Identifying the False Heat Transfer Statement

This question requires us to evaluate several statements about different modes of heat transfer: conduction, convection, and radiation. We need to determine which statement is factually incorrect based on established physics principles.

Analyzing Conduction Heat Flow

Statement 1: "Heat flow by conduction is directly proportional to the area and temperature gradient." This aligns with Fourier's Law of Heat Conduction. The law states that the rate of heat transfer through a material is proportional to the negative gradient of the temperature and to the area ($A$) at right angles to the gradient. Mathematically, the heat flow rate ($Q/t$) can be represented as:

$$ \frac{Q}{t} \propto A \frac{dT}{dx} $$

Where $A$ is the area and $dT/dx$ is the temperature gradient. Therefore, this statement is TRUE.

Analyzing Convection Heat Flow

Statement 2: "Heat flow by convection is directly proportional to the area and temperature difference." This is consistent with Newton's Law of Cooling, which describes convective heat transfer. The law states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. For forced convection, the heat flow rate ($Q/t$) is expressed as:

$$ \frac{Q}{t} = hA(T_{surface} - T_{fluid}) $$

Where $h$ is the convective heat transfer coefficient, $A$ is the surface area, and $(T_{surface} - T_{fluid})$ is the temperature difference. Thus, this statement is TRUE.

Analyzing Radiation Heat Flow

Statement 3: "Heat flow by radiation is directly proportional to the cube of absolute temperature of the radiating body." This statement relates to the energy radiated by an object. The Stefan-Boltzmann Law governs thermal radiation. It states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time is proportional to the *fourth power* of the black body's absolute temperature ($T$). The formula is:

$$ E = \sigma T^4 $$

Where $E$ is the emissive power and $\sigma$ is the Stefan-Boltzmann constant. Since the law involves the fourth power ($T^4$) and not the cube ($T^3$), this statement is FALSE.

Analyzing Emissivity

Statement 4: "Emissivity of perfect black body is unity." Emissivity ($\epsilon$) is a measure of how effectively a surface emits thermal radiation compared to a perfect black body. By definition, a perfect black body has an emissivity of 1 ($\epsilon = 1$), meaning it absorbs and emits all incident thermal radiation. Therefore, this statement is TRUE.

Conclusion on the False Statement

Based on the analysis of the laws governing heat transfer:

• Statement 1 (Conduction) is TRUE.
• Statement 2 (Convection) is TRUE.
• Statement 3 (Radiation) is FALSE because heat flow is proportional to $T^4$, not $T^3$.
• Statement 4 (Emissivity) is TRUE.

The question asks for the FALSE statement, which is Statement 3.