Thermal properties of materials

Red-hot quartz glass (fused silica) rarely cracks when dropped into water, whereas soda-lime glass cracks easily. What is the main reason for the high thermal shock resistance of quartz glass?

  1. AIts linear expansion coefficient is very small, about 0.5×10⁻⁶ K⁻¹, so the thermal stress from a temperature difference is small
  2. BIts thermal conductivity is as high as a metal's, so the surface–interior temperature difference vanishes quickly
  3. CIts fracture toughness is as high as a metal's, so even if thermal stress starts surface cracks they hardly grow
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Answer: A. Its linear expansion coefficient is very small, about 0.5×10⁻⁶ K⁻¹, so the thermal stress from a temperature difference is small

On quenching, only the surface tries to contract first and is held back by the interior, creating a tensile thermal stress σ ≈ EαΔT/(1 − ν) at the surface. The linear expansion coefficient of quartz glass is about 0.5×10⁻⁶ K⁻¹, only about one twentieth of the roughly 9×10⁻⁶ K⁻¹ of soda-lime glass, so the thermal stress is far smaller for the same temperature difference and it does not crack. The thermal conductivity of quartz glass is low, about 1.4 W/(m·K), and its fracture toughness of about 0.8 MPa·√m is on par with soda-lime glass, both far below metals. Thermal conductivity acts through how the temperature difference between surface and interior develops; under mild heat transfer, materials with higher thermal conductivity are more resistant to thermal shock.

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More Thermal properties of materials questions

  1. According to the Dulong–Petit law, the molar heat capacity of many solid elements near room temperature is about 3R (R is the gas constant, 8.31 J/(mol·K)). Estimating the specific heat per unit mass of aluminum (molar mass 26.98 g/mol) with this law, which value is closest?
  2. At temperatures well below the Debye temperature, how does the heat capacity of an insulating crystal (the lattice heat capacity) change with temperature?
  3. Diamond is an electrical insulator, yet its thermal conductivity at room temperature is about 2000 W/(m·K), higher than that of copper (about 400 W/(m·K)). What is the main reason?
  4. Using the Wiedemann–Franz law κ = LσT (Lorenz number L = 2.44×10⁻⁸ W·Ω/K²), which value is closest to the estimated thermal conductivity of copper with an electrical conductivity σ = 5.9×10⁷ S/m at 300 K?
  5. The thermal conductivity of pure copper at room temperature is about 400 W/(m·K), but in brass with about 30% zinc in solid solution it drops to about 120 W/(m·K). What is the main reason?