Which of the following substance has highest thermal diffusivity at room temperature?
Silver
Understanding Thermal Diffusivity
Thermal diffusivity is a material property that describes how quickly heat diffuses through a material. It is defined by the formula:
$$\alpha = \frac{k}{\rho c_p}$$
Where:
- $\alpha$ (alpha) is the thermal diffusivity ($m^2/s$)
- $k$ is the thermal conductivity ($W/(m \cdot K)$), which measures how well a material conducts heat.
- $\rho$ (rho) is the density ($kg/m^3$), which is mass per unit volume.
- $c_p$ is the specific heat capacity ($J/(kg \cdot K)$), which is the amount of heat required to raise the temperature of a unit mass of the material by one degree.
A high thermal diffusivity means that heat moves through the material quickly. This happens when a material has high thermal conductivity, low density, and low specific heat capacity.
Analyzing Thermal Diffusivity of Given Substances
Let's consider the properties of the given substances at room temperature (around 25°C):
- Silver: Silver is a metal well-known for its extremely high thermal conductivity. It is dense, but its very high $k$ dominates the formula, resulting in high thermal diffusivity.
- Mercury: Mercury is a liquid metal. Its thermal conductivity is higher than most liquids and non-metals, but significantly lower than solid metals like silver. It is very dense.
- Water: Water is a liquid. It has relatively low thermal conductivity compared to metals. Its density is moderate, and its specific heat capacity is relatively high (especially compared to metals). These factors contribute to a low thermal diffusivity.
- Glass: Glass is an amorphous solid, typically a thermal insulator, meaning it has very low thermal conductivity. Its density is moderate, and its specific heat capacity is also moderate. The low thermal conductivity is the dominant factor, leading to very low thermal diffusivity.
To compare more precisely, let's look at approximate thermal diffusivity values at room temperature:
| Substance | Approximate Thermal Diffusivity ($\times 10^{-6} \text{ m}^2/s$) |
|---|---|
| Silver | 165 |
| Mercury | 11 |
| Water | 0.14 |
| Typical Glass | 0.5 - 1.0 |
Comparing these approximate values, Silver clearly has the highest thermal diffusivity among the options provided. Heat diffuses through silver much faster than through mercury, water, or glass.
Conclusion on Highest Thermal Diffusivity
Based on the typical thermal properties and calculated thermal diffusivity values, Silver exhibits the highest thermal diffusivity at room temperature compared to Glass, Water, and Mercury. Its exceptionally high thermal conductivity is the primary reason for this.
Revision Table: Thermal Properties and Diffusivity
| Property | Thermal Diffusivity ($\alpha$) | Thermal Conductivity ($k$) | Density ($\rho$) | Specific Heat Capacity ($c_p$) |
|---|---|---|---|---|
| Definition | Rate of heat diffusion | Ability to conduct heat | Mass per volume | Heat needed to raise temperature |
| Relationship | $\alpha = k / (\rho c_p)$ | Higher $k$ leads to higher $\alpha$ (if other factors are similar) | Higher $\rho$ leads to lower $\alpha$ (if other factors are similar) | Higher $c_p$ leads to lower $\alpha$ (if other factors are similar) |
| High $\alpha$ implies | Heat spreads quickly | Good conductor | Lower mass for same volume | Needs less heat to change temperature |
Additional Information on Thermal Diffusion
Thermal diffusivity is a key property in understanding transient heat transfer problems, such as how quickly a material heats up or cools down when its temperature changes. Materials with high thermal diffusivity respond quickly to temperature changes, while those with low thermal diffusivity respond slowly.
Factors that can affect thermal diffusivity include:
- Temperature: Thermal conductivity, density, and specific heat capacity can all vary with temperature, thus changing thermal diffusivity.
- Phase: Solids generally have higher thermal conductivity than liquids, which in turn have higher conductivity than gases (except for certain specialized materials or conditions).
- Composition and Structure: The purity, crystalline structure, and presence of impurities or defects in a material can significantly impact its thermal properties and thus its thermal diffusivity.
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