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Heat Transfer - Conduction

Grade 8IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Conduction is the process by which heat energy is transmitted through collisions between neighboring atoms or molecules. It occurs primarily in solids where particles are closely packed.

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In non-metallic solids, heat is transferred solely through lattice vibrations. Particles at the hot end vibrate with greater amplitude and collide with adjacent particles, transferring kinetic energy.

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Metals are excellent conductors because they contain a 'sea' of delocalized (free) electrons. These electrons can move rapidly through the metal lattice, carrying thermal energy much faster than vibration alone.

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Thermal Conductivity (kk) is a measure of a material's ability to conduct heat. Materials with high kk (like copper or silver) are conductors, while materials with low kk (like wood, glass, or air) are insulators.

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The rate of heat transfer through conduction is directly proportional to the temperature difference ΔT\Delta T and the cross-sectional area AA, and inversely proportional to the thickness dd of the material.

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Practical applications include using wooden handles on metal pans (insulation) and using copper bottoms on cookware to ensure even and rapid heat distribution (conduction).

📐Formulae

ΔT=Thot−Tcold\Delta T = T_{hot} - T_{cold}

H=QtH = \frac{Q}{t}

H=kAΔTdH = \frac{kA\Delta T}{d}

Q=m⋅c⋅ΔTQ = m \cdot c \cdot \Delta T

💡Examples

Problem 1:

A copper rod and a glass rod of the same dimensions are heated at one end to 100∘C100^{\circ}C. Which rod will reach a temperature of 50∘C50^{\circ}C at the other end first, and why?

Solution:

The copper rod will reach 50∘C50^{\circ}C much faster than the glass rod.

Explanation:

Copper is a metal with high thermal conductivity (k≈400 W/mKk \approx 400 \text{ W/mK}) due to the presence of free electrons that transfer kinetic energy rapidly. Glass is an insulator (k≈0.8 W/mKk \approx 0.8 \text{ W/mK}) and relies only on slow atom-to-atom vibrations. Therefore, the rate of heat transfer HH is significantly higher in copper.

Problem 2:

Calculate the temperature difference ΔT\Delta T across a 0.05 m0.05 \text{ m} thick insulation board if the inside temperature is 22∘C22^{\circ}C and the outside temperature is −3∘C-3^{\circ}C.

Solution:

ΔT=22∘C−(−3∘C)=25∘C\Delta T = 22^{\circ}C - (-3^{\circ}C) = 25^{\circ}C

Explanation:

The temperature difference is found by subtracting the lower temperature from the higher temperature: Thot−TcoldT_{hot} - T_{cold}.

Problem 3:

A student touches a metal chair and a wooden chair in a room at 20∘C20^{\circ}C. Why does the metal chair feel colder even though both are at the same temperature?

Solution:

The metal chair feels colder because it is a better conductor of heat.

Explanation:

Since the human body temperature (approx. 37∘C37^{\circ}C) is higher than the room temperature (20∘C20^{\circ}C), heat flows from the hand to the chair. Metal has a high thermal conductivity, so it conducts heat away from the hand rapidly. Wood is an insulator and conducts heat away slowly, making the metal feel 'colder' to the touch.