Question

\(q = -k A \frac{\Delta T}{\Delta x}\) is called as

• A. Plank's Equation
• B. Stokes equation
• C. Fourier's equation
• D. Continuity equation

Hint:

Fourier's Law is the governing equation for heat conduction:
\[ q = -k A \frac{dT}{dx} \]
The negative sign is physically necessary because heat naturally transfers down a negative temperature gradient (from high to low temperature).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Conduction is the transfer of thermal energy through solid or stationary fluid media via direct molecular contact and free electron movement.
The rate of heat conduction is governed by a fundamental phenomenological law.

Step 2: Detailed Explanation:
Let us analyze the equation:
\[ q = -k A \frac{\Delta T}{\Delta x} \]
- \(q\) is the rate of heat transfer by conduction (in Watts, \(\text{W}\)).
- \(k\) is the thermal conductivity of the material (in \(\text{W m}^{-1}\ ^\circ\text{C}^{-1}\)).
- \(A\) is the cross-sectional area perpendicular to the direction of heat flow (in \(\text{m}^2\)).
- \(\frac{\Delta T}{\Delta x}\) is the temperature gradient across the thickness \(\Delta x\).
- The negative sign indicates that heat flows in the direction of decreasing temperature (from hot to cold), satisfying the Second Law of Thermodynamics.
This equation is the algebraic form of Fourier's Law of Heat Conduction.
Let us review the other options:
- Planck's equation describes the spectral blackbody radiation.
- Stokes' equation describes the drag force on a sphere moving through a viscous fluid.
- Continuity equation describes the conservation of mass in fluid flow.
Therefore, this equation is Fourier's equation.

Step 3: Final Answer:
The equation is known as Fourier's equation. Hence, the correct option is (C).