PHY3707
ASSIGNMENT 4
Solid State Physics
FULL SOLUTIONS
COMPLETE SOLUTIONS
MEMORANDUM
UNISA 2026
Page 1 of 5
, SOLUTION:
(1) The thermal conductivity is
1
𝐾= 𝐶𝑣𝜆
3
At the maximum thermal conductivity, the phonon mean free path is approximately equal to the
diameter of the sample.
𝜆 = 3 mm = 3 × 10−3 m
Given:
• 𝐾 = 2.7 × 104 W m−1 K−1
• 𝑣 = 104 m s−1
• 𝜆 = 3 × 10−3 m
Hence,
3𝐾
𝐶=
𝑣𝜆
3(2.7 × 104 )
𝐶=
(104 )(3 × 10−3 )
8.1 × 104
𝐶=
30
𝐶 = 2.7 × 103 J m−3 K−1
Page 2 of 5
ASSIGNMENT 4
Solid State Physics
FULL SOLUTIONS
COMPLETE SOLUTIONS
MEMORANDUM
UNISA 2026
Page 1 of 5
, SOLUTION:
(1) The thermal conductivity is
1
𝐾= 𝐶𝑣𝜆
3
At the maximum thermal conductivity, the phonon mean free path is approximately equal to the
diameter of the sample.
𝜆 = 3 mm = 3 × 10−3 m
Given:
• 𝐾 = 2.7 × 104 W m−1 K−1
• 𝑣 = 104 m s−1
• 𝜆 = 3 × 10−3 m
Hence,
3𝐾
𝐶=
𝑣𝜆
3(2.7 × 104 )
𝐶=
(104 )(3 × 10−3 )
8.1 × 104
𝐶=
30
𝐶 = 2.7 × 103 J m−3 K−1
Page 2 of 5
