(Ill) A sealed container containing 4.0 mol of gas

(I) How does the number of atoms in a 21.5-g gold ring compare to the number in a silver ring of the same mass?

(I) How many atoms are there in a 3.4-g copper penny?

(I) (a) Room temperature is often taken to be 68F. What is this on the Celsius scale? (b) The temperature of the filament in a lightbulb is about 1900C. What is this on the Fahrenheit scale?

(I) Among the highest and lowest natural air temperatures recorded are 136F in the Libyan desert and 129F in Antarctica. What are these temperatures on the Celsius scale?

(I) A thermometer tells you that you have a fever of 39.4C. What is this in Fahrenheit?

In an alcohol-in-glass thermometer, the alcohol column has length 11.82 cm at 0.0C and length 21.85 cm at 100.0C. What is the terrmerature if the mliimn has length (a\ 18 7 0 r.m and

(I) The Eiffel Tower (Fig. 17-19) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between January (average temperature of 2C) and July (average temperature of 25C). Ignore the angles of the iron beams and treat the tower as a vertical beam. FIGURE 17-19 Problem 7.

(I) A concrete highway is built of slabs 12 m long (20C). How wide should the expansion cracks between the slabs be (at 15C) to prevent buckling if the range of temperature is 30C to +50C?

(I) Super Invar, an alloy of iron and nickel, is a strong material with a very low coefficient of thermal expansion (0.20 X 10_6/C). A 1.6-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this alloy table expand along its length if the temperature increases 5.0 C? Compare to tabletops made of steel.

(II) To what temperature would you have to heat a brass rod for it to be 1.0% longer than it is at 25C?

(II) The density of water at 4C is 1.00 X 103 kg/m3. What is waters density at 94C? Assume a constant coefficient of volume expansion.

(II) At a given latitude, ocean water in the so-called mixed layer (from the surface to a depth of about 50 m) is at approximately the same temperature due to the mixing action of waves. Assume that because of global warming, the temperature of the mixed layer is everywhere increased by 0.5 C, while the temperature of the deeper portions of the ocean remains unchanged. Estimate the resulting rise in sea level. The ocean covers about 70% of the Earths surface.

(II) To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872 cm in diameter is to be placed in a hole 1.870 cm in diameter in a metal at 20 C. To what temperature must the rivet be cooled if it is to fit in the hole?

(II) A uniform rectangular plate of length and width w has a coefficient of linear expansion a. Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change AT is A A = 2aiwAT. See 1---------------h Af Fig. 17-20. FIGURE 17-20 Problem 14. A rectangular plate is heated.

(II) An aluminum sphere is 8.75 cm in diameter. What will be its change in volume if it is heated from 30 C to 180C?

(II) A typical car has 17 L of liquid coolant circulating at a temperature of 93C through the engines cooling system. Assume that, in this normal condition, the coolant completely fills the 3.5-L volume of the aluminum radiator and the 13.5-L internal cavities within the steel engine. When a car overheats, the radiator, engine, and coolant expand and a small reservoir connected to the radiator catches any resultant coolant overflow. Estimate how much coolant overflows to the reservoir if the system is heated from 93 C to 105C. Model the radiator and engine as hollow shells of aluminum and steel, respectively. The coefficient of volume expansion for coolant is (3 = 410 X 10 6/ C.

It is observed that 55.50 mL of water at 20C completely fills a container to the brim. When the container and the water are heated to 60C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container? (h\ What is the most likelv material o f the

(II) (a) A brass plug is to be placed in a ring made of iron. At 15C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit? (b) What if the plug were iron and the ring brass?

(II) If a fluid is contained in a long narrow vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion a is approximately equal to the coefficient of volume expansion /3.

(II) (a) Show that the change in the density p of a substance, when the temperature changes by AT, is given by Ap = (3p AT. (b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 C to -55C?

(II) Wine bottles are never completely filled: a small volume of air is left in the glass bottles cylindrically shaped neck (inner diameter d = 18.5 mm) to allow for wines fairly large coefficient of thermal expansion. The distance H between the surface of the liquid contents and the bottom of the cork is called the headspace height (Fig. 17-21), and is typically H = 1.5 cm for a 750-mL bottle filled at 20 C. Due to its alcoholic content, wines coefficient of volume expansion is about double that of water; in comparison, the thermal expansion of glass can be neglected. Estimate H if the bottle is kept (a) at 10C, (b) at 30C. FIGURE 17-21 Problem 21.

(Ill) (a) Determine a formula for the change in surface area of a uniform solid sphere of radius r if its coefficient of linear expansion is a (assumed constant) and its temperature is changed by AT. (b) What is the increase in area of a solid iron sphere of radius 60.0 cm if its temperature is raised from 15C to 275C?

(Ill) The pendulum in a grandfather clock is made of brass and keeps perfect time at 17C. How much time is gained or lost in a year if the clock is kept at 28C? (Assume the frequency dependence on length for a simple pendulum applies.)

(Ill) A 28.4-kg solid aluminum cylindrical wheel of radius 0.41 m is rotating about its axle in frictionless bearings with angular velocity (o = 32.8 rad/s. If its temperature is then raised from 20.0C to 95.0C, what is the fractional change in &>?

(I) An aluminum bar has the desired length when at 18C. How much stress is required to keep it at this length if the temperature increases to 35 C?

(a) A horizontal steel I-beam of cross-sectional area 0.041 m2 is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 25C, what stress is developed in the beam when the temperature drops to -25C? (b) Is the ultimate strength of the steel exceeded? (n\ What stress is develoned if the beam is concrete and has a

(Ill) A barrel of diameter 134.122 cm at 20C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20C. It is 9.4 cm wide and 0.65 cm thick, {a) To what temperature must the band be heated so that it will fit over the barrel? (b) What will be the tension in the band when it cools to 20 C?

(I) What are the following temperatures on the Kelvin scale: (a) 66C, (b) 92F, (c) -55C, (d) 5500C?

(I) Absolute zero is what temperature on the Fahrenheit scale?

(II) Typical temperatures in the interior of the Earth and Sun are about 4000C and 15 X 106 C, respectively, (a) What are these temperatures in kelvins? (b) What percent error is made in each case if a person forgets to change C to K?

(I) If 3.80 m3 of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0C. What is the volume?

(I) In an internal combustion engine, air at atmospheric pressure and a temperature of about 20 C is compressed in the cylinder by a piston to of its original volume (compression ratio = 8.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.

(II) Calculate the density of nitrogen at STP using the ideal gas law.

(II) If 14.00 mol of helium gas is at 10.0C and a gauge pressure of 0.350 atm, calculate (a) the volume of the helium gas under these conditions, and (b) the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

(II) A stoppered test tube traps 25.0 cm3 of air at a pressure of 1.00 atm and temperature of 18C. The cylindrically shaped stopper at the test tubes mouth has a diameter of 1.50 cm and will pop off the test tube if a net upward force of 10.0 N is applied to it. To what temperature would one have to heat the trapped air in order to pop off the stopper? Assume the air surrounding the test tube is always at a pressure of 1.00 atm.

(II) A storage tank contains 21.6 kg of nitrogen (N2) at an absolute pressure of 3.85 atm. What will the pressure be if the nitrogen is replaced by an equal mass of C02 at the same temperature?

(II) A storage tank at STP contains 28.5 kg of nitrogen (N2). (a) What is the volume of the tank? (b) What is the pressure if an additional 25.0 kg of nitrogen is added without changing the temperature?

(II) A scuba tank is filled with air to a pressure of 204 atm when the air temperature is 29C. A diver then jumps into the ocean and, after a short time treading water on the ocean surface, checks the tanks pressure and finds that it is only 194 atm. Assuming the diver has inhaled a negligible amount of air from the tank, what is the temperature of the ocean water?

(II) What is the pressure inside a 38.0-L container holding 105.0 kg of argon gas at 20.0C?

A tank contains 30.0 kg of 0 2 gas at a gauge pressure of 8.20 atm. If the oxygen is replaced by helium at the same temnerature. how manv kilograms of the latter will he

(II) A sealed metal container contains a gas at 20.0C and 1.00 atm. To what temperature must the gas be heated for the pressure to double to 2.00 atm? (Ignore expansion of the container.)

(II) A tire is filled with air at 15C to a gauge pressure of 250 kPa. If the tire reaches a temperature of 38C, what fraction of the original air must be removed if the original pressure of 250 kPa is to be maintained?

(II) If 61.5 L of oxygen at 18.0C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 56.0C, what will the new pressure be?

(II) A helium-filled balloon escapes a childs hand at sea level and 20.0C. When it reaches an altitude of 3600 m, where the temperature is 5.0C and the pressure only 0.68 atm, how will its volume compare to that at sea level?

(II) A sealed metal container can withstand a pressure difference of 0.50 atm. The container initially is filled with an ideal gas at 18C and 1.0 atm. To what temperature can you cool the container before it collapses? (Ignore any changes in the containers volume due to thermal expansion.)

(II) You buy an airtight bag of potato chips packaged at sea level, and take the chips on an airplane flight. When you take the potato chips out of your luggage, you notice it has noticeably puffed up. Airplane cabins are typically pressurized at 0.75 atm, and assuming the temperature inside an airplane is about the same as inside a potato chip processing plant, by what percentage has the bag puffed up in comparison to when it was packaged?

(II) A typical scuba tank, when fully charged, contains 12 L of air at 204 atm. Assume an empty tank contains air at 34 atm and is connected to an air compressor at sea level. The air compressor intakes air from the atmosphere, compresses it to high pressure, and then inputs this highpressure air into the scuba tank. If the (average) flow rate of air from the atmosphere into the intake port of the air compressor is 290L/min, how long will it take to fully charge the scuba tank? Assume the tank remains at the same temperature as the surrounding air during the filling process.

(Ill) A sealed container containing 4.0 mol of gas is squeezed, changing its volume from 0.020 m3 to 0.018 m3. During this process, the temperature decreases by 9.0 K while the pressure increases by 450 Pa. What was the original pressure and temperature of the gas in the container?

(Ill) Compare the value for the density of water vapor at exactly 100C and 1 atm (Table 13-1) with the value predicted from the ideal gas law. Why would you expect a difference?

(Ill) An air bubble at the bottom of a lake 37.0 m deep has a volume of 1.00 cm3. If the temperature at the bottom is 5.5C and at the top 18.5C, what is the volume of the bubble just before it reaches the surface?

(I) Calculate the number of molecules/m3 in an ideal gas at STP.

(I) How many moles of water are there in 1.000 L at STP? How many molecules?

(II) What is the pressure in a region of outer space where there is 1 molecule/cm3 and the temperature is 3 K?

Estimate the number of (a) moles and (b) molecules of water in all the F.arths oceans. Assume water covers 75% of

(II) The lowest pressure attainable using the best available vacuum techniques is about 10_12N/m2. At such a pressure, how many molecules are there per cm3 at 0C?

(II) Is a gas mostly empty space? Check by assuming that the spatial extent of common gas molecules is about = 0.3 nm so one gas molecule occupies an approximate volume equal to Assume STP.

(Ill) Estimate how many molecules of air are in each 2.0-L breath you inhale that were also in the last breath Galileo took. [Hint. Assume the atmosphere is about 10 km high and of constant density.]

(I) In a constant-volume gas thermometer, what is the limiting ratio of the pressure at the boiling point of water at 1 atm to that at the triple point? (Keep five significant figures.)

(I) At the boiling point of sulfur (444.6C) the pressure in a constant-volume gas thermometer is 187 torr. Estimate (a) the pressure at the triple point of water, (b) the temperature when the pressure in the thermometer is 118 torr.

(II) Use Fig. 17-17 to determine the inaccuracy of a constant-volume gas thermometer using oxygen if it reads a pressure P = 268 torr at the boiling point of water at 1 atm. Express answer (a) in kelvins and (b) as a percentage.

(Ill) A constant-volume gas thermometer is being used to determine the temperature of the melting point of a substance. The pressure in the thermometer at this temperature is 218 torr; at the triple point of water, the pressure is 286 torr. Some gas is now released from the thermometer bulb so that the pressure at the triple point of water becomes 163 torr. At the temperature of the melting substance, the pressure is 128 torr. Estimate, as accurately as possible, the melting-point temperature of the substance.

A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 350 mL of cool water, if the water and the cup are hot, at 95C, instead of at room temperature? Neglect the glass expansion.

A precise steel tape measure has been calibrated at 15C. At 36C, (a) will it read high or low, and (b) what will be the percentage error?

A cubic box of volume 6.15 X 10_2m3 is filled with air at atmospheric pressure at 15C. The box is closed and heated to 185C. What is the net force on each side of the box?

The gauge pressure in a helium gas cylinder is initially 32 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the original gas remains in the cylinder?

If a rod of original length ^ has its temperature changed from Ti to T2, determine a formula for its new length i2 in terms of T\,T2, and a. Assume (a) a = constant, (ib) a = a(T) is some function of temperature, and (c) a = a0 + bT where a 0 and b are constants.

If a scuba diver fills his lungs to full capacity of 5.5 L when 8.0 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?

(a) Use the ideal gas law to show that, for an ideal gas at constant pressure, the coefficient of volume expansion is equal to /3 = 1/T, where T is the kelvin temperature. Compare to Table 17-1 for gases at T = 293 K. (b) Show that the bulk modulus (Section 12-4) for an ideal gas held at constant temperature is B = P, where P is the pressure.

A house has a volume of 870 m3. (a) What is the total mass of air inside the house at 15C? (b) If the temperature drops to 15C, what mass of air enters or leaves the house?

Assume that in an alternate universe, the laws of physics are very different from ours and that ideal gases behave as follows: (i) At constant temperature, pressure is inversely proportional to the square of the volume, (ii) At constant pressure, the volume varies directly with the power of the temperature, (iii) At 273.15 K and 1.00 atm pressure, 1.00 mole of an ideal gas is found to occupy 22.4 L. Obtain the form of the ideal pas law in this alternate universe, including the

An iron cube floats in a bowl of liquid mercury at 0C. (a) If the temperature is raised to 25C, will the cube float higher or lower in the mercury? (b) By what percent will the fraction of volume submerged change?

(a) The tube of a mercury thermometer has an inside diameter of 0.140 mm. The bulb has a volume of 0.275 cm3. How far will the thread of mercury move when the temperature changes from 10.5C to 33.0C? Take into account expansion of the Pyrex glass. (b) Determine a formula for the change in length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

From the known value of atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earths atmosphere.

STP, and when it is a solid deep in the Earth where the temperature is 2000C and under 5000 atm of pressure. Assume the bulk modulus (90 X 109N/m2) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.

What is the average distance between nitrogen molecules at STP?

A helium balloon, assumed to be a perfect sphere, has a radius of 22.0 cm. At room temperature (20C), its internal pressure is 1.06 atm. Determine the number of moles of helium in the balloon, and the mass of helium needed to inflate the balloon to these values.

A standard cylinder of oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPa) and volume = 14 L (0.014 m3) at T = 295 K. How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min?

A brass lid screws tightly onto a glass jar at 15C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 75C. The inside diameter of the lid is 8.0 cm. Find the size of

The density of gasoline at 0C is 0.68 X 103 kg/m3, (a) What is the densitv on a hot dav when the terrmerature is 35C!?

A helium balloon has volume Vq and temperature T0 at sea level where the pressure is P0 and the air density is p0. The balloon is allowed to float up in the air to altitude y where the temperature is T\. (a) Show that the volume occupied by the balloon is then V = Vo(Ti/To)e+cy where c = Pog/Po = 1.25 X 10-4m-1. (b) Show that the buoyant force does not depend on altitude y. Assume that the skin of the balloon maintains the helium pressure at a constant factor of 1.05 times greater than the outside pressure. [Hint. Assume that the pressure change with altitude is P = Pq e~cy, as in Example 13-5, Chapter 13.]

The first length standard, adopted in the eighteenth century, was a platinum bar with two very fine marks separated by what was defined to be exactly one meter. If this standard bar was to be accurate to within 1.0 pm, how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion is 9 X 10_6/C.

A scuba tank when fully charged has a pressure of 180 atm at 20 C. The volume of the tank is 11.3 L. (a) What would the volume of the air be at 1.00 atm and at the same temperature? (b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last? (c) At a depth of 20.0 m in sea water at a temperature of 10C, how long would the same tank last assuming the breathing rate does not change?

A temperature controller, designed to work in a steam environment, involves a bimetallic strip constructed of brass and steel, connected at their ends by rivets. Each of the metals is 2.0 mm thick. At 20C, the strip is 10.0 cm long and straight. Find the radius of curvature r of the assembly at 100C. See Fig. 17-22. FIGURE 17-22 Problem 83.

A copper wire sags 50.0 cm between two utility poles 30.0 m apart when the temperature is 15C. Estimate the amount of sag when the temperature is +35C. [Hint: An estimate can be made by assuming the shape of the wire is approximately an arc of a circle; hard equations can sometimes be solved by guessing values.]

Snorkelers breathe through short tubular snorkels while swimming under water very near the surface. One end of the snorkel attaches to the snorkelers mouth while the other end protrudes above the waters surface. Unfortunately, snorkels cannot support breathing to any great depth: it is said that a typical snorkeler below a water depth of only about 30 cm cannot draw a breath through a snorkel. Based on this claim, what is the approximate fractional change in a typical persons lung volume when drawing a breath? Assume, in equilibrium, the air pressure in a snorkelers lungs matches that of the surrounding water pressure.

(II) A thermocouple consists of a junction of two different types of materials that produces a voltage depending on its temperature. A thermocouples voltages were recorded when at different temperatures as follows: Temperature (C) 50 100 200 300 Voltage (mV)________1.41 2.96 5.90 8.92 Use a spreadsheet to fit these data to a cubic equation and determine the temperature when the thermocouple produces 3.21 mV. Get a second value of the temperature by fitting the data to a quadratic equation.

(Ill) You have a vial of an unknown liquid which might be octane (gasoline), water, glycerin, or ethyl alcohol. You are trying to determine its identity by studying how its volume changes with temperature changes. You fill a Pyrex graduated cylinder to 100.00 mL with the liquid when the liquid and the cylinder are at 0.000C. You raise the temperature in five-degree increments, allowing the graduated cylinder and liquid to come to equilibrium at each temperature. You read the volumes listed below off the graduated cylinder at each temperature. Take into account the expansion of the Pyrex glass cylinder. Graph the data, possibly using a spreadsheet program, and determine the slope of the line to find the effective (combined) coefficient of volume expansion /3. Then determine (3 for the liquid and which liquid is in the vial.