At what temperature is the rms speed of equal to the rms

(a) Is the number of molecules in one mole of greater than, less than, or equal to the number of molecules in one mole of ? (b) Is the mass of one mole of greater than, less than, or equal to the mass of one mole of ?

Is the number of atoms in one mole of helium greater than, less than, or equal to the number of atoms in one mole of oxygen? Helium consists of individual atoms, He, and oxygen is a diatomic gas, O2.

Predict/Explain If you put a helium-lled balloon in the refrigerator, (a) will its volume increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. Lowering the temperature of an ideal gas at constant pressure results in a reduced volume. II. The same amount of gas is in the balloon; therefore, its volume remains the same. III. The balloon can expand more in the cool air of the refrigerator, giving an increased volume.

Two containers hold ideal gases at the same temperature. Container Ahas twice the volume and half the number of molecules as container B. What is the ratio , where is the pressure in container A and is the pressure in container B?

Standard temperature and pressure (STP) is dened as a temperature of 0 C and a pressure of 101.3 kPa. What is the volume occupied by one mole of an ideal gas at STP?

After emptying her lungs, a person inhales 4.1 Lof air at 0.0 C and holds her breath. How much does the volume of the air increase as it warms to her body temperature of 37 C?

In the morning, when the temperature is 286 K, a bicyclist nds that the absolute pressure in his tires is 501 kPa. That afternoon he nds that the pressure in the tires has increased to 554 kPa. Ignoring expansion of the tires, nd the afternoon temperature.

An automobile tire has a volume of . At a temperature of 294 K the absolute pressure in the tire is 212 kPa. How many moles of air must be pumped into the tire to increase its pressure to 252 kPa, given that the temperature and volume of the tire remain constant?

Amount of Helium in a Blimp The Goodyear blimp Spirit of Akron is 62.6 m long and contains of helium. When the temperature of the helium is 285 K, its absolute pressure is 112 kPa. Find the mass of the helium in the blimp.

Acompressed-air tank holds of air at a temperature of 285 K and a pressure of 880 kPa. What volume would the air occupy if it were released into the atmosphere, where the pressure is 101 kPa and the temperature is 303 K?

A typical region of interstellar space may contain atoms per cubic meter (primarily hydrogen) at a temperature of 100 K. What is the pressure of this gas?

Four ideal gases have the following pressures, P, volumes, V, and mole numbers, n: gas A, P = 100 kPa, V = 1 m3, Rank these gases in order of increasing temperature. Indicate ties where appropriate.

Aballoon contains 3.7 liters of nitrogen gas at a temperature of 87 K and a pressure of 101 kPa. If the temperature of the gas is allowed to increase to 24 C and the pressure remains constant, what volume will the gas occupy?

Aballoon is lled with helium at a pressure of . The balloon is at a temperature of 18 C and has a radius of 0.25 m. (a) How many helium atoms are contained in the balloon? (b) Suppose we double the number of helium atoms in the balloon, keeping the pressure and the temperature xed. By what factor does the radius of the balloon increase? Explain.

Agas has a temperature of 310 K and a pressure of 101 kPa. (a) Find the volume occupied by 1.25 mol of this gas, assuming it is ideal. (b) Assuming the gas molecules can be approximated as small spheres of diameter , determine the fraction of the volume found in part (a) that is occupied by the molecules. (c) In determining the properties of an ideal gas, we assume that molecules are points of zero volume. Discuss the validity of this assumption for the case considered here.

A ask contains 0.460 g of a gas at a pressure of 153 kPa and a temperature of 322 K. What is the molecular mass of this gas?

The Atmosphere of Mars On Mars, the average temperature is and the average atmospheric pressure is 0.92kPa.(a)What is the number of molecules per volume in the Martian atmosphere? (b) Is the number of molecules per volume on the Earth greater than, less than, or equal to the number per volume on Mars? Explain your reasoning. (c) Estimate the number of molecules per volume in Earths atmosphere.

The air inside a hot-air balloon has an average temperature of . The outside air has a temperature of . What is the ratio of the density of air in the balloon to the density of air in the surrounding atmosphere?

Acylindrical ask is tted with an airtight piston that is free to slide up and down, as shown in Figure 1724. Amass rests on top of the piston. The initial temperature of the system is 313 K and the pressure of the gas is held constant at 137 kPa. The temperature is now increased until the height of the piston rises from 23.4 cm to 26.0 cm. What is the nal temperature of the gas?

Consider the system described in Problem 19. Contained within the ask is an ideal gas at a constant temperature of 313 K. Initially the pressure applied by the piston and the mass is 137 kPa and the height of the piston above the base of the ask is 23.4 cm. When additional mass is added to the piston, the height of the piston decreases to 20.0 cm. Find the new pressure applied by the piston.

One mole of a monatomic ideal gas has an initial pressure of 210 kPa, an initial volume of , and an initial temperature of 350 K. The gas now undergoes three separate processes: (i) a constant-temperature expansion that triples its volume; (ii) a constant-pressure compression to its initial volume; and (iii) a constant-volume increase in pressure to its initial pressure. At the end of these three processes, the gas is back at its initial pressure, volume, and temperature. Plot these processes on a pressure-versus-volume graph, showing the values of P and V at the end points of each process.

Predict/Explain The air in your room is composed mostly of oxygen and nitrogen molecules. The oxygen molecules are more massive than the nitrogen molecules. (a) Is the rms speed of the molecules greater than, less than, or equal to the rms speed of the molecules? (b)Choose the best explanation from among the following: I. The more massive oxygen molecules have greater momentum and therefore greater speed. II. Equal temperatures for the oxygen and nitrogen molecules imply they have equal rms speeds. III. The temperature is the same for both molecules, and hence their average kinetic energies are equal. As a result, the more massive oxygen molecules have lower speeds.

If the translational speed of molecules in an ideal gas is doubled, by what factor does the Kelvin temperature change? Explain.

Apiston held at the temperature T contains a gas mixture with molecules of three different types; A, B, and C. The corresponding molecular masses are . Rank these molecular types in order of increasing (a) average kinetic energy and (b) rms speed. Indicate ties where appropriate.

The molecules in a tank of hydrogen have the same rms speed as the molecules in a tank of oxygen. State whether each of the following statements is true, false, or unknowable with the given information: (a) the pressures are the same; (b) the hydrogen is at the higher temperature; (c) the hydrogen has the higher pressure; (d) the temperatures are the same; (e) the oxygen is at the higher temperature.

At what temperature is the rms speed of equal to the rms speed that has at 313 K?

Suppose a planet has an atmosphere of pure ammonia at 0.0 C. What is the rms speed of the ammonia molecules?

Three moles of oxygen gas are placed in a portable container with a volume of .If the temperature of the gas is 295 C, nd (a) the pressure of the gas and (b) the average kinetic energy of an oxygen molecule. (c) Suppose the volume of the gas is doubled, while the temperature and number of moles are held constant. By what factor do your answers to parts (a) and (b) change? Explain.

The rms speed of is 1550 m/s at a given temperature. (a) Is the rms speed of at this temperature greater than, less than, or equal to 1550 m/s? Explain. (b)Find the rms speed of at this temperature

An ideal gas is kept in a container of constant volume. The pressure of the gas is also kept constant. (a) If the number of molecules in the gas is doubled, does the rms speed increase, decrease, or stay the same? Explain. (b) If the initial rms speed is 1300 m/s, what is the nal rms speed?

What is the temperature of a gas of molecules whose rms speed is 329 m/s?

The rms speed of a sample of gas is increased by 1%. (a)What is the percent change in the temperature of the gas? (b) What is the percent change in the pressure of the gas, assuming its volume is held constant?

Enriching UraniumIn naturally occurring uranium atoms, 99.3% are (atomic , where ) and only 0.7% are . Uranium-fueled reactors require an enhanced proportion of . Since both isotopes of uranium have identical chemical properties, they can be separated only by methods that depend on their differing masses. One such method is gaseous diffusion, in which uranium hexauoride gas diffuses through a series of porous barriers. The lighter molecules have a slightly higher rms speed at a given temperature than the heavier molecules, and this allows the two isotopes to be separated. Find the ratio of the rms speeds of the two isotopes at 23.0 C.

A350-mLspherical ask contains 0.075 mol of an ideal gas at a temperature of 293 K. What is the average force exerted on the walls of the ask by a single molecule?

Abrick has faces with the following dimensions: face 1 is 1 cm by 2 cm; face 2 is 2 cm by 3 cm; face 3 is 1 cm by 3 cm. On which face should the brick be placed if it is to have the smallest change in dimensions due to its own weight? Explain.

Predict/Explain A hollow cylindrical rod (rod 1) and a solid cylindrical rod (rod 2) are made of the same material. The two rods have the same length and the same outer radius. If the same compressional force is applied to each rod, (a) is the change in length of rod 1 greater than, less than, or equal to the change in length of rod 2? (b)Choose the bestexplanation from among the following: I. The solid rod has the larger effective cross-sectional area, since the empty part of the hollow rod doesnt resist compression. Therefore, the solid rod has the smaller change in length. II. The rods have the same outer radius and hence the same cross-sectional area. As a result, their change in length is the same. III. The walls of the hollow rod are hard and resist compression more than the uniform material in the solid rod. Therefore the hollow rod has the smaller change in length.

A rock climber hangs freely from a nylon rope that is 14 m long and has a diameter of 8.3 mm. If the rope stretches 4.6 cm, what is the mass of the climber?

To stretch a relaxed biceps muscle 2.5 cm requires a force of 25 N. Find the Youngs modulus for the muscle tissue, assuming it to be a uniform cylinder of length 0.24 m and crosssectional area

A22-kg chimpanzee hangs from the end of a horizontal, broken branch 1.1 m long, as shown in Figure 1725. The branch is a uniform cylinder 4.6 cm in diameter, and the end of the branch supporting the chimp sags downward through a vertical distance of 13 cm. What is the shear modulus for this branch?

The Marianas Trench The deepest place in all the oceans is the Marianas Trench, where the depth is 10.9 km and the pressure is . If a copper ball 15.0 cm in diameter is taken to the bottom of the trench, by how much does its volume decrease?

Four cylindrical rods with various cross-sectional areas and initial lengths are stretched by an applied force, as in Figure 1710. The resulting change in length of each rod is given in the following table. Rank these rods in order of increasing Youngs modulus. Indicate ties where appropriate.

Asteel wire 4.7 m long stretches 0.11 cm when it is given a tension of 360 N. (a) What is the diameter of the wire? (b) If it is desired that the stretch be less than 0.11 cm, should its diameter be increased or decreased? Explain.

SpiderwebAn orb weaver spider with a mass of 0.26 g hangs vertically by one of its threads. The thread has a Youngs modulus of and a radius of . (a) What is the fractional increase in the threads length caused by the spider? (b)Suppose a 76-kg person hangs vertically from a nylon rope. What radius must the rope have if its fractional increase in length is to be the same as that of the spiders thread?

Two rods of equal length (0.55 m) and diameter (1.7 cm) are placed end to end. One rod is aluminum, the other is brass. If a compressive force of 8400 N is applied to the rods, (a) how much does their combined length decrease? (b) Which of the rods changes its length by the greatest amount? Explain.

Apiano wire 0.82 m long and 0.93 mm in diameter is xed on one end. The other end is wrapped around a tuning peg 3.5 mm in diameter. Initially the wire, whose Youngs modulus is , has a tension of 14 N. Find the tension in the wire after the tuning peg has been turned through one complete revolution.

The formation of ice from water is accompanied by which of the following: (a) an absorption of heat by the water; (b) an increase in temperature; (c)a decrease in volume; (d)a removal of heat from the water; (e) a decrease in temperature?

Vapor Pressure for WaterFigure 1726shows a portion of the vapor-pressure curve for water. Referring to the gure, estimate the pressure that would be required for water to boil at 30 C.

Using the vapor-pressure curve given in Figure 1726, nd the temperature at which water boils when the pressure is 1.5 kPa.

A portion of the vaporpressure curve for carbon dioxide is given in Figure 1727. (a)Estimate the pressure at which boils at 0 C. (b)If the temperature is increased, does the boiling pressure increase, decrease, or stay the same? Explain.

Referring to the vapor-pressure curve for carbon dioxide given in Figure 1727, (a) estimate the temperature at which boils when the pressure is . (b) If the pressure is increased, does the boiling temperature increase, decrease, or stay the same? Explain.

Phase Diagram for Water The phase diagram for water is shown in Figure 1728. (a) What is the temperature on the phase diagram? (b)What is the temperature on the phase diagram? (c) What happens to the melting/freezing temperature of water if atmospheric pressure is decreased? Justify your answer by referring to the phase diagram. (d) What happens to the boiling/condensation temperature of water if atmospheric pressure is increased? Justify your answer by referring to the phase diagram.

Phase Diagram for The phase diagram for is shown in Figure 1729.(a)What is the phase of at and ? (b) What is the phase of at and ? (c)For reasons of economy and convenience, bulk is often transported in liquid form in pressurized tanks. Using the phase diagram, determine the minimum pressure required to keep in the liquid phase at 20 C.

Asample of water ice at atmospheric pressure has a temperature just below the freezing point. Refer to Figure 1728 to answer the following questions. (a) What phase changes occur if the temperature of the system is increased while the pressure is held constant? (b)Suppose, instead, that the temperature of the system is held constant just below the freezing point while the pressure is decreased. What phase changes occur now?

Asample of liquid water at atmospheric pressure has a temperature just above the freezing point. Refer to Figure 1728 to answer the following questions. (a) What phase changes occur if the temperature of the system is increased while the pressure is held constant? (b) Suppose, instead, that the temperature of the system is held constant just above the freezing point while the pressure is decreased. What phase changes occur now?

A sample of solid carbon dioxide at a pressure of 5707 kPa has a temperature just below the freezing point. Refer to Figure 1729to answer the following questions. (a)What phase changes occur if the temperature of the system is increased while the pressure is held constant? (b) Suppose, instead, that the temperature of the system is held constant just below the freezing point while the pressure is decreased. What phase changes occur now?

Four liquids are at their freezing temperature. Heat is now removed from each of the liquids until it becomes completely solidied. The amount of heat that must be removed, Q, and the mass, m, of each of the liquids are as follows: liquid A, liquid B, liquid C, liquid D, Rank these liquids in order of increasing latent heat of fusion. Indicate ties where appropriate

How much heat must be removed from 0.96 kg of water at 0 C to make ice cubes at 0 C?

Aheat transfer of is required to convert a block of ice at to water at 15 C. What was the mass of the block of ice?

How much heat must be added to 1.75 kg of copper to change it from a solid at 1358 K to a liquid at 1358 K?

A 1.1-kg block of ice is initially at a temperature of . (a) If of heat are added to the ice, what is the nal temperature of the system? Find the amount of ice, if any, that remains. (b) Suppose the amount of heat added to the ice block is doubled. By what factor must the mass of the ice be increased if the system is to have the same nal temperature? Explain.

Referring to the previous problem, suppose the amount of heat added to the block of ice is reduced by a factor of 2 to . Note that this amount of heat is still sufcient to melt at least some of the ice. (a) Do you expect the temperature increase in this case to be one-half that found in the previous problem? Explain. (b) What is the nal temperature of the system in this case? Find the amount of ice, if any, that remains.

Figure 1721 shows a temperature-versus-heat plot for 1.000 kg of water. (a) Calculate the heat corresponding to the points A, B, C, and D. (b) Calculate the slope of the line from point B to point C. Show that this slope is equal to 1/c, where c is the specic heat of liquid water.

Suppose the 1.000 kg of water in Figure 1721 starts at point Aat time zero. Heat is added to this system at the rate of 12,250 J/s. How long does it take for the system to reach (a)point B, (b) point C, and (c) point D? (d) Describe the physical state of the system at time .

Figure 1722 shows a temperature-versus-heat plot for 0.550 kg of water. (a) Calculate the slope of the line from point Ato point B. Show that the slope is equal to 1/mc, where cis the specic heat of ice. (b)Calculate the slope of the line from point C to point D. Show that the slope is equal to 1/mc, where cis the specic heat of liquid water.

In Conceptual Checkpoint 175 we pointed out that steam can cause more serious burns than water at the same temperature. Here we examine this effect quantitatively, noting that esh becomes badly damaged when its temperature reaches 50.0 C. (a) Calculate the heat released as 12.5 g of liquid water at 100 C is cooled to 50.0 C. (b)Calculate the heat released when 12.5 g of steam at 100 C is condensed and cooled to 50.0 C. (c) Find the mass of esh that can be heated from 37.0 C (normal body temperature) to 50.0 C for the cases considered in parts (a) and (b). (The average specic heat of esh is .)

When you go out to your car one cold winter morning you discover a 0.58-cm-thick layer of ice on the windshield, which has an area of . If the temperature of the ice is , and its density is , nd the heat required to melt all the ice.

Alarge punch bowl holds 3.99 kg of lemonade (which is essentially water) at 20.5 C. A 0.0550-kg ice cube at is placed in the lemonade. What is the nal temperature of the

A155-g aluminum cylinder is removed from a liquid nitrogen bath, where it has been cooled to . The cylinder is immediately placed in an insulated cup containing 80.0 g of water at 15.0 C. What is the equilibrium temperature of this system? If your answer is 0 C, determine the amount of water that has frozen. The average specic heat of aluminum over this temperature range is .

An 825-g iron block is heated to 352 C and placed in an insulated container (of negligible heat capacity) containing 40.0 g of water at 20.0 C. What is the equilibrium temperature of this system? If your answer is 100 C, determine the amount of water that has vaporized. The average specic heat of iron over this temperature range is .

A35-g ice cube at 0.0 C is added to 110 g of water in a 62-g aluminum cup. The cup and the water have an initial temperature of 23 C. (a) Find the equilibrium temperature of the cup and its contents. (b)Suppose the aluminum cup is replaced with one of equal mass made from silver. Is the equilibrium temperature with the silver cup greater than, less than, or the same as with the aluminum cup? Explain.

A48-g block of copper at is added to 110 g of water in a 75-g aluminum cup. The cup and the water have an initial temperature of 4.1 C. (a) Find the equilibrium temperature of the cup and its contents. (b) What mass of ice, if any, is present when the system reaches equilibrium?

A0.075-kg ice cube at 0.0 C is dropped into a Styrofoam cup holding 0.33 kg of water at 14 C. (a)Find the nal temperature of the system and the amount of ice (if any) remaining. Assume the cup and the surroundings can be ignored. (b) Find the initial temperature of the water that would be enough to just barely melt all of the ice.

To help keep her barn warm on cold days, a farmer stores 865 kg of warm water in the barn. How many hours would a 2.00-kilowatt electric heater have to operate to provide the same amount of heat as is given off by the water as it cools from 20.0 C to 0 C and then freezes at 0 C?

Plastic bubble wrap is used as a protective packing material. Is the bubble wrap more effective on a cold day or on a warm day? Explain.

Two adjacent rooms in a hotel are equal in size and connected by an open door. Room 1 is warmer than room 2. Which room contains more air? Explain.

As you go up in altitude, do you expect the ratio of oxygen to nitrogen in the atmosphere to increase, decrease; or stay the same? Explain.

Predict/Explain Suppose the Celsius temperature of an ideal gas is doubled from 100 C to 200 C. (a)Does the average kinetic energy of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2? (b) Choose the best explanation from among the following: I. Changing the temperature from 100 C to 200 C goes beyond the boiling point, which will increase the kinetic energy by more than a factor of 2. II. The average kinetic energy is directly proportional to the temperature, so doubling the temperature doubles the kinetic energy. III. Doubling the Celsius temperature from 100 C to 200 C changes the Kelvin temperature from 373.15 K to 473.15 K, which is an increase of less than a factor of 2.

Predict/Explain Suppose the absolute temperature of an ideal gas is doubled from 100 K to 200 K. (a) Does the average speed of the molecules in this gas increase by a factor that is greater than, less than, or equal to 2? (b) Choose the best explanation from among the following: I. Doubling the Kelvin temperature doubles the average kinetic energy, but this implies an increase in the average speed by a factor of , which is less than 2. II. The Kelvin temperature is the one we use in the ideal-gas law, and therefore doubling it also doubles the average speed of the molecules. III. The change in average speed depends on the mass of the molecules in the gas, and hence doubling the Kelvin temperature generally results in an increase in speed that is greater than a factor of 2.

Largest Raindrops Atmospheric scientists studying clouds in the Marshall Islands have observed what they believe to be the worlds largest raindrops, with a radius of 0.52 cm. How many molecules are in these monster drops?

Cooling Computers Researchers are developing heat exchangers for laptop computers that take heat from the laptopto keep it from being damaged by overheatingand use it to vaporize methanol. Given that 5100 J of heat is removed from the laptop when 4.6 g of methanol is vaporized, what is the latent heat of vaporization for methanol?

Scuba Tanks In scuba diving circles, an 80 refers to a scuba tank that holds 80 cubic feet of air, a standard amount for recreational diving. Given that a scuba tank is a cylinder 2 feet long and half a foot in diameter, determine (a) the volume of a tank and (b) the pressure in a tank when 80 cubic feet of air is compressed into its relatively small volume. (c) What is the mass of air in a tank that holds 80 cubic feet of air. Assume the temperature is 21 C and that the walls of the tank are of negligible thickness.

Areaction vessel contains 8.06 g of and 64.0 g of at a temperature of 125 C and a pressure of 101 kPa. (a)What is the volume of the vessel? (b)The hydrogen and oxygen are now ignited by a spark, initiating the reaction . This reaction consumes all the hydrogen and oxygen in the vessel. What is the pressure of the resulting water vapor when it returns to its initial temperature of 125 C?

Abicycle tire with a radius of 0.68 m has a gauge pressure of . Treating the tire as a hollow hoop with a crosssectional area of , nd the number of air molecules in the tire when its temperature is 24 C.

Peter catches a 4.8-kg striped bass on a shing line 0.54 mm in diameter and begins to reel it in. He shes from a pier well above the water, and his sh hangs vertically from the line out of the water. The shing line has a Youngs modulus of . (a) What is the fractional increase in length of the shing line if the sh is at rest? (b)What is the fractional increase in the shing lines length when the sh is pulled upward with a constant speed of 1.5 m/s? (c) What is the fractional increase in the shing lines length when the sh is pulled upward with a constant acceleration of ?

You use a steel socket wrench 28 cm long to loosen a rusty bolt, applying a force F at the end of the handle. The handle undergoes a shear deformation of 0.11 mm. (a) If the cross sectional area of the handle is , what is the magnitude of the applied force F? (b) If the cross-sectional area of the handle is doubled, by what factor does the shear deformation change? Explain.

Asteel ball with a diameter of 6.4 cm is tied to an aluminum wire 82 cm long and 2.5 mm in diameter. The ball is whirled about in a vertical circle with a tangential speed of 7.8 m/s at the top of the circle and 9.3 m/s at the bottom of the circle. Find the amount of stretch in the wire (a)at the top and (b) at the bottom of the circle.

Alead brick with the dimensions shown in Figure 1730 rests on a rough solid surface. A force of 2400 N is applied as indicated. Find (a) the change in height of the brick and (b) the amount of shear deformation.

Five molecules have the following speeds: 221 m/s, 301 m/s, 412 m/s, 44.0 m/s, and 182 m/s. (a)Find for these molecules.(b)Do you expect to be greater than, less than, or equal to ? Explain. (c) Calculate and comment on your results. (d) Calculate and compare with

(a)Find the amount of heat that must be extracted from 1.5 kg of steam at 110 C to convert it to ice at 0.0 C. (b) What speed would this 1.5-kg block of ice have if its translational kinetic energy were equal to the thermal energy calculated in part (a)?

When water freezes into ice it expands in volume by 9.05%. Suppose a volume of water is in a household water pipe or a cavity in a rock. If the water freezes, what pressure must be exerted on it to keep its volume from expanding? (If the pipe or rock cannot supply this pressure, the pipe will burst and the rock will split.)

Suppose the 0.550 kg of ice in Figure 1722 starts at point A. How much ice is left in the system after (a) , (b) , and (c) of heat are added to the system?

Students on a spring break picnic bring a cooler that contains 5.1 kg of ice at 0.0 C. The cooler has walls that are 3.8 cm thick and are made of Styrofoam, which has a thermal conductivity of . The surface area of the cooler is , and it rests in the shade where the air temperature is 21 C. (a) Find the rate at which heat ows into the cooler. (b)How long does it take for the ice in the cooler to melt?

A5.5-kg block of ice at slides on a horizontal surface with a coefcient of kinetic friction equal to 0.062. The initial speed of the block is 6.9 m/s and its nal speed is 5.5 m/s. Assuming that all the energy dissipated by kinetic friction goes into melting a small mass mof the ice, and that the rest of the ice block remains at , determine the value of m.

Acylindrical copper rod 37 cm long and 7.5 cm in diameter is placed upright on a hot plate held at a constant temperature of 120 C, as indicated in Figure 1731. Asmall depression on top of the rod holds a 25-g ice cube at an initial temperature of 0.0 C. How long does it take for the ice cube to melt? Assume there is no heat loss through the vertical surface of the rod, and that the thermal conductivity of copper is .

What pressure did the bathysphere experience at its record depth? A. 9.37 atm B. 89.6 atm C. 91.9 atm D. 92.9 atm

How many moles of air did the bathysphere contain when it was sealed at the surface, assuming a temperature of 297 K and ignoring the thickness of the metal shell? (Note: Aresting person breathes roughly 0.5 mol of air per minute.) A. 65.2 mol B. 270 mol C. 392 mol D. 523 mol

How much did the volume of the bathysphere decrease as it was lowered to its record depth? (For simplicity, treat the bathysphere as a solid metal sphere.) A. B. C. D

Suppose the bathysphere and its occupants had a combined mass of 12,700 kg. How much did the cable stretch when the bathysphere was at a depth of 923 m? (Neglect the weight of the cable itself, but include the effects of the bathyspheres buoyancy.) A. 47 cm B. 48 cm C. 52 cm D. 53 cm

Referring to Example 176(a)Find the nal temperature of the system if two0.0450-kg ice cubes are added to the warm lemonade. The temperature of the ice is 0 C; the temperature and mass of the warm lemonade are 20.0 C and 3.95 kg, respectively. (b) How many 0.0450-kg ice cubes at 0 C must be added to the original warm lemonade if the nal temperature of the system is to be at least as cold as 15.0 C?

Referring to Example 176 (a) Find the nal temperature of the system if a single 0.045-kg ice cube at 0 C is added to 2.00 kg of lemonade at 1.00 C. (b)What initial temperature of the lemonade will be just high enough to melt all of the ice in a single ice cube and result in an equilibrium temperature of 0 C? The mass of the lemonade is 2.00 kg and the temperature of the ice cube is 0 C.