# How do the thermal conductivity and specific heat influence the amount of heat transferred between two objects

Through research on the topic I found that the one with the higher thermal effusivity would be able to transfer more heat. I was wondering what the effect of one material being in liquid state vs solid state would have on the transfer of heat if any at all?

• Thermal conductivity is how fast heat moves and specific heat is how much heat it can hold. 2 variables so 4 combinations or types of material. Transferring heat also involves the interface between the materials, so thermal compound is important and surface smoothness, for liquids (tending to be less dense) heat transfer is slower. These are some of the main general factors.... – PhysicsDave Jul 11 '19 at 17:50
• You have two objects at different temperatures, and you want to determine the heat transfer rate between them as a function of time, correct? – Chet Miller Jul 11 '19 at 19:45

Through research on the topic I found that the one with the higher thermal effusivity would be able to transfer more heat.

Not only would the object with higher effusivity be able to transfer more heat, but it is likely do so at a much higher heat transfer rate because of the dominance of a materials thermal conductivity in its effusivity.

Although I am not familiar with the term, Wikipedia defines the "thermal effusivity" of a material as the square root of the product of a materials thermal conductivity and volumetric heat capacity, or

$$e=(kρc)^{-1/2}$$

Where $$k$$ is the thermal conductivity, $$ρ$$ is the density, and $$c$$ is the specific heat capacity. The product $$ρc$$ is called the volumetric heat capacity. I am familiar with the term "thermal inertia" which Wiki defined the same way, although I have found it defined also without the square root.

The thermal inertia, or effusivity, can be considered as a measure of the ability of a material to exchange thermal energy with its surroundings, where the term "ability" refers not only to how much heat it is able to transfer, which is primarily due to its volumetric heat capacity, but also the rate at which it can transfer heat, which is primarily due to its thermal conductivity.

The reason for combining these properties is that materials with high thermal conductivities (e.g., metals) generally have low specific heats, whereas materials with low thermal conductivities (e.g. plastics) have high specific heats. On a per unit mass basis, plastics have a higher heat capacity than metals, i.e., have more thermal energy available. On the other hand, metals have much higher densities, $$ρ$$, than plastics. So when you consider the heat capacity as the volumetric heat capacity, the disparity between metals and plastic regarding how much thermal energy is available is much reduced.

In my work in studying the thermal burn potential of different objects, I needed to consider the same volume of plastic and metal to compare apples to apples. In looking at the range from the most thermally conductive metals such as aluminum and the least thermally conductive engineering plastics such as polystyrene, the difference in volumetric heat capacities between metals and plastics is in the range of about 1.5:1, whereas the difference in thermal conductivities between metals and plastics can be in the range of about 2000:1. So unless one considers a very small volume of metal (for example, the thermal burn potential (or lack of potential) of aluminum foil taken out of an oven), the thermal conductivity property of a material is the dominant factor in both the amount and rate at which heat is transferred.

I was wondering what the effect of one material being in liquid state vs solid state would have on the transfer of heat if any at all?

Generally the thermal conductivities of solids are higher than liquids of the same material. On the other hand, the specific heats of liquids are generally higher than solids. Given that the density of the same material in solid or liquid form is generally about the same, one would have to look at a specific material to determine the difference in effusivity (thermal inertia).

(p.s. I suspect, but haven't checked various materials, that since there are typically greater differences in the thermal conductivities of solids vs liquids than differences in specific heats, the effusivity of a material in solid form would be greater than liquid form. At least that's what I found comparing liquid water and ice)

Hope this helps.

One essential difference between a solid and a liquid is that the liquid is mobile, so it can transfer heat via convection in addition to thermal conductivity. How much of a difference that makes will depend on a number of factors, such as the viscosity of the liquid or initial speed at which the liquid is moving.

Another important factor is the contact area. If we assume perfect contact with no gaps, there will be no difference between solids and liquids, but in practice the surface finish of the solids will play a very important role in the heat transfer, as will the wettability of the solid by the liquid, and what the gaps will be filled with.