# 1.6 Mechanisms of heat transfer  (Page 13/27)

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Putting a lid on a boiling pot greatly reduces the heat transfer necessary to keep it boiling. Explain why.

Your house will be empty for a while in cold weather, and you want to save energy and money. Should you turn the thermostat down to the lowest level that will protect the house from damage such as freezing pipes, or leave it at the normal temperature? (If you don’t like coming back to a cold house, imagine that a timer controls the heating system so the house will be warm when you get back.) Explain your answer.

Turn the thermostat down. To have the house at the normal temperature, the heating system must replace all the heat that was lost. For all three mechanisms of heat transfer, the greater the temperature difference between inside and outside, the more heat is lost and must be replaced. So the house should be at the lowest temperature that does not allow freezing damage.

You pour coffee into an unlidded cup, intending to drink it 5 minutes later. You can add cream when you pour the cup or right before you drink it. (The cream is at the same temperature either way. Assume that the cream and coffee come into thermal equilibrium with each other very quickly.) Which way will give you hotter coffee? What feature of this question is different from the previous one?

Broiling is a method of cooking by radiation, which produces somewhat different results from cooking by conduction or convection. A gas flame or electric heating element produces a very high temperature close to the food and above it. Why is radiation the dominant heat-transfer method in this situation?

Air is a good insulator, so there is little conduction, and the heated air rises, so there is little convection downward.

On a cold winter morning, why does the metal of a bike feel colder than the wood of a porch?

## Problems

(a) Calculate the rate of heat conduction through house walls that are 13.0 cm thick and have an average thermal conductivity twice that of glass wool. Assume there are no windows or doors. The walls’ surface area is $120\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ and their inside surface is at $18.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , while their outside surface is at $5.00\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ . (b) How many 1-kW room heaters would be needed to balance the heat transfer due to conduction?

a. $1.01\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{W}$ ; b. One 1-kilowatt room heater is needed.

The rate of heat conduction out of a window on a winter day is rapid enough to chill the air next to it. To see just how rapidly the windows transfer heat by conduction, calculate the rate of conduction in watts through a $3.00{\text{-m}}^{2}$ window that is 0.634 cm thick (1/4 in.) if the temperatures of the inner and outer surfaces are $5.00\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ and $-10.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , respectively. (This rapid rate will not be maintained—the inner surface will cool, even to the point of frost formation.)

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is $37.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , the skin temperature is $34.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ , the thickness of the fatty tissues between the core and the skin averages 1.00 cm, and the surface area is $1.40\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ .

84.0 W

Suppose you stand with one foot on ceramic flooring and one foot on a wool carpet, making contact over an area of $80.0\phantom{\rule{0.2em}{0ex}}{\text{cm}}^{2}$ with each foot. Both the ceramic and the carpet are 2.00 cm thick and are $10.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ on their bottom sides. At what rate must heat transfer occur from each foot to keep the top of the ceramic and carpet at $33.0\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ ?

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