If you place an ice cube on your kitchen table, wrap it in a wet paper towel to keep it frozen longer. Why?

The rate at which radiant energy from the sun reaches the earth's upper atmosphere is about $1.50 \mathrm{~kW} / \mathrm{m}^2$. The distance from the earth to the sun is $1.50 \times 10^{11}$ m, and the radius of the sun is $6.96 \times 10^8$ m.
(b) If the sun radiates as an ideal blackbody, what is the temperature of its surface?

The rate at which radiant energy from the sun reaches the earth’s upper atmosphere is about $1.50 \mathrm{kW} / \mathrm{m}^{2}$. The distance from the earth to the sun is $1.50 \times 10^{11} \mathrm{m}$, and the radius of the sun is $6.96 \times 10^{8} m$. (a) What is the rate of radiation of energy per unit area from the sun’s surface? (b) If the sun radiates as an ideal blackbody, what is the temperature of its surface?

How long will it take for a $2.50$-cm-thick layer of ice to melt if the solar radiation energy incident per second on the frozen surface of a lake is  $600 \mathrm{~W} / \mathrm{m}^2$ and $70 \%$ of this energy is absorbed by the ice? The temperature of the ice and the water beneath it is  $0^{\circ} \mathrm{C}$.

A rod is initially at a uniform temperature of $0^{\circ} \mathrm{C}$ throughout. One end is kept at $0^{\circ} \mathrm{C}$, and the other is brought into contact with a steam bath at $100^{\circ} \mathrm{C}$. The surface of the rod is insulated so that heat can flow only lengthwise along the rod. The cross-sectional area of the rod is $2.50 \mathrm{~cm}^2$, its length is $120 \mathrm{~cm}$, its thermal conductivity is $380 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$, its density is $1.00 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$, and its specific heat is $520 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$. Consider a short cylindrical element of the rod $1.00 \mathrm{~cm}$ in length. $(a)$ If the temperature gradient at the cooler end of this element is $140 \mathrm{C}^{\circ} / \mathrm{m}$, how many joules of heat energy flow across this end per second? $(b)$ If the average temperature of the element is increasing at the rate of what is the temperature gradient at the other end of the element?

If the lake in previous part is uniformly 40 m deep, how long would it take to freeze all the water in the lake? Is this likely to occur?

Assuming that the upper surface of the ice sheet is at -10 degree C and the bottom surface is at $0\degree\mathrm{C}$, calculate the time it will take to form an ice sheet $25$ cm thick.

Show that the thickness of the ice sheet formed on the surface of a lake is proportional to the square root of the time if the heat of fusion of the water freezing on the underside of the ice sheet is conducted through the sheet.

(a) When the air temperature is below $0^{\circ} \mathrm{C}$, the water at the surface of a lake freezes to form an ice sheet. Why doesn’t freezing occur throughout the entire volume of the lake? (b) Show that the thickness of the ice sheet formed on the surface of a lake is proportional to the square root of the time if the heat of fusion of the water freezing on the underside of the ice sheet is conducted through the sheet. (c) Assuming that the upper surface of the ice sheet is at $-10^{\circ} C$ and the bottom surface is at $0^{\circ} C$, calculate the time it will take to form an ice sheet 25 cm thick. (d) If the lake in part (c) is uniformly 40 m deep, how long would it take to freeze all the water in the lake? Is this likely to occur?

Rods of copper, brass, and steel$-$each with cross- sectional area of $2.00$ cm$^2$ $-$are welded together to form a Y-shaped figure. The free end of the copper rod is maintained at $100.0\degree\mathrm{C}$, and the free ends of the brass and steel rods at $0.0\degree\mathrm{C}$. Assume that there is no heat loss from the surfaces of the rods. The lengths of the rods are: copper, $13.0$ cm; brass, $18.0$ cm; steel, $24.0$ cm. What is
(b) the heat current in each of the three rods?

A steel tube has an outside diameter of $3.000 \mathrm{~cm}$ at room temperature $\left(20^{\circ} \mathrm{C}\right)$. A brass tube has an inside diameter of $2.997 \mathrm{~cm}$ at the same temperature. To what temperature must the ends of the tubes be heated if the steel tube is to be inserted into the brass tube?

Rods of copper, brass, and steel—each with cross-sectional area of $2.00 \mathrm{cm}^{2}$—are welded together to form a Y-shaped figure. The free end of the copper rod is maintained at $100.0^{\circ} \mathrm{C}$, and the free ends of the brass and steel rods at $0.0^{\circ} C$. Assume that there is no heat loss from the surfaces of the rods. The lengths of the rods are: copper, 13.0 cm; brass, 18.0 cm; steel, 24.0 cm. What is (a) the temperature of the junction point; (b) the heat current in each of the three rods?

A cold block of metal feels colder than a block of wood at the same temperature. Why? A hot block of metal feels hotter than a block of wood at the same temperature. Again, why? Is there any temperature at which the two blocks feel equally hot or cold? What temperature is this?

Compute the ratio of the rate of heat loss through a single-pane window with area $0.15 m^{2}$ to that for a double-pane window with the same area. The glass of a single pane is 4.2 mm thick, and the air space between the two panes of the double-pane window is 7.0 mm thick. The glass has thermal conductivity $0.80 \mathrm{W} / \mathrm{m} \cdot \mathrm{K}$. The air films on the room and outdoor surfaces of either window have a combined thermal resistance of $0.15 \mathrm{m}^{2} \cdot \mathrm{K} / \mathrm{W}$.