smc-4282-20-Thermal conductivity

PHYSICS, M3 EQ-Bank 7 MC

Which of the following statements about energy transfer is the most accurate?

Conduction and convection require a medium; radiation does not.
Convection transfers energy through direct contact.
Conduction occurs only in gases.
Radiation requires denser materials for faster energy transfer.

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\(A\)

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Option A is correct: Radiation involves the transfer of energy by electromagnetic waves that can occur through a vacuum. Conduction and convection require a medium.
Other options:
Conduction involves the transfer of thermal energy through direct particle-to-particle contact. It occurs in solids (especially metals) and, to a lesser extent, in liquids and gases, but always requires a material medium.
Convection occurs in fluids (liquids and gases), where warmer, less dense regions rise and cooler, denser regions sink, transferring heat through bulk movement of the medium itself.
B is incorrect because convection involves the bulk movement of fluids, not direct contact between particles (which describes conduction).
C is incorrect because conduction occurs best in solids, not gases, since solids have tightly packed particles that transfer energy more efficiently.
D is incorrect because radiation does not require any material medium and transfers energy most efficiently through a vacuum.

\(\Rightarrow A\)

PHYSICS, M3 EQ-Bank 1 MC

Objects \(\text{X}\) and \(\text{Y}\) are in thermal equilibrium. Objects \(\text{Y}\) and \(\text{Z}\) are also in thermal equilibrium.

Which of the following statements must be true?

\(\text{I.}\)	Objects \(\text{X}\), \(\text{Y}\), and \(\text{Z}\) are all at the same temperature.
\(\text{II.}\)	Heat is flowing from object \(\text{X}\) to object \(\text{Z}\).
\(\text{III.}\)	Objects \(\text{X}\) and \(\text{Z}\) are in thermal equilibrium.
\(\text{IV.}\)	Object \(\text{Y}\) must be cooler than object \(\text{X}\).

\(\text{I}\) and \(\text{II}\)
\(\text{I}\) and \(\text{III}\)
\(\text{II}\) and \(\text{IV}\)
\(\text{I}\) and \(\text{IV}\)

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\(B\)

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\(\text{I}\) is true. If \(\text{X}\) is in thermal equilibrium with \(\text{Y}\), and \(\text{Y}\) is in thermal equilibrium with \(\text{Z}\), that means no heat is being exchanged between \(\text{X}\) and \(\text{Y}\) or between \(\text{Y}\) and \(\text{Z}\). This can only happen if all three objects are at the same temperature.
\(\text{II}\) is false. Since there is no temperature difference between any of the objects, no heat transfer occurs. Heat only flows from a hotter object to a cooler one.
\(\text{III}\) is true. If \(\text{X}\) and \(\text{Y}\) have equal temperatures, and \(\text{Y}\) and \(\text{Z}\) also have equal temperatures, then \(\text{X}\) and \(\text{Z}\) must also be at the same temperature. This means they are in thermal equilibrium, even if they are not directly in contact.
\(\text{IV}\) is false. They are all the same temperature as they are all in thermal equilibrium with one another.

\(\Rightarrow B\)

A student investigates how heat travels through different materials. They smear small pieces of wax onto rods made of aluminium and plastic, placing identical metal pins into the wax at regular intervals. The rods are then heated at one end using a Bunsen burner. The student times how long it takes for each pin to fall as the wax melts.

After testing the aluminium rod, the experiment is repeated using a plastic rod under the same conditions.

Using your understanding of heat transfer in solids, explain what property of the materials is being investigated. Describe what you expect to observe for each material, and explain your reasoning using principles of thermal conduction. (4 marks)

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This experiment investigates the thermal conductivity of different materials. When one end of each rod is heated by the Bunsen burner, heat energy travels along the rod via conduction, where thermal energy is transferred through collisions between particles.
Metals like aluminium are good conductors because they have free-moving electrons that rapidly transfer energy through the material.
In contrast, plastics are poor conductors (insulators) because they lack these free electrons, and energy is transferred only through slower molecular vibrations.
On the aluminium rod, the pins will fall off more quickly and in succession, starting from the end nearest the heat source. This shows that heat is conducted rapidly and efficiently along the metal rod.
On the plastic rod, the pins will either not fall off at all or will fall off much more slowly and inconsistently, because plastic does not effectively transfer heat along its length.

Show Worked Solution

This experiment investigates the thermal conductivity of different materials. When one end of each rod is heated by the Bunsen burner, heat energy travels along the rod via conduction, where thermal energy is transferred through collisions between particles.
Metals like aluminium are good conductors because they have free-moving electrons that rapidly transfer energy through the material.
In contrast, plastics are poor conductors (insulators) because they lack these free electrons, and energy is transferred only through slower molecular vibrations.
On the aluminium rod, the pins will fall off more quickly and in succession, starting from the end nearest the heat source. This shows that heat is conducted rapidly and efficiently along the metal rod.
On the plastic rod, the pins will either not fall off at all or will fall off much more slowly and inconsistently, because plastic does not effectively transfer heat along its length.

PHYSICS, M3 EQ-Bank 3

A concrete wall has the dimensions 3 m × 5.5 m and a depth \((d)\) of 0.25 metres.

Calculate the heat energy that passes through the wall if the outside temperature is 5°C and the temperature inside is 26°C across a 5 minute period. \((k= 2.25\ \text{W m}^{-1}\ K^{-1}) \) (3 marks)

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\(935\ 550\ \text{J}\)

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\(\dfrac{Q}{t}\)	\(=\dfrac{kA(T_{hot}-T_{cold})}{d}\)
\(Q\)	\(=\dfrac{kA(T_{hot}-T_{cold})}{d} \times t\)
	\(=\dfrac{2.25 \times 3 \times 5.5 \times (26-5)}{0.25} \times (5 \times 60)\)
	\(=935\ 550\ \text{J}\)

PHYSICS, M3 EQ-Bank 2

A glass panel has thickness \(d\) mm and a temperature difference between its two sides of \(\Delta T\).

If the surface area of a glass panel was increased from \(A\) m² to \(4A\) m², what two changes could be made to the glass panel to ensure the rate of change of heat energy through the glass remains the same. (3 marks)

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Thermal conductivity equation \(\ \Rightarrow \dfrac{Q}{t}=\dfrac{kA\Delta T}{d}\).

Given \(A\) increases to \(4A\):

\(\dfrac{Q}{t} \) remains the same if the distance through which the heat travels through the glass increases from \(d\) to \(4d\).
\(\dfrac{Q}{t} \) remains the same if the temperature difference between the two sides of the glass panel decreases from \(\Delta T\) to \(\dfrac{\Delta T}{4}\).

Show Worked Solution

Thermal conductivity equation \(\ \Rightarrow \dfrac{Q}{t}=\dfrac{kA\Delta T}{d}\).

Given \(A\) increases to \(4A\):

\(\dfrac{Q}{t} \) remains the same if the distance through which the heat travels through the glass increases from \(d\) to \(4d\).
\(\dfrac{Q}{t} \) remains the same if the temperature difference between the two sides of the glass panel decreases from \(\Delta T\) to \(\dfrac{\Delta T}{4}\).