Question

1. By using the free electron theory of metals, explain thermal conduction in metals and how the conduction electrons contribute to heat capacity. (25 marks) 2. Sodium (Na) has a density of 0.97 g cm$^{-3}$. Calculate the Fermi energy for the electrons in the metal in electron-volt (eV) by assuming that each Na atom donates one electron to the electron gas. (20 marks) 3. A system consists of N distinguishable particles and n phase space cells. The energy of the particles is non-degenerate where, $\epsilon_1 = \epsilon_2 = \epsilon_3 = \dots = \epsilon_n = \epsilon$ Determine the internal energy, U and entropy, S. (25 marks) 4. Based on the Kinetic Theory of Gases, determine the Sackur-Tetrode equation for the entropy of a monatomic ideal gas and elucidate the significance of the Sackur-Tetrode equation. (35 marks) 5. Elucidate what is likely to happen to the mean velocity of the gas if the Boltzmann constant is 1.38 x 10$^{-2}$ J/K. (10 marks) 6. A scientist wants to create a micro-box using a novel material to contain the particles of a newly discovered gas. However, he has only 64 µm$^2$ of this novel material (i.e. the total surface area is only 64 µm$^2$). Determine the dimensions of the box that will give the largest volume that he can get from this material. (35 marks)

          1. By using the free electron theory of metals, explain thermal conduction
in metals and how the conduction electrons contribute to heat capacity.
(25 marks)
2. Sodium (Na) has a density of 0.97 g cm$^{-3}$. Calculate the Fermi energy
for the electrons in the metal in electron-volt (eV) by assuming that each
Na atom donates one electron to the electron gas. (20 marks)
3. A system consists of N distinguishable particles and n phase space cells.
The energy of the particles is non-degenerate where,
$\epsilon_1 = \epsilon_2 = \epsilon_3 = \dots = \epsilon_n = \epsilon$
Determine the internal energy, U and entropy, S. (25 marks)
4. Based on the Kinetic Theory of Gases, determine the Sackur-Tetrode
equation for the entropy of a monatomic ideal gas and elucidate the
significance of the Sackur-Tetrode equation. (35 marks)
5. Elucidate what is likely to happen to the mean velocity of the gas if the
Boltzmann constant is 1.38 x 10$^{-2}$ J/K. (10 marks)
6. A scientist wants to create a micro-box using a novel material to contain
the particles of a newly discovered gas. However, he has only 64 µm$^2$ of
this novel material (i.e. the total surface area is only 64 µm$^2$). Determine
the dimensions of the box that will give the largest volume that he can
get from this material. (35 marks)

1. By using the free electron theory of metals, explain thermal conduction
in metals and how the conduction electrons contribute to heat capacity.
(25 marks)
2. Sodium (Na) has a density of 0.97 g cm^-3. Calculate the Fermi energy
for the electrons in the metal in electron-volt (eV) by assuming that each
Na atom donates one electron to the electron gas. (20 marks)
3. A system consists of N distinguishable particles and n phase space cells.
The energy of the particles is non-degenerate where,
ϵ1 = ϵ2 = ϵ3 = … = = ϵ
Determine the internal energy, U and entropy, S. (25 marks)
4. Based on the Kinetic Theory of Gases, determine the Sackur-Tetrode
equation for the entropy of a monatomic ideal gas and elucidate the
significance of the Sackur-Tetrode equation. (35 marks)
5. Elucidate what is likely to happen to the mean velocity of the gas if the
Boltzmann constant is 1.38 x 10^-2 J/K. (10 marks)
6. A scientist wants to create a micro-box using a novel material to contain
the particles of a newly discovered gas. However, he has only 64 µm^2 of
this novel material (i.e. the total surface area is only 64 µm^2). Determine
the dimensions of the box that will give the largest volume that he can
get from this material. (35 marks)

Added by Nathaniel P.

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