Question

Fourier's law of heat conduction states that the rate of heat transfer is proportional to the:

• A. Temperature difference only
• B. Thermal conductivity only
• C. Area and temperature gradient
• D. Density and viscosity

Hint:

Logic Tip: To move more heat faster, you need a bigger window (Area) and a harsher winter outside (steeper Temperature Gradient).

Answer 1

The Correct Option is C

Concept:
Fourier's Law is the fundamental empirical law describing heat transfer by conduction through solid materials. It dictates how fast thermal energy will move from a hot region to a cold region.

Step 1: Fourier's law is mathematically expressed as: $q = -kA \frac{dT}{dx}$.

Step 2: * $q$ is the rate of heat transfer (Watts). * $k$ is the thermal conductivity (a material property constant, not a variable to be proportional to in this context). * $A$ is the cross-sectional Area perpendicular to the direction of heat flow. * $\frac{dT}{dx}$ is the temperature gradient (change in temperature over change in distance).

Step 3: The equation shows that the heat transfer rate ($q$) scales directly with the size of the surface Area ($A$) available for heat to pass through.

Step 4: The rate also scales directly with the temperature gradient ($\frac{dT}{dx}$), which represents how sharply the temperature drops over a given thickness. A steeper gradient drives faster heat flow.

Step 5: Therefore, the rate of conduction is directly proportional to both the Area and the temperature gradient.