Lecture Notes on Specific Heat

Overview of Specific Heat

• Definition: Specific heat (also known as heat capacity) refers to the amount of energy required to raise the temperature of a material.

• Unit of Measurement:

  • Specific heat capacity Cp​):

  • SI Unit: [J/kg⋅K]

  • In relation to density:

  • [J/m3⋅K][J/m3⋅K] (where ρρ is density)

Energy Required to Raise Temperature

• Energy (U) required to raise the temperature of a mass (m) by a temperature change (ΔT) is calculated using the formula: U=mcp​ΔT

• Examples of energy required for different materials to increase temperature by 20°C (ΔT=20 K):

  • Steel:

  • Calculation:

    • \U=1 kg×470 J/kg⋅K×20 K=9400 J

  • Concrete:

  • Calculation:

    • U=1 kg×925 J/kg⋅K×20 K=18500 J

  • Pine:

  • Calculation:

    • U=1 kg×1680 J/kg⋅K×20 K=33600 J

Energy for 1 m³ of Materials

• To calculate energy required for 1 m³ of the same materials:

  • Formula: U=ρcp​ΔT

  • Results:

  • Steel:

    • Calculation:

    • U=7800 kg/m3×470 J/kg⋅K×20 K=73.3 MJ/m3

  • Concrete:

    • Calculation:

    • U=2400 kg/m3×925 J/kg⋅K×20 K=44.4 MJ/m3

  • Pine:

    • Calculation:

    • U=520 kg/m3×1680 J/kg⋅K×20 K=33.6 MJ/m3

Relationship Between Material Density and Specific Heat

• Notable Observation:

  • The increase in energy required reflects the increasing density of materials.

  • Few atoms per kg in metals compared to polymers and other materials.

Categories of Materials and Their Specific Heat Capacities

• Overview of Specific Heat Capacities (J/kg⋅∘CJ/kg⋅∘C):

  • Metals and Alloys:

  • Specific heat capacity around 200 J/kg⋅∘C200 J/kg⋅∘C

  • Ceramics and Glasses:

  • Specific heat capacity around 500 J/kg⋅∘C500 J/kg⋅∘C

  • Polymers and Elastomers:

  • Specific heat capacity around 1000 J/kg⋅∘C1000 J/kg⋅∘C

  • Hybrids (Composites, Foams, Natural Materials):

  • Specific heat capacity around 2000 J/kg⋅∘C2000 J/kg⋅∘C

Thermal Energy in Atomic Bonds

• Conceptual Understanding:

  • The thermal energy stored in atomic bonds can be expressed as

  • Thermal Energy=3kBTThermal Energy=3kB​T

  • Where:

    • kB​ = Boltzmann constant

    • T = Temperature

• Energy Per Unit Volume:

  • For a volume occupied by an atom (Ω):

  • Energy density=Ω3kB​T​

Calculation of Specific Heat Capacity per Unit Volume

• Determination of specific heat per volume:

  • Assuming atomic volumes do not vary significantly, we can find specific heat capacity as:

  • CV≈Ω3kB​

• Typical range for specific heat capacity per unit volume can reach approximately

  • CV​ is near 2×106 J/m3⋅K