Define thermal diffusivity alpha and its units.

Define thermal diffusivity alpha and its units.

• A. alpha = rho * c / k; units s/m^2
• B. alpha = k / (rho * c); units m^2 / s
• C. alpha = k * rho * c; units J/(m^3 s)
• D. alpha = 1 / (k * rho * c); units s/m^2

Answer: (B)

Thermal diffusivity describes how quickly a temperature change spreads through a material. It captures the balance between how easily heat is conducted (k) and how much heat the material stores per degree of temperature rise, which is the volumetric heat capacity (rho times c). The defining relation is alpha = k / (rho c). Here k is the thermal conductivity, rho is density, and c is specific heat capacity, so rho c is the volumetric heat capacity. Dimensional check confirms the units: k has units of W/(m K) or J/(s m K), while rho c has units of J/(m^3 K). Dividing gives (J/(s m K)) / (J/(m^3 K)) = m^2/s. So the diffusion rate of heat in a material is measured in square meters per second. Materials with high conductivity or low volumetric heat capacity have larger alpha, meaning heat diffuses faster. The other expressions would mix or invert these quantities and yield incorrect units for diffusivity.

Thermal diffusivity describes how quickly a temperature change spreads through a material. It captures the balance between how easily heat is conducted (k) and how much heat the material stores per degree of temperature rise, which is the volumetric heat capacity (rho times c). The defining relation is alpha = k / (rho c). Here k is the thermal conductivity, rho is density, and c is specific heat capacity, so rho c is the volumetric heat capacity. Dimensional check confirms the units: k has units of W/(m K) or J/(s m K), while rho c has units of J/(m^3 K). Dividing gives (J/(s m K)) / (J/(m^3 K)) = m^2/s. So the diffusion rate of heat in a material is measured in square meters per second. Materials with high conductivity or low volumetric heat capacity have larger alpha, meaning heat diffuses faster. The other expressions would mix or invert these quantities and yield incorrect units for diffusivity.