Question 11.9: Energy Transfer through a Concrete Wall Goal Apply the equat...
Energy Transfer through a Concrete Wall
Goal Apply the equation of heat conduction.
Problem Find the energy transferred in 1.00 \mathrm{~h} by conduction through a concrete wall 2.0 \mathrm{~m} high, 3.65 \mathrm{~m} long, and 0.20 \mathrm{~m} thick if one side of the wall is held at 20^{\circ} \mathrm{C} and the other side is at 5^{\circ} \mathrm{C}.
Strategy Equation 11.7
\mathscr{P}=k A\,{\frac{(T_{h}-T_{c})}{L}} (11.7)
gives the rate of energy transfer by conduction in joules per second. Multiply by the time and substitute given values to find the total thermal energy transferred.
Multiply Equation 11.7 by \Delta t to find an expression for the total energy Q transferred through the wall:
Q=\mathscr{P} \Delta t=k A\left(\frac{T_{h}-T_{c}}{L}\right) \Delta t
Substitute the numerical values to obtain Q, consulting Table 11.3 for k :
\begin{aligned} Q & =\left(1.3 \mathrm{~J} / \mathrm{s} \cdot \mathrm{m} \cdot{ }^{\circ} \mathrm{C}\right)\left(7.3 \mathrm{~m}^{2}\right)\left(\frac{15^{\circ} \mathrm{C}}{0.20 \mathrm{~m}}\right)(3600 \mathrm{~s}) \\ & =2.6 \times 10^{6} \mathrm{~J} \end{aligned}
Remarks Early houses were insulated with thick masonry walls, which restrict energy loss by conduction because k is relatively low. The large thickness L also decreases energy loss by conduction, as shown by Equation 11.7. There are much better insulating materials, however, and layering is also helpful. Despite the low thermal conductivity of masonry, the amount of energy lost is still rather large – enough to raise the temperature of 600 \mathrm{~kg} of water by more than 1^{\circ} \mathrm{C}. There are better insulating materials than masonry.
TABLE 11.3
Thermal Conductivities
| Substance | Thermal Conductivity ( J/s · m · °C) Metals (at 25°C) |
| Metals (at 25°C) | |
| Aluminum | 238 |
| Copper | 397 |
| Gold | 314 |
| Iron | 79.5 |
| Lead | 34.7 |
| Silver | 427 |
| Gases (at 20°C) | |
| Air | 0.023 4 |
| Helium | 0.138 |
| Hydrogen | 0.172 |
| Nitrogen | 0.023 4 |
| Oxygen | 0.023 8 |
| Nonmetals | |
| Asbestos | 0.25 |
| Concrete | 1.3 |
| Glass | 0.84 |
| Ice | 1.6 |
| Rubber | 0.2 |
| Water | 0.60 |
| Wood | 0.10 |