20. Heat and Temperature

The temperature within the Earth’s crust increases about 1.0 C° for each 30 m of depth. The thermal conductivity of the crust is 0.80 J/s C°. Compare this heat to the 1000 W/m² that reaches the Earth’s surface in 1.0 h from the Sun.

The temperature within the Earth’s crust increases about 1.0 C° for each 30 m of depth. The thermal conductivity of the crust is 0.80 J/s C°. Determine the heat transferred from the interior to the surface for the entire Earth in 1.0 h.

A cubic Styrofoam cooler containing ice on a hot day is shown in the following figure. The thickness of each wall of the cooler is 15 mm, with a side length of 1 m. If it is 40°C outside, how long will 2 kg of ice last in the cooler? Assume that during the melting process, the temperature inside the cooler remains at 0°C and that no heat enters from the bottom of the cooler. Note that the latent heat of fusion for water is 334 kJ/kg and the thermal conductivity of Styrofoam is 0.033 W/mK.

If the intensity of sunlight measured at the Earth's surface is 1400 W/m² , what is the surface temperature of the Sun? Treat the Sun like a true blackbody. Note that the distance from the Earth to the Sun is 1.5 x 10¹¹ m and the radius of the Sun is 696 million meters.

300g of water at 40°C is in an insulated cup. What mass of copper at 500°C must be added to heat the water to 60°C?

The blood plays an important role in removing heat from the body by bringing this energy directly to the surface where it can radiate away. Nevertheless, this heat must still travel through the skin before it can radiate away. Assume that the blood is brought to the bottom layer of skin at $37.0$°C and that the outer surface of the skin is at $30.0$°C. Skin varies in thickness from $0.50$ mm to a few millimeters on the palms and soles, so assume an average thickness of $0.75$ mm. A $165$-lb, $6$-ft-tall person has a surface area of about $2.0$ m² and loses heat at a net rate of $75$ W while resting. On the basis of our assumptions, what is the thermal conductivity of this person's skin?

Two rods, one made of brass and the other made of copper, are joined end to end. The length of the brass section is $0.300$ m and the length of the copper section is $0.800$ m. Each segment has cross-sectional area $0.00500$ m². The free end of the brass segment is in boiling water and the free end of the copper segment is in an ice–water mixture, in both cases under normal atmospheric pressure. The sides of the rods are insulated so there is no heat loss to the surroundings. What mass of ice is melted in $5.00$ min by the heat conducted by the composite rod?

The emissivity of tungsten is $0.350$. A tungsten sphere with radius $1.50$ cm is suspended within a large evacuated enclosure whose walls are at $290.0$ K. What power input is required to maintain the sphere at $3000.0$ K if heat conduction along the supports is ignored?

A spherical pot contains $0.75$ L of hot coffee (essentially water) at an initial temperature of $95$°C. The pot has an emissivity of $0.60$, and the surroundings are at $20.0$°C. Calculate the coffee's rate of heat loss by radiation.

An electric kitchen range has a total wall area of $1.40$ m² and is insulated with a layer of fiberglass $4.00$ cm thick. The inside surface of the fiberglass has a temperature of $175$°C, and its outside surface is at $35.0$°C. The fiberglass has a thermal conductivity of $0.040W/m\cdot K$. What is the heat current through the insulation, assuming it may be treated as a flat slab with an area of $1.40$ m² ?

Suppose that the rod in Fig. $17.24$a is made of copper, is $45.0$ cm long, and has a cross-sectional area of $1.25$ cm² . Let $TH=100.0$°C and $TC=0.0$°C. What is the final steady-state temperature gradient along the rod?