PHY3707 Assignment 4 Solutions 2026
UNISA
DUE: 10 JULY 2026
, Question 1
Given
Thermal conductivity:
𝐾 = 2.7 × 104 W m−1 K−1
Diameter of sapphire:
𝑑 = 3 mm = 3 × 10−3 m
Speed of sound:
𝑣 = 104 m s−1
Temperature:
𝑇 = 30 K
According to kinetic theory, the thermal conductivity of a solid is
1
𝐾 = 𝐶𝑣ℓ
3
where
• 𝐶= heat capacity per unit volume
• 𝑣= speed of sound
• ℓ= phonon mean free path.
At the thermal conductivity maximum, the phonon mean free path becomes
approximately equal to the sample diameter.
Hence,
ℓ=𝑑
Therefore,
ℓ = 3 × 10−3 m
UNISA
DUE: 10 JULY 2026
, Question 1
Given
Thermal conductivity:
𝐾 = 2.7 × 104 W m−1 K−1
Diameter of sapphire:
𝑑 = 3 mm = 3 × 10−3 m
Speed of sound:
𝑣 = 104 m s−1
Temperature:
𝑇 = 30 K
According to kinetic theory, the thermal conductivity of a solid is
1
𝐾 = 𝐶𝑣ℓ
3
where
• 𝐶= heat capacity per unit volume
• 𝑣= speed of sound
• ℓ= phonon mean free path.
At the thermal conductivity maximum, the phonon mean free path becomes
approximately equal to the sample diameter.
Hence,
ℓ=𝑑
Therefore,
ℓ = 3 × 10−3 m
