Apply the results of the given example earlier to estimate the temperature of the dwarf planet Pluto. In your calculation, assume Pluto is at its mean distance from the Sun, $5.9 \times 10^{12} \mathrm{~m}$. Compare your answer with the measured temperature of Pluto, about $40 \mathrm{~K}$. How do you think astronomers are able to measure the temperature of Pluto?

Suppose the height and width of the windowpane in the given figure are both increased by a factor of two. By what factor does the heat flow through the window change?

(a) There is no change.

(b) It increases by a factor of two.

(c) It increases by a factor of four.

On a hot summer day, an electric fan can make a difference in comfort. The fan does not cool the air, however. In fact, it slightly raises the temperature of the air that it circulates. How is it that a fan can make you cooler?

Water filling a thin crack in a rock wall and then freezing can put large forces on the rock, making the cracks bigger (shown in the given figure).

(a) Calculate the force exerted by a $10-\mathrm{m}^2$ area of a thin $(0.50 \mathrm{~mm})$ sheet of water freezing between two slabs of rock.

(b) Take the sheet of water to be oriented in a horizontal plane (unlike the case in the given figure) and assume a large slab of rock sits on top of the ice. By how much is the rock on top of the water displaced vertically?

(c) If the column of rock is $15 \mathrm{~m}$ tall and has a density of $5.2 \mathrm{~g} / \mathrm{cm}^3$, how much work is done by the expansion of the ice on this rock mass?

The owners of a cabin in the mountains forgot to turn off and purge the water out of the plumbing system before the winter season. One particularly cold night, a pipe near an outside wall freezes. Consider a length of " $\frac{1}{2}$-in." copper plumbing pipe filled with water. Although called $\frac{1}{2}$ in., the outside diameter of this standard pipe is $\frac{5}{8}$ in. and the inside diameter is $0.537$ in.

(a) Water freezes in a $50-\mathrm{cm}$ length of this pipe capped at both ends by closed valves such that the expansion of the ice is constrained by the pipe. Calculate the pressure on the wall of the pipe.

(b) Is the diameter of the pipe just before the water freezes significantly different from the diameter at room temperature? What is the percent change?

(c) The pipe has a connection (shown in the given figure). Assume the water freezes so that the separation between ice and water occurs right in the middle of the connector. Calculate the force that pulls on the connector when the water freezes.

The given figure shows a modern electronic circuit board. It features standard miniature components such as the resistor (R$516$), which measures $1.6 \mathrm{~mm}$ long, $0.80 \mathrm{~mm}$ wide, and $0.20 \mathrm{~mm}$ high. The ceramic material of the resistor has a Young's modulus of $1.2 \times 10^{10} \mathrm{~Pa}$. When electricity flows through the circuit, the components, especially resistors, can heat up substantially. The resistor has a coefficient of thermal expansion of $2.2 \times 10^{-6} \mathrm{~K}^{-1}$, and that of the circuit board it is soldered to is $6.0 \times 10^{-6} \mathrm{~K}^{-1}$.

(a) If the temperature of the circuit rises $30^{\circ} \mathrm{C}$, how much longer will the circuit's "footprint" be than the resistor that is soldered to it?

(b) If the resistor is stretched by this amount by the circuit board, how much stress is the resistor subjected to?

(c) The resistor has a maximum stress of $25 \mathrm{MPa}$ before it will break. If a power glitch raises the temperature of the circuit by $120^{\circ} \mathrm{C}$, will the resistor suffer damage from the stress?