Match each heat transfer process or physical phenomenon on the left with its underlying go… — JAMB UTME

Match each heat transfer process or physical phenomenon on the left with its underlying governing mechanism or quantitative relationship on the right.

Steady-state rate of heat conduction through a uniform plane slab of cross-sectional area $A$ Directly proportional to the temperature gradient $\frac{\Delta T}{\Delta x}$ across the material
Total radiant energy emitted per unit time per unit surface area by an ideal blackbody radiatorDirectly proportional to the fourth power of absolute thermodynamic temperature ( $T^4$ )
Natural heat transport mechanism in fluids under the influence of a gravitational fieldDriven by buoyant forces resulting from temperature-induced fluid density variations
Dominant microscopic thermal conduction mechanism in solid electrical insulatorsPropagated via quantized lattice vibrations (phonons) without free electron motion

Answer

The steady-state rate of heat conduction through a uniform slab corresponds to being directly proportional to the temperature gradient. The radiant energy emitted per unit area by an ideal blackbody corresponds to being directly proportional to the fourth power of absolute temperature. Natural heat transport in fluids under gravity corresponds to being driven by buoyant forces resulting from density variations. The microscopic conduction mechanism in electrical insulators corresponds to propagation via quantized lattice vibrations (phonons).

Each heat transfer mechanism matches its fundamental law and microscopic process: conduction across a plane wall is governed by Fourier's law and proportional to the temperature gradient; thermal radiation from a blackbody obeys Stefan's law and scales with the fourth power of absolute temperature; natural convection in fluids requires gravity to drive density-based buoyant circulation; and thermal conduction in non-metallic insulators relies on atomic lattice vibrations (phonons) due to the absence of free electrons.

Step-by-Step Solution

Analyze conduction governing equation (Fourier's Law)

Heat current

\frac{Q}{t} = kA \frac{\Delta T}{d}

, showing that heat flow per unit area depends directly on the temperature gradient

\frac{\Delta T}{\Delta x}

Identify the quantitative relationship governing thermal conduction in solid materials.

Analyze radiation power equation (Stefan-Boltzmann Law)

Total power per unit area

P/A = \sigma T^4

, establishing fourth-power dependence on thermodynamic temperature

T

Identify the law governing thermal radiation emissions.

Examine natural convection mechanics

Thermal expansion leads to density differences

\Delta \rho

, causing buoyant forces under gravity to set up fluid circulation currents.

Identify the physical drive behind natural convection in fluids.

Examine microscopic heat transfer mechanisms in insulators

Insulators lack mobile valence electrons, leaving atomic lattice vibrations (phonons) as the sole mechanism for thermal energy transport.

Distinguish between electronic conduction in metals and lattice/phonon conduction in non-metals.

Key Concept

Physical Principles and Microscopic Mechanisms of Conduction, Convection, and Radiation

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic