In the laser flash method, a pulse of light was applied to the front of a disk of thickness L = 2.0 mm, and the time for the temperature rise of the back face to reach half its maximum was t½ = 0.050 s. Which value is closest to the thermal diffusivity found with Parker's equation α = 0.1388L²/t½, which neglects heat loss?

Answer: B. About 1.1×10⁻⁵ m²/s

L = 2.0×10⁻³ m, so L² = 4.0×10⁻⁶ m², and α = 0.1388×4.0×10⁻⁶/0.050 ≈ 1.1×10⁻⁵ m²/s. The time for heat absorbed at the front to diffuse through the thickness and reach the back is proportional to L²/α, so the thermal diffusivity is found from the time for half the temperature rise. About 8.0×10⁻⁵ m²/s forgets to multiply by the factor 0.1388, and about 5.6×10⁻³ m²/s forgets to square the thickness, which does not even have units of m²/s. The thermal conductivity is then found as κ = αρc using a separately measured density and specific heat. Because the time scales with the square of the thickness, thicker samples are used for materials with larger thermal diffusivity to keep the time easy to measure.