20. Heat and Temperature

Which of the following situations is an example of transferring heat by means of $\mathrm{convection}$?

A carpenter builds an exterior house wall with a layer of wood $3.0$ cm thick on the outside and a layer of Styrofoam insulation $2.2$ cm thick on the inside wall surface. The wood has $k=0.080W/m\cdot K$ , and the Styrofoam has $k=0.027W/m\cdot K$. The interior surface temperature is $19.0$°C, and the exterior surface temperature is $-10.0$°C. What is the temperature at the plane where the wood meets the Styrofoam?

Through which of the following ways does the $\mathrm{Sun}$ primarily transfer its $\mathrm{heat}$ energy to the $\mathrm{Earth}$?

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.

In the context of heat transfer, what is always the direction of heat flow between two objects?

A carpenter builds an exterior house wall with a layer of wood $3.0$ cm thick on the outside and a layer of Styrofoam insulation $2.2$ cm thick on the inside wall surface. The wood has $k=0.080\,W/m\(\cdot\) K$ , and the Styrofoam has $k=0.027\,W/m\(\cdot\) K$. The interior surface temperature is $19.0$°C, and the exterior surface temperature is $-10.0$°C. What is the rate of heat flow per square meter through this wall?

(II) When a diver jumps into the ocean, water leaks into the gap region between the diver’s skin and her wetsuit, forming a water layer about 0.5 mm thick. Assuming the total surface area of the wetsuit covering the diver is about 1.0m², and that ocean water enters the suit at 10°C and is warmed by the diver to skin temperature of 35°C, estimate how much energy (in units of candy bars = 300kcal) is required by this heating process.

Estimate the rate at which heat can be conducted from the interior of the body to the surface. As a model, assume that the thickness of tissue is 4.0 cm, that the skin is at 34°C and the interior at 37°C, and that the surface area is 1.5m². Compare this to the measured value of about 230 W that must be dissipated by a person working lightly. This clearly shows the necessity of convective cooling by the blood.

A ceramic teapot (e = 0.70) and a shiny metal one (e = 0.10) each hold 0.55 L of tea at 85°C. (a) Estimate the rate of heat loss from each, and (b) estimate the temperature drop after 30 min for each. Consider only radiation, and assume the surroundings are at 20°C.

A ceramic cube 3.0 cm on each side radiates heat at 630 W. At what wavelength, in μm, does its emission spectrum peak? Assume e=1.

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?

A 2.0-cm-diameter metal sphere is glowing red, but a spectrum shows that its emission spectrum peaks at an infrared wavelength of 2.0 μm. How much power does the sphere radiate? Assume e=1 .

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.

A leaf of area 40 cm² and mass 4.5 x 10^-4 kg directly faces the Sun on a clear day. The leaf has an emissivity of 0.85 and a specific heat of 0.80 kcal/kg K. Will the temperature rise continue for hours? Why or why not?

(a) How much power is radiated by a tungsten sphere (emissivity ∈ = 0.35) of radius 19 cm at a temperature of 25°C?

(b) If the sphere is enclosed in a room whose walls are kept at - 5 °C, what is the net flow rate of energy out of the sphere?