Worksheet: Thermal Conduction

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

Q1:

A glass window has an area of 6.00 m2 and a thickness of 0.500 cm. The inner surface of the window is at a temperature of 10.0∘C and the outer surface of the window is at a temperature of −18.0∘C. Determine the rate of heat loss through the window. Use a value of 0.840/⋅WmC∘ for the thermal conductivity of glass.

Q2:

Calculate the rate of heat conduction out of the human body, assuming that the core internal temperature is 37.0∘C, the skin temperature is 34.0∘C, the thickness of the fatty tissues between the core and the skin averages 1.00 cm, and the surface area is 1.40 m2. The thermal conductivity of human fatty tissues is 0.200/⋅WmC∘.

Q3:

The walls of a house have a surface area of 120 m2. The walls are 13.0 cm thick and their thermal conductivity is 0.0840/⋅WmC∘. The temperature inside the house is 5.00∘C and the temperature outside is 18.00∘C. Calculate the rate of heat loss through the walls.

  • A 8 7 . 5 × 1 0 W
  • B 1 . 1 4 × 1 0 W
  • C 1 . 0 1 × 1 0 W
  • D 1 . 2 5 × 1 0 W
  • E 1 . 3 7 × 1 0 W

Q4:

A 13.0-cm-thickness wall has an area of 10.0 m2 and a thermal conductivity of 0.0840/⋅WmC∘. A 0.750-cm-thickness window has an area of 2.00 m2 and a thermal conductivity of 0.840/⋅WmC∘. 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 1.40 m2 surface area. The animal’s surface is covered with 3.00-cm-thickness fur that has a thermal conductivity of 0.0230/⋅WmC∘. The animal’s skin is at a temperature of 32.00∘C and the air temperature around the animal is −5.00∘C.

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 0.040/⋅WmC∘, and its inner surface is at a temperature of 22∘C. 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 6.00∘C. The walrus’s internal core temperature is 37.00∘C, and its skin surface area is 1.20 m2. Determine the average thickness of the walrus’s blubber. Use a value of 0.200/⋅WmC∘ 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 cm2. 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 16.0∘C. 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 0.120/⋅WmC∘ for the thermal conductivity of wood and use a value of 0.0400/⋅WmC∘ 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 25.0∘C?

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 25.0∘C?

Q9:

A firewalker walks across a bed of hot coals without sustaining burns. The coals are at a temperature of 1,000.0∘C and the firewalker’s feet remain at a temperature of 38.0∘C 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 cm2, and has a thermal conductivity of 0.100/⋅WmC∘. 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 0.042/⋅WmC∘ for the thermal conductivity of fiberglass and assume that the interior and exterior of the house are maintained uniformly at two different temperatures.

  • A 5 %
  • B 4 %
  • C 7 %
  • D 8 %
  • E 6 %

Q11:

A person who has a surface area of 2.00 m2 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 0.400/⋅WmC∘ for the thermal conductivity of wool.

Q12:

The 𝑅 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 𝑅 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 𝑅 factor of 2.1. Determine the rate of conductive heat loss through the wall of the house when the interior temperature is 25∘C and the exterior temperature is −8.0∘C. Use a value of 0.042/⋅WmC∘ for the thermal conductivity of fiberglass.

Q13:

The thermal conductivity of a brick is 1 W/m⋅K. The thickness of the brick is 10 cm. What is the heat flux through the brick if a temperature difference of 100 K is applied across it?

Q14:

The total surface area of a house is 300 m2. The average thickness of the house walls is 0.10 m and their thermal conductivity is 5.0×10 kW/m⋅K. How much energy must be supplied to the house in a day to keep its interior temperature 10∘C higher than the temperature outside.

  • A 0 . 3 0 × 1 0 J
  • B 2 . 3 × 1 0 J
  • C 1 . 3 × 1 0 J
  • D 3 . 0 × 1 0 J
  • E 5 . 3 × 1 0 J

Q15:

How are the rate of cooling of an object, its temperature, and the temperature of its surroundings related in Newton’s law of cooling?

  • A 𝑞 = 𝑚 𝐿
  • B 𝑞 = 𝑚 𝑐 𝑇
  • C 𝑞 ′ ′ = − 𝑘 𝑇 𝑥 d d
  • D 𝑞 ′ ′ = ℎ ( 𝑇 − 𝑇 ) ∞
  • E 𝐸 = 𝜎 𝑇

Q16:

What is the thermal resistance of a layer of rubber 1 cm thick that has a surface area of 10 m2? Use a value of 0.2 W/m⋅K for the thermal conductivity of rubber.

Q17:

One face of a metal layer has a temperature of 50∘C and the other face has a temperature of 30∘C. The thickness of the metal layer is 100 mm. The thermal conductivity of the metal is 1/⋅WCm∘. What is the heat transfer rate per unit area of the layer?

Q18:

What is heat conduction?

  • AThe transfer of thermal energy between regions of matter due to a temperature gradient.
  • BThe transfer of kinetic energy due to collisions.
  • CThe transfer of energy due to bulk movement of liquids.
  • DThe transfer of electrical energy from one object to another.

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/m3 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 0.0∘C, while the top surface of the ice, in contact with the air in the freezer, is at a temperature of −25∘C. 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 2.2/⋅WmC∘ for the thermal conductivity of ice and use a value of 333.55 J/g for the specific latent heat of fusion of water.

Q20:

Metals that exhibit high thermal conductivity also generally exhibit what other characteristic?

  • Ahigh elastic modulus
  • Blow density
  • Clow electrical resistivity
  • Dlow electrical conductivity
  • Ehigh melting temperature

Q21:

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

  • AConvection
  • BConduction
  • CAdvection
  • DDiffusion
  • EInfrared radiation

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