A blackened, solid copper sphere that has a radius equal

Why does the mercury level of a thermometer first decrease slightly when the thermometer is first placed in warm water?

A large sheet of metal has a hole cut in the middle of it. When the sheet is heated, the area of the hole will (a) not change, (b) always increase, (c) always decrease, (d) increase if the hole is not in the exact center of the sheet, (e) decrease only if the hole is in the exact center of the sheet.

Why is it a bad idea to place a tightly sealed glass bottle that is completely full of water, into your kitchen freezer in order to make ice?

The windows of your physics laboratory are left open on a night when the temperature of the outside drops well below freezing. A steel ruler and a wooden ruler were left on the window sill, and when you arrive in the morning they are both very cold. The coefficient of linear expansion of wood is about Which ruler should you use to make the most accurate length measurements? Explain your answer.

ENGINEERING APPLICATION Bimetallic strips are used both for thermostats and electrical circuit breakers. A bimetallic strip 5 _ 106K_1. SSM consists of a pair of thin strips of metal that have different coefficients of linear expansion and are bonded together to form one doubly thick strip. Suppose a bimetallic strip is constructed out of one steel strip and one copper strip, and suppose the bimetallic strip is curled in the shape of a circular arc with the steel strip on the outside. If the temperature of the strip is decreased, will the strip straighten out or curl more tightly?

Metal A has a coefficient of linear expansion that is three times the coefficient of linear expansion of metal B. How do their coefficients of volume expansion compare? (a) (b) (c) (d) (e) You cannot tell from the data given.

The summit of Mount Rainier is ft above sea level. Mountaineers say that you cannot hard boil an egg at the summit. This statement is true because at the summit of Mount Rainier (a) the air temperature is too low to boil water, (b) the air pressure is too low for alcohol fuel to burn, (c) the temperature of boiling water is not hot enough to hard boil the egg, (d) the oxygen content of the air is too low to support combustion, (e) eggs always break in climbers backpacks.

Which gases in Table 20-3 cannot be condensed by applying pressure at 20C? Explain your answer.

The phase diagram in Figure 20-15 can be interpreted to yield information on how the boiling and melting points of water change with altitude. (a) Explain how this information can be obtained. (b) How might this information affect cooking procedures in the mountains? SSM

Sketch a phase diagram for carbon dioxide using information from Section 20-3.

Explain why the carbon dioxide on Mars is found in the solid state in the polar regions, even though the atmospheric pressure at the surface of Mars is only about 1 percent of the atmospheric pressure at the surface of Earth.

Explain why decreasing the temperature of your house at night in winter can save money on heating costs. Why does the cost of the fuel consumed to heat the house back to the daytime temperature in the morning not equal the savings realized by cooling it down in the evening and keeping it cool throughout the night?

Two solid cylinders made of materials A and B have the same lengths; their diameters are related by When the same temperature difference is maintained between the ends of the cylinders, they conduct heat at the same rate. Their thermal conductivities are therefore related by which of the following equations? (a) (b) (c) (d) (e)

Two solid cylinders made of materials A and B have the same diameter; their lengths are related by When the same temperature difference is maintained between the ends of the cylinders, they conduct heat at the same rate. Their thermal conductivities are therefore related by which of the following equations? (a) (b) (c) (d) (e)

If you feel the inside of a single-pane window during a very cold day, it is cold, even though the room temperature can be quite comfortable. Assuming the room temperature is and the outside temperature is construct a plot of temperature versus position, starting from a point 5.0 m behind the window (inside the room) and ending at a point 5.0 m in front of the window. Explain the heat transfer mechanisms that occur along this path.

During the thermal retrofitting of many older homes in California, it was found that the 3.5-in-deep spaces between the wallboards and the outer sheathing were filled with just air (no insulation). Filling the spaces with insulating material certainly reduces heating and cooling costs; although, the insulating material is a better conductor of heat than air is. Explain why adding the insulation is a good idea.

You are using a cooking pot to boil water for a pasta dish. The recipe calls for at least 4.0 L of water to be used. You fill the pot with 4.0 L of room temperature water and note that this amount of water filled the pot to the brim. Knowing some physics, you are counting on the volume expansion of the steel pot to keep all of the water in the pot while the water is heated to a boil. Is your assumption correct? Explain. If your assumption is not correct, how much water runs over the sides of the pot due to the thermal expansion of the water?

Liquid helium is stored in containers fitted with 7.00-cmthick superinsulation, consisting of numerous layers of very thin aluminized Mylar sheets. The rate of evaporation of liquid helium in a 200-L container is about 0.700 L per day when the container is stored at room temperature The density of liquid helium is and the latent heat of vaporization is Estimate the thermal conductivity of the superinsulation.

BIOLOGICAL APPLICATION Estimate the thermal conductivity of human skin.

You are visiting Finland with a college friend and have met some Finnish friends. They talk you into taking part in a traditional Finnish after-sauna exercise, which consists of leaving the sauna, wearing only a bathing suit, and running out into the midwinter Finnish air. Estimate the rate at which you initially lose energy to the cold air. Compare this rate of initial energy loss to the resting metabolic rate of a typical human under normal temperature conditions. Explain the difference.

Estimate the rate of heat conduction through a 2.0-inthick wooden door during a cold winter day in Minnesota. Include the brass doorknob. What is the ratio of the heat that escapes through the doorknob to the heat that escapes through the whole door? What is the total overall R-factor for the door, including the knob? The thermal conductivity of brass is

Estimate the effective emissivity of Earth, given the following information. The solar constant, which is the intensity of radiation incident on Earth from the Sun, is about Seventy percent of this energy is absorbed by Earth, and Earths average surface temperature is 288 K. (Assume that the effective area that is absorbing the light is where is Earths radius, while the blackbody-emission area is )

Black holes are highly condensed remnants of stars. Some black holes, together with a normal star, form binary systems. In such systems the black hole and the normal star orbit about the center of mass of the system. One way black holes can be detected from Earth is by observing the frictional heating of the atmospheric gases from the normal star that fall into the black hole. These gases can reach temperatures greater than Assuming that the falling gas can be modeled as a blackbody radiator, estimate for use in an astronomical detection of a black hole. (This region is in the X-ray region of the electromagnetic spectrum.)

ENGINEERING APPLICATION, CONTEXT-RICH Your cabin in northern Michigan has walls that consist of pine logs that have average thicknesses of about 20 cm. You decide to finish the interior of the cabin to improve the look and to increase the insulation of the exterior walls. You choose to buy insulation with an R-factor of 31 to cover the walls. In addition, you cover the insulation with 1.0-in.-thick gypsum wallboard. Assuming heat transfer is only due to conduction, estimate the ratio of thermal current through the walls during a cold winter night before the renovation to the thermal current through the walls following the renovation.

CONTEXT-RICH You are in charge of transporting a liver from New York, New York, to Los Angeles, California, for a transplant surgery. The liver is kept cold in a styrofoam ice chest initially filled with 1.0 kg of ice. It is crucial that the liver temperature is never warmer than Assuming the trip from the hospital in New York to the hospital in Los Angeles takes 7.0 h, estimate the -value the styrofoam walls of the ice chest must have.

You have inherited your grandfathers grandfather clock that was calibrated when the temperature of the room was Assume that the pendulum consists of a thin brass rod of negligible mass with a compact heavy bob at its end. (a) During a hot day, when the temperature is does the clock run fast or slow? Explain. (b) How much time does it gain or lose during this day?

ENGINEERING APPLICATION You need to fit a copper collar tightly around a steel shaft that has a diameter of 6.0000 cm at The inside diameter of the collar at that temperature is 5.9800 cm. What temperature must the copper collar have so that it will just slip on the shaft, assuming the shaft itself remains at

ENGINEERING APPLICATION You have a copper collar and a steel shaft. At the collar has an inside diameter of 5.9800 cm and the steel shaft has diameter of 6.0000 cm. The copper collar was heated. When its inside diameter exceeded 6.0000 cm it was slipped on the shaft. The collar fitted tightly on the shaft after they cooled to room temperature. Now, several years later, you need to remove the collar from the shaft. To do this you heat them both until you can just slip the collar off the shaft. What temperature must the collar have so that the collar will just slip off the shaft?

A container is filled to the brim with 1.4 L of mercury at As the temperature of the container and mercury is increased to a total of 7.5 mL of mercury spill over the brim of the container. Determine the linear expansion coefficient of the material that makes up the container.

A car with a 60.0-L steel gas tank is filled to the brim with 60.0 L of gasoline when the outside temperature is The coefficient of volume expansion for gasoline at is . How much gasoline spills out of the tank when the outside temperature increases to Take the expansion of the steel tank into account.

What is the tensile stress in the copper collar of Problem 27 when its temperature returns to

(a) Calculate the volume of 1.00 mol of an ideal gas at a temperature of and a pressure of 1.00 atm. (b) Calculate the temperature at which 1.00 mol of steam at a pressure of 1.00 atm has the volume calculated in part (a). Use and

Using Figure 20-16, find the following quantities. (a) The temperature at which water boils on a mountain where the atmospheric pressure is 70.0 kPa, (b) the temperature at which water boils in a container where the pressure inside the container is 0.500 atm, and (c) the pressure at which water boils at 115C. SSM

The van der Waals constants for helium are and Use these data to find the volume in cubic centimeters occupied by one helium atom. Then, estimate the radius of the helium atom.

A slab of insulation has an factor of 11. At what rate is heat conducted through the slab if the temperature on one side is a constant and the temperature on the other side is a constant

A copper cube and an aluminum cube, each with 3.00-cm-long edges, are arranged as shown in Figure 20-17. Find (a) the thermal resistance of each cube, (b) the thermal resistance of the two-cube combination, (c) the thermal current and (d) the temperature at the interface of the two cubes.

Two metal cubes, one copper and one aluminum, with 3.00-cm-long edges, are arranged in parallel, as shown in Figure 20-18. Find (a) the thermal current in each cube, (b) the total thermal current, and (c) the thermal resistance of the two-cube combination.

ENGINEERING APPLICATION The cost of air conditioning a house is approximately proportional to the rate at which heat is absorbed by the house from its surroundings divided by the coefficient of performance (COP) of the air conditioner. Let us denote the temperature difference between the inside temperature and the outside temperature as Assuming that the rate at which heat is absorbed by a house is proportional to and that the air conditioner is operating ideally, show that the cost of air conditioning is proportional to divided by the temperature inside the house.

A spherical shell of thermal conductivity has inside radius and outside radius (Figure 20-19). The inside of the shell is held at a temperature and the outside of the shell is held at temperature with In this problem, you are to show that the thermal current through the shell is given by where is positive if heat is transferred in the direction. Here is a suggested procedure for obtaining this result: (1) obtain an expression for the thermal current through a thin spherical shell of radius and thickness when there is a temperature difference across the thickness of the shell; (2) explain why the thermal current is the same through each such thin shell; (3) express the thermal current through such a shell element in terms of the area the thickness and the temperature difference across the element; and (4) separate variables (solve for in terms of r and dr) and integrate.

BIOLOGICAL APPLICATION Calculate (the wavelength at which the emitted power is maximum) for a human skin. Assume the human skin is a blackbody emitter with a temperature of 33C.

The universe is filled with radiation that is believed to be left from the Big Bang. If the entire universe is considered to be a blackbody with a temperature equal to 2.3 K, what is the (the wavelength at which the power of the radiation is maximum) of this radiation?

What is the range of temperatures for star surfaces for which (the wavelength at which the power of the emitted radiation is maximum) is in the visible range?

The heating wires of a 1.00-kW electric heater are red hot at a temperature of Assuming that 100 percent of the heat released is due to radiation and that the wires act as blackbody emitters, what is the effective area of the radiating surface? (Assume a room temperature of )

A blackened, solid copper sphere that has a radius equal to 4.0 cm hangs in an evacuated enclosure whose walls have a temperature of If the sphere is initially at find the initial rate at which its temperature changes, assuming that heat is transferred by radiation only. (Assume the sphere is a blackbody emitter.)

The surface temperature of the filament of an incandescent lamp is If the electric power input is doubled, what will the new temperature be? Hint: Show that you can neglect the temperature of the surroundings.

Liquid helium is stored at its boiling point (4.2 K) in a spherical can that is separated by an evacuated region of space from a surrounding shield that is maintained at the temperature of liquid nitrogen (77 K). If the can is 30 cm in diameter and is blackened on the outside so that it acts as a blackbody emitter, how much helium boils away per hour? GENERAL PROBLEMS

A steel tape is placed around Earth at the equator when the temperature is What will the clearance between the tape and the ground (assumed to be uniform) be if the temperature of the tape increases to Neglect the expansion of Earth.

Show that change in the density of an isotropic material due to an increase in temperature is given by

The solar constant is the power received from the Sun per unit area perpendicular to the Suns rays at the mean distance of Earth from the Sun. Its value at the upper atmosphere of Earth is about Calculate the effective temperature of the Sun if it radiates like a blackbody. (The radius of the Sun is )

ENGINEERING APPLICATION As part of your summer job as an engineering intern at an insulation manufacturer, you are asked to determine the -factor of insulating material. This particular material comes in sheets. Using this material, you construct a hollow cube that has 12-in-long edges. You place a thermometer and a 100-W heater inside the box. After thermal equilibrium has been attained, the temperature inside the box is when the temperature outside the box is Determine the R-factor of the material.

(a) From the definition of the coefficient of volume expansion (at constant pressure), show that for an ideal gas. (b) The experimentally determined value of for gas at is By what percent does this measured value of differ from the value obtained by modeling as an ideal gas?

A rod of length , made from material A, is placed next to a rod of length , made from material B. The rods remain in thermal equilibrium with each other. (a) Show that even though the lengths of each rod will change with changes in the ambient temperature, the difference between the two lengths will remain constant if the lengths and are chosen such that where and are the coefficients of linear expansion, respectively. (b) If material B is steel, material A is brass, and at what is the value of LB0C, ?

On average, the temperature of Earths crust increases for every increase in depth of 30 m. The average thermal conductivity of Earths crust material is What is the heat loss of Earth per second due to conduction from the core? How does this heat loss compare with the average power received from the Sun?

A copper-bottomed saucepan containing 0.800 L of boiling water boils dry in 10.0 min. Assuming that all the heat is transferred through the flat copper bottom, which has a diameter of 15.0 cm and a thickness of 3.00 mm, calculate the temperature of the outside of the copper bottom while some water is still in the pan.

ENGINEERING APPLICATION A cylindrical steel hot-water tank of cylindrical shape has an inside diameter of 0.550 m and inside height of 1.20 m. The tank is enclosed by a 5.00-cm-thick insulating layer of glass wool whose thermal conductivity is The insulation is covered by a thin sheet-metal skin. The steel tank and the sheet-metal skin have thermal conductivities that are much greater than that of the glass wool. How much electrical power must be supplied to this tank in order to maintain the water temperature at 75.0C when the external temperature is 1.0C?

The diameter of a tapered rod of length is given by where is a constant and is the distance from one end. If the thermal conductivity of the material is what is the thermal resistance of the rod?

A solid disk of radius and mass is spinning about a frictionless axis through its center and perpendicular to the disk, with angular velocity at temperature The temperature of the disk decreases to Express the angular velocity rotational kinetic energy and angular momentum in terms of their values at the temperature and the linear expansion coefficient of the disk.

SPREADSHEET Write a spreadsheet program to graph the average temperature of the surface of Earth as a function of emissivity, using the results of Problem 22. How much does the emissivity have to change in order for the average temperature to increase by 1 K? This result can be thought of as a model for the effect of increasing concentrations of greenhouse gases such as methane and in Earths atmosphere.

A small pond has a layer of ice 1.00 cm thick floating on its surface. (a) If the air temperature is on a day when there is a breeze, find the rate in centimeters per hour at which ice is added to the bottom of the layer. The density of ice is (b) How long do you and your friends have to wait for a 20.0-cm layer to be built up so you can play hockey?

A blackened copper cube that has 1.00-cm-long edges is heated to a temperature of and then is placed in a vacuum chamber whose walls are at a temperature of In the vacuum chamber, the cube cools radiatively. (a) Show that the (absolute) temperature of the cube follows the differential equation: where is the heat capacity of the cube, is its surface area, the emissivity, and the temperature of the vacuum chamber. (b) Using Eulers method (Section 5.4 of Chapter 5), numerically solve the differential equation to find and graph it. Assume How long does it take the cube to cool to a temperature of 15C? SSM