Specific Heat, Volumetric Heat Capacity, and Thermal Diffusivity
Dr. Patrick Hopkins
How much energy is needed to change the temperature of a material by one degree? How fast does energy transfer from one side of a slab of material to the other? How fast does energy move away from a surface? These questions all depend on a material’s temperature changing as a function of time, whether that means the time it takes to reach some ΔT or the time it takes for one side of a material to heat up when heat is applied to the other side.
These questions can be answered in part by considering a material’s thermal conductivity, but thermal conductivity alone is not enough. For any situation where temperature changes as a function of time, in other words any transient heat flow problem, the material’s specific heat also enters the picture to fully describe the transient temperature response.
Specific Heat and Volumetric Heat Capacity
The specific heat of a material is the amount of heat, in Joules, per unit mass (g) or mole (mol) required to raise its temperature by one degree Celsius or Kelvin.
In heat transfer analysis, it is usually more useful to work with volumetric heat capacity instead. Volumetric heat capacity is the specific heat per unit mass (J/g/K) multiplied by the mass density (g/cm³). This gives the volumetric heat capacity, C, in J/m³/K: the amount of heat per unit volume required to raise the temperature by one degree.
C enters the heat transfer picture in two places: the time it takes for heat to flow across the thickness of a material, and the ability of a material’s surface or interface to exchange heat with another material or its surroundings.
Thermal Diffusivity: Conducting Heat vs. Storing It
When considering the rate of heat transfer inside a material, the relevant property is thermal diffusivity, D (also written as α), defined as the ratio of thermal conductivity to volumetric heat capacity:
D = k / C (m²/s)
Thermal diffusivity describes the competition between a material’s ability to conduct heat (k) and its ability to store that heat (C). A high thermal diffusivity value does not necessarily mean heat is better dissipated. It means heat is dissipated more effectively than it is stored.
Because of this, thermal diffusivity is not a direct measure of a material’s ability to dissipate heat. Comparing materials on that basis requires thermal conductivity or thermal resistance. To get there from a diffusivity value or measurement, that value must be multiplied by the material’s heat capacity to recover k. This means thermal conductivity measurements and thermal diffusivity measurements answer technically different questions, even though both are often used to describe how a material handles heat.
Diffusion Time and Reaching Steady State
Thermal diffusivity matters most during temperature transients. It can be used to estimate how long heat takes to travel across a distance, or how long a material takes to reach steady-state conditions.
The time it takes for heat to travel across a material of thickness d can be approximated by the diffusion time:
t_diffusion = d² / D
This diffusion time can then be used to estimate how long a material system takes to reach steady state. When the timescale of heating is much longer than the diffusion time, temperature gradients in the material will progress toward steady state. The ratio of heating time to diffusion time indicates how close a material is to steady-state conditions.
This ratio is captured by a non-dimensional number, the Fourier number (Fo):
Fo = t / t_diffusion = Dt / d²
Steady-state conditions are reached when Fo ≫ 1. Under this condition, temperature gradients are no longer changing in time, and temperature changes across the material can be predicted directly from thermal conductivity and thermal resistance.
Why This Distinction Matters
Thermal conductivity and thermal diffusivity describe two different things: one describes a material’s ability to conduct heat, the other describes how quickly a temperature change propagates through it once heat capacity is factored in. A transient measurement produces D, which only becomes a usable thermal conductivity value once the material’s heat capacity is known or assumed. A steady-state measurement produces thermal conductivity directly, without that extra step.
Neither approach is inherently better. Which one is appropriate depends on the question being asked. But knowing which property a measurement is actually reporting, k or D, is essential before using that value in any downstream calculation, comparison, or design decision.