Thermal properties of materials
Learn the Dulong–Petit law and the Debye T³ law for heat capacity, the heat carriers in metals and insulators, the Wiedemann–Franz law, thermal diffusivity and its measurement, the origin of thermal expansion, Invar and materials that resist thermal shock through three-choice questions.
Thermal properties of materials: key points
Many thermal properties of solids can be explained by phonons, the quantized vibrations of atoms. The molar heat capacity of many elements near room temperature is about 3R, but at low temperatures vibrations become hard to excite, and the heat capacity of insulators shrinks in proportion to T³. Heat is carried mainly by conduction electrons in metals and by phonons in insulators, and the thermal conductivity of metals is linked to the electrical conductivity by the Wiedemann–Franz law.
While thermal conductivity expresses how easily heat flows in a steady state, thermal diffusivity α = κ/(ρc) expresses how quickly a change in temperature spreads, and it can be measured by the laser flash method. Thermal expansion arises from the asymmetry of the interatomic potential and is smaller in more strongly bonded materials. Against thermal shock, the cracking caused by sudden temperature changes, materials with smaller linear expansion coefficients are more resistant.
All Thermal properties of materials questions (15)
- 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?
- At temperatures well below the Debye temperature, how does the heat capacity of an insulating crystal (the lattice heat capacity) change with temperature?
- 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?
- 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?
- 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?
- The lattice thermal conductivity of an insulating single crystal decreases roughly in proportion to 1/T as temperature rises, at temperatures comparable to or above the Debye temperature. What is the main reason?
- For silicon (density 2330 kg/m³, specific heat 700 J/(kg·K)), take the room-temperature thermal conductivity as 150 W/(m·K) and the average phonon speed as 6000 m/s. Estimating the phonon mean free path l from κ = (1/3)Cvl, which has the same form as in the kinetic theory of gases (C is the heat capacity per unit volume), which value is closest?
- Which value is closest to the thermal diffusivity α = κ/(ρc) of aluminum (thermal conductivity 237 W/(m·K), density 2700 kg/m³, specific heat 900 J/(kg·K))?
- A metal plate and a wooden board are left long enough at the same room temperature (about 20℃). When touched by hand, the metal feels colder. What is the main reason?
- In the laser flash method, a pulse of light was applied to the front of a disk of thickness L = 2.0 mm, and the time for the temperature rise of the back face to reach half its maximum was t½ = 0.050 s. Which value is closest to the thermal diffusivity found with Parker's equation α = 0.1388L²/t½, which neglects heat loss?
- What is the main cause of solids expanding when heated (thermal expansion)?
- Which ordering of linear thermal expansion coefficients near room temperature, from largest to smallest, is correct?
- Which statement correctly explains why the linear thermal expansion coefficient of Fe-36%Ni alloy (Invar) is very small near room temperature, about 1×10⁻⁶ K⁻¹?
- According to the Grüneisen relation, the volume expansion coefficient of a solid is roughly proportional to its constant-volume heat capacity. Which statement correctly describes the linear expansion coefficient of an insulator at low temperatures near absolute zero?
- 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?