper sphere that has the same mass as a 10 cm * 10 cm * 10 cm cube of aluminum?

A hollow aluminum sphere with outer diameter 10.0 cm has a mass of 690 g. What is the spheres inner diameter?

How many moles are in a 2.0 cm * 2.0 cm * 2.0 cm cube of copper?

How many atoms are in a 2.0 cm * 2.0 cm * 2.0 cm cube of aluminum?

What is the number density of (a) aluminum and (b) lead?

An element in its solid phase has mass density 1750 kg/m3 and number density 4.39 * 1028 atoms/m3 . What is the elements atomic mass number?

1.0 mol of gold is shaped into a sphere. What is the spheres diameter?

What volume of aluminum has the same number of atoms as 10 cm3 of mercury?

The lowest and highest natural temperatures ever recorded on earth are -129F in Antarctica and 134F in Death Valley. What are these temperatures in C and in K?

At what temperature does the numerical value in F match the numerical value in C?

A demented scientist creates a new temperature scale, the Z scale. He decides to call the boiling point of nitrogen 0Z and the melting point of iron 1000Z. a. What is the boiling point of water on the Z scale? b. Convert 500Z to degrees Celsius and to kelvins.

A concrete bridge is built of 325-cm-long concrete slabs with an expansion joint between them. The slabs just touch on a 115F day, the hottest day for which the bridge is designed. What is the gap between the slabs when the temperature is 0F?

A surveyor has a steel measuring tape that is calibrated to be 100.000 m long (i.e., accurate to {1 mm) at 20C. If she measures the distance between two stakes to be 65.175 m on a 3C day, does she need to add or subtract a correction factor to get the true distance? How large, in mm, is the correction factor

Two students each build a piece of scientific equipment that uses a 655-mm-long metal rod. One student uses a brass rod, the other an invar rod. If the temperature increases by 5.0C, how much more does the brass rod expand than the invar rod?

A 60.00 L fuel tank is filled with gasoline on a 10C day, then rolled into a storage shed where the temperature is 20C. If the tank is not vented, what minimum volume needs to be left empty at filling time so that the tank doesnt rupture as it warms?

What is the temperature in F and the pressure in Pa at the triple point of (a) water and (b) carbon dioxide?

A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, a. Has the mass density of the gas changed? If so, by what factor? If not, why not? b. Has the number of moles of gas changed? If so, by what factor? If not, why not?

3.0 mol of gas at a temperature of -120C fills a 2.0 L container. What is the gas pressure?

A rigid container holds 2.0 mol of gas at a pressure of 1.0 atm and a temperature of 30C. a. What is the containers volume? b. What is the pressure if the temperature is raised to 130C?

A gas at 100C fills volume V0. If the pressure is held constant, what is the volume if (a) the Celsius temperature is doubled and (b) the Kelvin temperature is doubled?

The total lung capacity of a typical adult is 5.0 L. Approximately 20% of the air is oxygen. At sea level and at a body temperature of 37C, how many oxygen molecules do the lungs contain at the end of a strong inhalation?

A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20C. a. How many moles of oxygen are in the cylinder? b. How many oxygen molecules are in the cylinder? c. What is the number density of the oxygen? d. What is the reading of a pressure gauge attached to the tank?

The solar corona is a very hot atmosphere surrounding the visible surface of the sun. X-ray emissions from the corona show that its temperature is about 2 * 106 K. The gas pressure in the corona is about 0.03 Pa. Estimate the number density of particles in the solar corona.

A gas at temperature T0 and atmospheric pressure fills a cylinder. The gas is transferred to a new cylinder with three times the volume, after which the pressure is half the original pressure. What is the new temperature of the gas?

A gas with initial state variables p1, V1, and T1 expands isothermally until V2 = 2V1. What are (a) T2 and (b) p2?

A gas with initial state variables p1, V1, and T1 is cooled in an isochoric process until p2 = 1 3 p1. What are (a) V2 and (b) T2?

A rigid, hollow sphere is submerged in boiling water in a room where the air pressure is 1.0 atm. The sphere has an open valve with its inlet just above the water level. After a long period of time has elapsed, the valve is closed. What will be the pressure inside the sphere if it is then placed in (a) a mixture of ice and water and (b) an insulated box filled with dry ice?

A rigid container holds hydrogen gas at a pressure of 3.0 atm and a temperature of 20C. What will the pressure be if the temperature is lowered to -20C?

A 24-cm-diameter vertical cylinder is sealed at the top by a frictionless 20 kg piston. The piston is 84 cm above the bottom when the gas temperature is 303C. The air above the piston is at 1.00 atm pressure. a. What is the gas pressure inside the cylinder? b. What will the height of the piston be if the temperature is lowered to 15C?

0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20C. The gas then undergoes an isochoric heating to a temperature of 300C. a. What is the final pressure of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes

0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20C. The gas then undergoes an isobaric heating to a temperature of 300C. a. What is the final volume of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes

| 0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20C. The gas then undergoes an isothermal expansion to a volume of 200 cm3 . a. What is the final pressure of the gas? b. Show the process on a pV diagram. Include a proper scale on both axes.

0.0040 mol of gas undergoes the process shown in FIGURE EX18.35. a. What type of process is this? b. What are the initial and final temperatures in C?

A gas with an initial temperature of 900C undergoes the process shown in FIGURE EX18.36. a. What type of process is this? b. What is the final temperature in C? c. How many moles of gas are there?

0.020 mol of gas undergoes the process shown in FIGURE EX18.37. a. What type of process is this? b. What is the final temperature in C? c. What is the final volume V2?

0.0050 mol of gas undergoes the process 1 S 2 S 3 shown in Figure P16.38. What are (a) temperature T1, (b) pressure p2, and (c) volume V3?

An ideal gas starts with pressure p1 and volume V1. Draw a pV diagram showing the process in which the gas undergoes an isochoric process that doubles the pressure, then an isobaric process that doubles the volume, followed by an isothermal process that doubles the volume again. Label each of the three processes

An ideal gas starts with pressure p1 and volume V1. Draw a pV diagram showing the process in which the gas undergoes an isothermal process during which the volume is halved, then an isochoric process during which the pressure is halved, followed by an isobaric process during which the volume is doubled. Label each of the three processes.

The atomic mass number of copper is A = 64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the atoms left behind are in a cubic crystal lattice. What is the smallest distance between two copper atoms?

The molecular mass of water (H2O) is A = 18. How many protons are there in 1.0 L of liquid water?

A brass ring with inner diameter 2.00 cm and outer diameter 3.00 cm needs to fit over a 2.00-cm-diameter steel rod, but at 20C the hole through the brass ring is 50 mm too small in diameter. To what temperature, in C, must the rod and ring be heated so that the ring just barely slips over the rod?

A 15C, 2.0-cm-diameter aluminum bar just barely slips between two rigid steel walls 10.0 cm apart. If the bar is warmed to 25C, how much force does it exert on each wall?

The semiconductor industry manufactures integrated circuits in large vacuum chambers where the pressure is 1.0 * 10-10 mm of Hg. a. What fraction is this of atmospheric pressure? b. At T = 20C, how many molecules are in a cylindrical chamber 40 cm in diameter and 30 cm tall?

A 6.0-cm-diameter, 10-cm-long cylinder contains 100 mg of oxygen (O2) at a pressure less than 1 atm. The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is 100 kPa, it takes a 184 N force to pull the cap off. What is the temperature of the gas?

A nebulaa region of the galaxy where new stars are formingcontains a very tenuous gas with 100 atoms/cm3 . This gas is heated to 7500 K by ultraviolet radiation from nearby stars. What is the gas pressure in atm?

On average, each person in the industrialized world is responsible for the emission of 10,000 kg of carbon dioxide (CO2) every year. This includes CO2 that you generate directly, by burning fossil fuels to operate your car or your furnace, as well as CO2 generated on your behalf by electric generating stations and manufacturing plants. CO2 is a greenhouse gas that contributes to global warming. If you were to store your yearly CO2 emissions in a cube at STP, how long would each edge of the cube be?

To determine the mass of neon contained in a rigid, 2.0 L cylinder, you vary the cylinders temperature while recording the reading of a pressure gauge. Your data are as follows: Temperature (C) Pressure gauge (atm) 100 6.52 150 7.80 200 8.83 250 9.59 Use the best-fit line of an appropriate graph to determine the mass of the neon

The 3.0-m-long pipe in FIGURE P18.50 is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the waters surface. What is the length L of the trapped volume of air?

A diving bell is a 3.0-m-tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is 20C. The bell is lowered into the ocean until its lower end is 100 m deep. The temperature at that depth is 10C. a. How high does the water rise in the bell after enough time has passed for the air inside to reach thermal equilibrium? b. A compressed-air hose from the surface is used to expel all the water from the bell. What minimum air pressure is needed to do this?

An electric generating plant boils water to produce highpressure steam. The steam spins a turbine that is connected to the generator. a. How many liters of water must be boiled to fill a 5.0 m3 boiler with 50 atm of steam at 400C? b. The steam has dropped to 2.0 atm pressure at 150C as it exits the turbine. How much volume does it now occupy?

On a cool morning, when the temperature is 15C, you measure the pressure in your car tires to be 30 psi. After driving 20 mi on the freeway, the temperature of your tires is 45C. What pressure will your tire gauge now show?

The air temperature and pressure in a laboratory are 20C and 1.0 atm. A 1.0 L container is open to the air. The container is then sealed and placed in a bath of boiling water. After reaching thermal equilibrium, the container is opened. How many moles of air escape?

10,000 cm3 of 200C steam at a pressure of 20 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in cm3 .

The mercury manometer shown in FIGURE P18.56 is attached to a gas cell. The mercury height h is 120 mm when the cell is placed in an ice-water mixture. The mercury height drops to 30 mm when the device is carried into an industrial freezer. What is the freezer temperature? Hint: The right tube of the manometer is much narrower than the left tube. What reasonable assumption can you make about the gas volume?

The U-shaped tube in FIGURE P18.57 has a total length of 1.0 m. It is open at one end, closed at the other, and is initially filled with air at 20C and 1.0 atm pressure. Mercury is poured slowly into the open end without letting any air escape, thus compressing the air. This is continued until the open side of the tube is completely filled with mercury. What is the length L of the column of mercury?

The 50 kg circular piston shown in FIGURE P18.58 floats on 0.12 mol of compressed air. a. What is the piston height h if the temperature is 30C? b. How far does the piston move if the temperature is increased by 100C?

A diver 50 m deep in 10C fresh water exhales a 1.0-cmdiameter bubble. What is the bubbles diameter just as it reaches the surface of the lake, where the water temperature is 20C? Hint: Assume that the air bubble is always in thermal equilibrium with the surrounding water.

8.0 g of helium gas follows the process 1 S 2 S 3 shown in FIGURE P18.60. Find the values of V1, V3, p2, and T3

FIGURE P18.61 shows two different processes by which 1.0 g of nitrogen gas moves from state 1 to state 2. The temperature of state 1 is 25C. What are (a) pressure p1 and (b) temperatures (in C) T2, T3, and T4?

FIGURE P18.62 shows two different processes by which 80 mol of gas move from state 1 to state 2. The dashed line is an isotherm. a. What is the temperature of the isothermal process? b. What maximum temperature is reached along the straightline process?

4.0 g of oxygen gas, starting at 820C, follow the process 1 S 2 shown in FIGURE P18.63. What is temperature T2 (in C)?

10 g of dry ice (solid CO2) is placed in a 10,000 cm3 container, then all the air is quickly pumped out and the container sealed. The container is warmed to 0C, a temperature at which CO2 is a gas. a. What is the gas pressure? Give your answer in atm. The gas then undergoes an isothermal compression until the pressure is 3.0 atm, immediately followed by an isobaric compression until the volume is 1000 cm3 . b. What is the final temperature of the gas (in C)? c. Show the process on a pV diagram.

A container of gas at 2.0 atm pressure and 127C is compressed at constant temperature until the volume is halved. It is then further compressed at constant pressure until the volume is halved again. a. What are the final pressure and temperature of the gas? b. Show this process on a pV diagram

Five grams of nitrogen gas at an initial pressure of 3.0 atm and at 20C undergo an isobaric expansion until the volume has tripled. a. What is the gas volume after the expansion? b. What is the gas temperature after the expansion (in C)? The gas pressure is then decreased at constant volume until the original temperature is reached. c. What is the gas pressure after the decrease? Finally, the gas is isothermally compressed until it returns to its initial volume. d. What is the final gas pressure? e. Show the full three-step process on a pV diagram. Use appropriate scales on both axes.

In Problems 67 through 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the solution of the problem.p2 = 300 cm3 100 cm3 * 1 * 2 atm

In Problems 67 through 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the solution of the problem.1T2 + 2732 K = 200 kPa 500 kPa * 1 * 1400 + 2732 K

In Problems 67 through 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the solution of the problem.V2 = 1400 + 2732 K 150 + 2732 K * 1 * 200 cm3

In Problems 67 through 70 you are given the equation(s) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation(s). b. Draw a pV diagram. c. Finish the solution of the problem.12.0 * 101,300 Pa21100 * 10-6 m3 2 = n18.31 J/mol K2T1 n = 0.12 g 20 g/mol T2 = 200 cm3 100 cm3 * 1 * T1

An inflated bicycle inner tube is 2.2 cm in diameter and 200 cm in circumference. A small leak causes the gauge pressure to decrease from 110 psi to 80 psi on a day when the temperature is 20C. What mass of air is lost? Assume the air is pure nitrogen

The cylinder in FIGURE CP18.72 has a moveable piston attached to a spring. The cylinders cross-section area is 10 cm2 , it contains 0.0040 mol of gas, and the spring constant is 1500 N/m. At 20C the spring is neither compressed nor stretched. How far is the spring compressed if the gas temperature is raised to 100C?

Containers A and B in FIGURE CP18.73 hold the same gas. The volume of B is four times the volume of A. The two containers are connected by a thin tube (negligible volume) and a valve that is closed. The gas in A is at 300 K and pressure of 1.0 * 105 Pa. The gas in B is at 400 K and pressure of 5.0 * 105 Pa. Heaters will maintain the temperatures of A and B even after the valve is opened. After the valve is opened, gas will flow one way or the other until A and B have equal pressure. What is this final pressure?

The closed cylinder of FIGURE CP18.74 has a tight-fitting but frictionless piston of mass M. The piston is in equilibrium when the left chamber has pressure p0 and length L0 while the spring on the right is compressed by L. a. What is L in terms of p0, L0, A, M, and k? b. Suppose the piston is moved a small distance x to the right. Find an expression for the net force (Fx)net on the piston. Assume all motions are slow enough for the gas to remain at the same temperature as its surroundings. c. If released, the piston will oscillate around the equilibrium position. Assuming x V L0 find an expression for the oscillation period T. Hint: Use the binomial approximation.