Chapter 18: Temperature, Heat, and the First Law of Thermodynamics

The temperature of a Pyrex disk is changed from$\mathbf{10}\mathbf{.0}\mathbf{°}\mathbf{\text{Cto60.0°C}}$. Its initial radius is$\mathbf{8}\mathbf{.00}\mathbf{}\mathbf{\text{cm}}$; its initial thickness is$\mathbf{0}\mathbf{.500}\mathbf{}\mathbf{\text{cm}}$. Take these data as being exact.What is the change in the volume of the disk?

(a) Calculate the rate at which body heat is conducted through the clothing of a skier in a steady-state process, given the following data: the body surface area is $\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{}{\mathit{m}}^{\mathbf{2}}$and the clothing is 1.0 cmthick; the skin surface temperature is $\mathbf{33}\mathbf{°}\mathit{C}$and the outer surface of the clothing is at$\mathbf{1}\mathbf{°}\mathit{C}$; the thermal conductivity of the clothing is$\mathbf{0}\mathbf{.}\mathbf{040}\mathbf{}\mathit{W}\mathbf{/}\mathit{m}\mathit{K}$.(b) If, after a fall, the skier’s clothes became soaked with water of thermal conductivity$\mathbf{0}\mathbf{.}\mathbf{60}\mathbf{}\mathit{W}\mathbf{/}\mathit{m}\mathbf{}\mathit{K}$, by how much is the rate of conduction multiplied?

A $2.50\text{kg}$lump of aluminum is heated to$\mathbf{92}\mathbf{.0}\mathbf{°}\mathbf{\text{C}}$and then dropped into$\mathbf{8}\mathbf{.00}\mathbf{}\mathbf{\text{kg}}$of water at$\mathbf{5}\mathbf{.00}\mathbf{°}\mathbf{\text{C}}$. Assuming that the lump–water system is thermally isolated, what is the system’s equilibrium temperature?

A glass window pane is exactly$\mathbf{20}\mathbf{}\mathbf{\text{cm}}$by$\mathbf{30}\mathbf{}\mathbf{\text{cm}}$at.${10}^0\text{C}$ By how much has its area increased when its temperature is$\mathbf{40}{\mathbf{}}^{\mathbf{0}}\mathbf{\text{C}}$, assuming that it can expand freely?

A recruit can join the semi-secret “$\mathbf{300}\mathit{F}$” club at the Amundsen–Scott South Pole Station only when the outside temperature is below $\mathbf{-}{\mathbf{70}}^{\mathbf{0}}\mathbf{}\mathit{C}$. On such a day, the recruit first basks in a hot sauna and then runs outside wearing only shoes. (This is, of course, extremely dangerous, but the rite is effectively a protest against the constant danger of the cold). Assume that upon stepping out of the sauna, the recruit’s skin temperature is ${\mathbf{102}}^{\mathbf{0}}\mathbf{}\mathit{F}$and the walls, ceiling, and floor of the sauna room have a temperature of ${\mathbf{30}}^{\mathbf{0}}\mathit{C}$. Estimate the recruit’s surface area, and take the skin emissivity to be 0.80. (a) What is the approximate net rate P_net at which the recruit loses energy via thermal radiation exchanges with the room? Next, assume that when outdoors, half the recruit’s surface area exchanges thermal radiation with the sky at a temperature ofand the other half exchanges thermal radiation with the snow and ground at a temperature of.What is the approximate net rate at which the recruit loses energy via thermal radiation exchanges with (b) the sky and (c) the snow and ground?

A steel rod at$\mathbf{25}\mathbf{.0}\mathbf{\text{°C}}$is bolted at both ends and then cooled. At what temperature will it rupture? Use Table 12-1.

An athlete needs to lose weight and decides to do it by “pumping iron.” (a) How many times must a $\mathbf{80}\mathbf{.}\mathbf{0}\mathbf{kg}$weight be lifted a distance of $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$in order to burn off $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{lb}$of fat, assuming that that much fat is equivalent to $\mathbf{3500}\mathbf{}\mathbf{Cal}\mathbf{?}$(b) If the weight is lifted once every$\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{s}$, how long does the task take?

At ${\mathbf{20}}^{\mathbf{°}}\mathit{C}$, a brass cube has an edge length of $\mathbf{30}\mathbf{}\mathit{c}\mathit{m}$.What is the increase in the cube’s surface area when it is heated from${\mathbf{20}}^{\mathbf{°}}\mathit{C}\mathbf{}\mathit{t}\mathit{o}\mathbf{}\mathbf{75}\mathbf{°}\mathit{C}$?

For which cycle in Fig. 18-27, traversed clockwise, is (a) Wgreater and (b) Qgreater?

Soon after Earth was formed, heat released by the decay of radioactive elements raised the average internal temperature from$\mathbf{300}\mathbf{}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}to}}\mathbf{}\mathbf{3000}\mathbf{}\mathbf{\text{K}}$, at about which value it remains today. Assuming an average coefficient of volume expansion of$3.0\times {10}^{-5}{\text{K}}^{\text{-1}}$, by how much has the radius of Earth increased since the planet was formed?