The quantity α = κ/(ρc), the thermal conductivity divided by the heat capacity per unit volume. It expresses how quickly a change in temperature spreads through a material and has units of m²/s.
Japanese name: 熱拡散率
Thermal diffusivity appears in 2 practice questions across 1 topic, including Thermal properties of materials.
Thermal conductivity κ expresses how much heat flows under a temperature gradient, that is, how easily heat flows in a steady state. Thermal diffusivity α = κ/(ρc), by contrast, is the ratio of conducting heat easily to being hard to warm up (the heat capacity per unit volume ρc), and it expresses how quickly a change in temperature spreads. The transient heat conduction equation is ∂T/∂t = α∇²T, so the change of temperature with time is set by α, not by κ alone. A rough time for the temperature to change through a plate of thickness L is L²/α, which can be used to estimate heating and cooling times.
Near room temperature, the thermal diffusivity is about 1.1×10⁻⁴ m²/s for copper, about 1×10⁻⁴ m²/s for aluminum, about 1×10⁻⁵ m²/s for carbon steel, about 4×10⁻⁶ m²/s for stainless steel, about 5×10⁻⁷ m²/s for glass, and about 1×10⁻⁷ m²/s for wood and polymers. Diamond exceeds 10⁻³ m²/s. The heat capacity per unit volume differs only by a few times among solids, so thermal diffusivities rank broadly in the same order as thermal conductivities. Gases have low thermal conductivity but also low density, so their thermal diffusivity is larger than that of solid polymers.
Thermal diffusivity is commonly measured by the laser flash method. A pulse of light is applied to the front of a disk sample, and α is found as α = 0.1388L²/t½ from the time t½ for the temperature rise of the back face to reach half its maximum. Because the sample can be small and measurements can be made up to high temperatures, the thermal conductivity is often obtained by multiplying the measured α by the density and specific heat, as κ = αρc. Thermal diffusivity matters in heat problems that involve time, such as the spread of temperature in welding and heat treatment, the temperature difference between surface and interior on quenching, and estimates of transient heating in semiconductor devices.
Answer: A. About 9.8×10⁻⁵ m²/s
α = 237/(2700×900) = 237/(2.43×10⁶) ≈ 9.75×10⁻⁵ m²/s, about 9.8×10⁻⁵ m²/s. Thermal diffusivity expresses how quickly a change in temperature spreads through a material, and it appears in the transient heat conduction equation ∂T/∂t = α∇²T. A rough time for the temperature to change through a material of thickness L is L²/α, which for aluminum 10 mm thick is about 1 s. About 9.8×10⁻² m²/s uses the specific heat as 0.9 in J/(g·K), shifting the result by a factor of 1000. About 0.26 m²/s forgets to multiply by the density, giving κ/c, which does not even have units of m²/s.
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.
Among solids this is often so, but materials with a large heat capacity per unit volume ρc have a small thermal diffusivity for their thermal conductivity. Choose the quantity according to whether the aim is to compare steady heat flow or the speed of temperature change.
Thermal diffusivity κ/(ρc) expresses how quickly a change in temperature spreads through a material, while thermal effusivity √(κρc) expresses how much heat a surface absorbs when heat is applied to it. The coldness felt on touching and the momentary temperature rise of a surface depend on the effusivity.
Because the transient heat conduction equation ∂T/∂t = α∇²T has the same form as Fick's second law for the diffusion of matter, ∂C/∂t = D∇²C. The spread of temperature can be treated like the diffusion of atoms, with a characteristic distance of √(αt).
Thermal diffusivity expresses how quickly a change in temperature spreads through a material, and it appears in the transient heat conduction equation ∂T/∂t = α∇²T.
Which value is closest to the thermal diffusivity α = κ/(ρc…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.
In the laser flash method, a pulse of light was applied to …Coefficient of linear thermal expansion Debye temperature Dulong–Petit law Invar Phonon Umklapp process Wiedemann–Franz law