Worksheet: Thermal Conduction

In this worksheet, we will practice calculating the rate of energy transfer through solid objects due to temperature differences across the objects’ faces.

Q1:

The rate of power transfer through a rectangular-prism-shaped object of thermal conductivity 15/WmC is 600 W when a 2.5 m2 area face of the object is heated. The power is transferred across a distance of 0.25 m. Find the difference in temperature between the heated face of the object and the opposite face. Answer to two significant figures.

Q2:

A 5.0 m2 area face of a cuboid-shaped object is heated and has a constant temperature of 32C. The object is made of a material with a thermal conductivity of 6.4/WmC. The object transfers energy to the face opposite to its heated face across a distance of 16 cm to where the temperature is a constant 24C. What is the rate at which energy is transferred through the object? Answer to two significant figures.

Q3:

The rate of power transfer through a rectangular-prism-shaped object of thermal conductivity 5.5/WmC is 180 W when a 2.0 m2 area face of the object is heated. The difference in temperature between the heated face of the object and the opposite face is 36C. What is the distance between the object’s heated face and the opposite face? Answer to two significant figures.

Q4:

Energy is transferred by thermal conduction through an object due to a constant temperature difference between the sides of the object, as shown in the diagram. Temperature 𝑇 is 76C and temperature 𝑇 is 31C. The distance between the heated and unheated sides of the object is 1.2 m. The temperature inside the object varies linearly.

What is the temperature gradient within the object?

What is the temperature at a point 0.15 m from the heated side of the object to the nearest degree?

What is the temperature at a point 0.15 m from the unheated side of the object to the nearest degree?

Q5:

Which of the following formulas correctly represents the rate of energy transfer 𝑄𝑡 by the process of thermal conduction through a solid rectangular prism of thermal conductivity 𝑘? Energy is transferred across a length 𝑙 from one face of the rectangular prism of area 𝐴 and temperature 𝑇 to the opposite face of temperature 𝑇.

  • A𝑄𝑡=𝑘𝑙𝐴(𝑇+𝑇)
  • B𝑄𝑡=𝑘𝐴𝑙𝑇𝑇2
  • C𝑄𝑡=𝑘𝑙𝐴(𝑇𝑇)
  • D𝑄𝑡=𝑘𝐴𝑙(𝑇𝑇)

Q6:

The casing of an electronic appliance has an area of 0.015 m2 and is 1.2 cm thick. The thermal conductivity of the casing material is 2.5/WmC. The electronics inside the appliance maintain the air temperature inside it at 75C and the air temperature of the room the appliance is stored in is maintained at 20C. How much is the room heated by the appliance in a time of 3,600 seconds? Give your answer in kilojoules to two significant figures.

Q7:

A coffee mug on a table has a base area of 0.0015 m2 and a thickness of 0.25 cm. The mug is made of a material with a thermal conductivity of 1.5/WmC. The area of the table in contact with the base is heated at a rate of 20 W, and its temperature is 25C at a time 𝑡. What is the temperature of the coffee in the mug at the time 𝑡? Give your answer to the nearest degree.

Q8:

A brick wall of thickness 𝑑=45cm is connected to a layer of cladding of thickness 𝑑=10cm, as shown in the diagram. The temperature 𝑇 of the side of the wall opposite to the cladded side is 25.0C. The temperature of 𝑇 of the side of the wall in contact with the cladding is 12.5C. The temperature of 𝑇 of the side of the cladding opposite to the wall is 2.5C. The temperature inside the wall and the cladding vary linearly. What is the ratio of the temperature gradient in the cladding to the temperature gradient in the wall?

Q9:

A wall of a house has a constant temperature of 28C on its interior side and a constant temperature of 11C on its exterior side. The wall has a surface area of 8.2 m2 and is 25 cm thick. The wall is made of a substance with a thermal conductivity of 1.5/WmC. What is the rate of energy transfer through the wall? Answer to the nearest watt.

Q10:

The rate of power transfer through a rectangular-prism-shaped object of thermal conductivity 2.5/WmC is 500 W when a face of the object is heated transferring energy a distance of 0.15 m through the object. The difference in temperature between the heated face of the object and the opposite face is 12C. What is the area of the heated face? Give your answer to two significant figures.

Q11:

Two objects that have different thermal conductivities are connected by faces, which both have an area of 4.25 m2, as shown in the diagram. There is a constant rate of energy transfer through the objects due to a constant temperature difference of the faces of the objects opposite to their connected faces. The smaller object’s thermal conductivity is 2.5/WmC and the larger object’s thermal conductivity is 4.5/WmC. What is the temperature 𝑇 where the objects are connected? Give your answer to three significant figures.

Q12:

As energy passes by conduction from one side of a brick to another, the motions of the molecules in the brick do not only change perpendicular to the face of the brick that is heated, but also parallel to the face, as shown in diagram (a). The divergence of the lines of direction of conduction can be represented by making the value of the thermal conductivity of the brick different depending on which face of the brick is heated. A brick has opposite faces, top and bottom, and different opposite faces, left and right, as shown in diagram (b). The rate of energy transfer through the brick from top to bottom is found to be ten times the rate found when energy is transferred from left to right. What is the ratio of the thermal conductivity of the brick between left and right to the thermal conductivity of the brick between top and bottom?

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