# Worksheet: Thermal Conduction

In this worksheet, we will practice calculating the rate at which heat moves through a material given its thermal conductivity.

**Q2: **

Calculate the rate of heat conduction out of the human
body, assuming that the core internal temperature is
,
the skin temperature is , the thickness of
the fatty tissues between the core and the skin averages 1.00 cm,
and the surface area is 1.40 m^{2}.
The thermal conductivity of human fatty tissues is .

**Q4: **

A wall of thickness 13.0 cm has an area of
10.0 m^{2} and a thermal conductivity of
.
A window of thickness 0.750 cm has an area of
2.00 m^{2} and a thermal conductivity
of . The
temperature difference across the window is equal to the temperature difference across the
wall. What is the ratio of the rate of heat conduction through the window to the rate of
heat conduction through the wall?

**Q5: **

A large animal has a surface area of 1.40 m^{2}. The animal’s surface is covered with fur that is 3.00 cm
thick and that has a thermal conductivity of .
The animal’s skin is at a temperature of
and the air temperature around the animal is
.

What is the rate of heat conduction through the fur?

What daily intake of energy from food will the animal need to replace energy lost by heat conduction?

**Q6: **

An astronaut is performing an extravehicular activity while shaded from sunlight. The astronaut is wearing a spacesuit that can be modeled as perfectly white, with an emissivity of exactly 0. However, one part of the spacesuit, a rectangular patch with side lengths of 2 cm and 4 cm, is not white. The patch has an emissivity 0.220. The spacesuit under the patch is 0.720 cm thick, with a thermal conductivity of , and its inner surface is at a temperature of . Assume the patch is so thin that its outer surface is at the same temperature as the outer surface of the spacesuit under it. Determine the temperature of the patch. Use a value of 3 K for the temperature of space around the astronaut.

**Q7: **

A walrus transfers energy by conduction through its blubber at a rate
of 183 W
when immersed in water that is at a temperature of
.
The walrus’s internal core temperature is
,
and its skin surface area is
1.20 m^{2}.
Determine the average thickness of the walrus’s blubber.
Use a value of
for the thermal conductivity of the blubber.

**Q8: **

A woman stands with one of her feet on a wooden floorboard and her
other foot on a wool carpet. Each foot has a contact area with the
ground of 68.0 cm^{2}.
The carpet and the floorboard are both
5.00 cm thick and their surfaces opposite to those in contact
with the woman’s feet are both at a temperature of
.
The heat flow rate necessary to maintain the foot-contacting surfaces
of the carpet and floorboard at a particular temperature depends on the
thermal conductivity of the wood and of the wool. Use a value of
for the thermal conductivity of wood and use a value of
for the thermal conductivity of wool.

What is the rate of heat flow from foot to wood needed to maintain the floorboard surface in contact with the woman’s foot at a temperature of ?

What is the rate of heat flow from foot to wool needed to maintain the carpeted surface in contact with the woman’s foot at a temperature of ?

**Q9: **

A firewalker walks across a bed of hot coals without sustaining burns.
The coals are at a temperature of
and the firewalker’s
feet remain at a temperature of
throughout the walk.
Heat is conducted to the firewalker’s feet by a layer of callused skin
that is 6.50 mm thick,
has an area of 21.0 cm^{2}, and has a thermal
conductivity of .
During one step, the firewalker’s
foot is in contact with the coals for 1.50 s.
What magnitude heat transfer
occurs from the coals to the firewalker’s foot during this step? Assume evaporative cooling is negligible.

**Q10: **

A single-story house has all its surfaces insulated with a 24 cm thick layer of fiberglass. The house is modeled as a cuboid with side lengths of 8.0 m, 13 m, and 2.7 m. Determine the percent reduction in heat loss from the house resulting from an increase of the insulation thickness by 5 cm. Use a value of for the thermal conductivity of fiberglass and assume that the interior and exterior of the house are maintained uniformly at two different temperatures.

- A
- B
- C
- D
- E

**Q11: **

A person who has a surface area of 2.00 m^{2}
is completely covered with
wool clothing that has an average thickness of 3.15 cm. The person loses
heat through the clothing at a rate of 38.0 W. Determine the difference in
temperature between the inner and the
outer surfaces of the clothing. Use a value of
for the thermal conductivity of wool.

**Q12: **

The factor of an object is the ratio of its length in the direction in which it conducts heat to the thermal conductivity of its constituent materials.

A layer of drywall has an factor of 0.80. An exterior wall of a house is 4.5 m tall and 8.5 m wide. The exterior wall consists of an exterior layer of drywall which covers a layer of fiberglass batts that is 3.5 cm thick, behind which is a layer of insulated siding that has an factor of 2.1. Determine the rate of conductive heat loss through the wall of the house when the interior temperature is and the exterior temperature is . Use a value of for the thermal conductivity of fiberglass.

**Q19: **

A Dewar flask has an open top and straight sides, as shown in the diagram.
The flask can be modeled as a perfect thermal insulator except for its open top.
The flask is filled with water of density
1,000 kg/m^{3}
and placed in a freezer.
The water cools and a layer of ice forms on its surface. The liquid water and the
bottom surface of the ice, in contact with the liquid water, are both at a temperature
of ,
while the top surface of the ice, in contact with the air in the freezer,
is at a temperature of .
Assume that the heat conduction rate through the ice
is equal to the specific latent heat of fusion of water, and so determine the rate at which the
layer of ice is increasing in thickness at the instant
that its thickness is 0.46 cm.
Use a value of
for the thermal conductivity of ice and use a value of
333.55 J/g for the
specific latent heat of fusion of water.

**Q21: **

Which of the following is the method of heat transfer that occurs mainly in solids?

- AConvection
- BConduction
- CAdvection
- DDiffusion
- EInfrared radiation