Thermal Diffusivity Explained

Thermal diffusivity is a fundamental thermophysical property of a substance that quantifies the rate at which temperature propagates through the material. It is a critical parameter in transient heat conduction problems. It is derived from other primary thermal properties of a material.

The mathematical formula for thermal diffusivity, often denoted by the Greek letter \( \alpha \) (alpha), is given by:

Where:

• \( k \) represents the thermal conductivity (W/(m·K)) of the substance, which measures its ability to conduct heat.
• \( \rho \) represents the density (kg/m\(^3\)) of the substance, which is its mass per unit volume.
• \( c_p \) represents the specific heat capacity at constant pressure (J/(kg·K)) of the substance, which is the amount of heat required to raise the temperature of a unit mass of the substance by one degree Kelvin.

Analyzing Thermal Diffusivity Statements

Let's carefully examine each statement provided in the question regarding the thermal diffusivity of a substance and determine its correctness based on the established formula:

Statement 1: It is directly proportional to density.

• From the formula \( \alpha = \frac{k}{\rho c_p} \), density \( \rho \) is in the denominator.
• This indicates an inverse proportional relationship between thermal diffusivity \( \alpha \) and density \( \rho \). If the density of a substance increases, its thermal diffusivity decreases, assuming other properties remain constant.
• Therefore, statement 1 is INCORRECT.

Statement 2: It is inversely proportional to specific heat.

• Looking at the formula \( \alpha = \frac{k}{\rho c_p} \), specific heat \( c_p \) is also located in the denominator.
• This demonstrates an inverse proportional relationship between thermal diffusivity \( \alpha \) and specific heat \( c_p \). If the specific heat capacity of a substance increases, its thermal diffusivity decreases.
• Therefore, statement 2 is CORRECT.

Statement 3: It is inversely proportional to thermal conductivity.

• Referring to the formula \( \alpha = \frac{k}{\rho c_p} \), thermal conductivity \( k \) is found in the numerator.
• This indicates a direct proportional relationship between thermal diffusivity \( \alpha \) and thermal conductivity \( k \). If the thermal conductivity of a substance increases, its thermal diffusivity also increases.
• Therefore, statement 3 is INCORRECT.

Statement 4: It is directly proportional to thermal conductivity.

• As confirmed by the formula \( \alpha = \frac{k}{\rho c_p} \), thermal conductivity \( k \) is in the numerator.
• This means thermal diffusivity \( \alpha \) is indeed directly proportional to thermal conductivity \( k \).
• Therefore, statement 4 is CORRECT.

Identifying Incorrect Statements

To summarize our analysis of the given statements about thermal diffusivity:

• Statement 1: Thermal diffusivity is directly proportional to density (INCORRECT).
• Statement 2: Thermal diffusivity is inversely proportional to specific heat (CORRECT).
• Statement 3: Thermal diffusivity is inversely proportional to thermal conductivity (INCORRECT).
• Statement 4: Thermal diffusivity is directly proportional to thermal conductivity (CORRECT).

The question asks to identify the statements that are INCORRECT. Based on our evaluation, statements 1 and 3 are incorrect.

Summary of Thermal Property Relationships

Thus, the statements found to be INCORRECT are 1 and 3.