# Why about 1 kJ/kg/K for so many solids?

• lalbatros
In summary, solid components commonly found in the workplace have a specific heat of approximately 1 kJ/kg/K. This is due to mode-counting, similar to perfect gases, where the vibrational modes of each atom in the lattice contribute to the kinetic and potential energies. This also applies to "heavier" molecules, such as 3(CaO).SiO2 and 3(CaO)(MgO)2(SiO2), which have more flexibility and therefore a higher specific heat. This concept is further supported by the Law of Dulong and Petit, which states that most solids have a specific heat of 25 J/mol/K, as explained by Conway.
lalbatros
Most solid components I need to consider at work have a specific heat of about 1 kJ/kg/K.
Why is that so?
Any explanation as simple as for perfect gases?

Thanks

Yes, it's mode-counting, similar to perfect gasses. Counting the vibrational modes of each atom in the lattice it's 3/2 kT for the kinetic modes and another 3/2 kT for the potential energies.

Thanks conway.

One of the solids in my long list is 3(CaO).SiO2 and another is 3(CaO)(MgO)2(SiO2).
This would mean that "heavier" molecules are not very rigid, therefore making room for more modes and more specific heat per molecule. The end result around 1 kJ/kg/K depends also on the atoms involved.

This makes more sense when you express it as 25 J/mol/K. Most solids have that as their specific heat. This is called the Law of Dulong and Petit. It works for exactly the reason Conway said.

## 1. Why is 1 kJ/kg/K the standard unit for specific heat for many solids?

1 kJ/kg/K is the standard unit for specific heat because it is a measure of how much energy is required to raise the temperature of 1 kilogram of a substance by 1 Kelvin. It is used for many solids because it is a convenient unit that allows for easy comparison between different materials.

## 2. How is specific heat determined for solids?

Specific heat for solids is determined through experiments where the amount of energy required to raise the temperature of a known mass of the substance by a certain amount is measured. This value is then divided by the mass and the temperature change to obtain the specific heat.

## 3. Why does specific heat vary between different solids?

The specific heat of a solid can vary based on its composition, structure, and density. Different substances have different chemical and physical properties that affect how they absorb and retain heat. For example, metals generally have a lower specific heat than non-metals due to their higher density and molecular structure.

## 4. How does specific heat affect the thermal properties of a solid?

The specific heat of a solid is directly related to its thermal properties. Materials with a higher specific heat can absorb and retain more heat, making them better insulators. On the other hand, materials with a lower specific heat will heat up and cool down more quickly, making them better conductors of heat.

## 5. Can specific heat change with temperature for solids?

Yes, the specific heat of a solid can change with temperature. This is because the molecular structure and physical properties of a substance can change as it is heated or cooled. In some cases, the specific heat may increase with temperature, while in others it may decrease. This is an important consideration when studying the thermal properties of materials.

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