14.5 Conduction

How does the rate of heat transfer by conduction change when all spatial dimensions are doubled?

For the experiment that you devised the reference, which variables can be changed, and how should they be changed, so as to shorten the time in which a measurement is made?

1. Use a smaller quantity of ice (smaller m).
2. Use containers with greater thickness (larger d).
3. Use containers with smaller surface areas (smaller A).
4. Use a lower ambient temperature outside the container (smaller T₂).

Which of the following correctly describes the rate of conductive heat transfer for a substance?

1. The rate decreases with increased surface area and decreased thickness.
2. The rate increases with increased temperature difference and surface area.
3. The rate increases with decreased temperature difference and increased thickness.
4. The rate decreases with decreased temperature difference and increased su…

(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and that have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The surface area of the walls is $\text{120} \text{m}^{2}$ and their inside surface is at $\text{18}. 0º \text{C}$, while their outside surface is at $5 .\text{00}º \text{C}$. (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is $\text{37} . 0º \text{C}$, the skin temperature is $\text{34} . 0º \text{C}$, the thickness of the tissues between averages $1 .\text{00}\textrm{ }\text{cm}$, and the surface area is $1 . \text{40} \text{m}^{2}$.

A man consumes 3000 kcal of food in one day, converting most of it to maintain body temperature. If he loses half this energy by evaporating water (through breathing and sweating), how many kilograms of water evaporate?

(a) What is the rate of heat conduction through the 3.00-cm-thick fur of a large animal having a $1 . \text{40}-\text{m}^{2}$ surface area? Assume that the animal’s skin temperature is $\text{32} . 0º \text{C}$, that the air temperature is $- 5 . \text{00}º \text{C}$, and that fur has the same thermal conductivity as air. (b) What food intake will the animal need in one day to replace this heat transfer?

Compare the rate of heat conduction through a 13.0-cm-thick wall that has an area of $\text{10} . 0 \textrm{ }\text{m}^{2}$ and a thermal conductivity twice that of glass wool with the rate of heat conduction through a window that is 0.750 cm thick and that has an area of $2 . \text{00} \textrm{ }\text{m}^{2}$, assuming the same temperature difference across each.

Some stove tops are smooth ceramic for easy cleaning. If the ceramic is 0.600 cm thick and heat conduction occurs through the same area and at the same rate as computed in the example, what is the temperature difference across it? Ceramic has the same thermal conductivity as glass and brick.

(a) Calculate the rate of heat conduction through a double-paned window that has a $1 . \text{50} -\text{m}^{2}$ area and is made of two panes of 0.800-cm-thick glass separated by a 1.00-cm air gap. The inside surface temperature is $\text{15} . 0º \text{C}$, while that on the outside is $- \text{10} . 0º \text{C}$. (Hint: There are identical temperature drops across the two glass panes. First find these and then the temperature drop across the air gap. This problem ignores…

For the human body, what is the rate of heat transfer by conduction through the body’s tissue with the following conditions: the tissue thickness is 3.00 cm, the change in temperature is $2 . \text{00}º \text{C}$, and the skin area is $1 . \text{50} \textrm{ }\text{m}^{2}$. How does this compare with the average heat transfer rate to the body resulting from an energy intake of about 2400 kcal per day? (No exercise is included.)