# Question On Thermal Properties with Answers

Practice Question On Thermal Properties with Answers.

## Question On Thermal Properties with Answers

Q1. In two dimensions two metals A and B, have the number density of free electrons in the ratio n:m = 1:2. The ratio of their Fermi energies is

• (A) 2:3
• (B) 1:2
• (C) 1:8
• (D) 1:4

Q2. Fermi energy of a certain metal M is 5 eV. A second metal M’ has an electron density which is 6% higher than that of M. Assuming that the free electron theory is valid for both the metals, the Fermi energy of M’ is closest to

• (A) 5.6 eV
• (B) 4.8 eV
• (C) 5.2 eV
• (D) 4.4 eV

Q3. The Dulong-Petit law fails near room temperature (300 K) for many light clements (such as boron and beryllium) because their Debye temperature is

• (A) >> 300 K
• (B) ~ 300 K
• (C) << 300 K
• (D) 0 K

Q4. What is the contribution of the condition electrons in the molar entropy of a metal with electronic coefficient of specific heat ?

• (A) γT
• (B) γT
• (C) γT
• (D) γT4

Q5. According to Dulong-Petit’s law, the specific heat of a solid

• (A) is proportional to the temperature
• (B) depends on square of temperature
• (C) does not depend on temperature
• (D) is inversely proportional to temperature

Q6. The Debye temperature of a metal is 450 K. Its Debye frequency in Hz is of the order of

• (A) 1011
• (B) 1016
• (C) 1013
• (D) 1026

Q7. Debye temperatures of copper and gold are 340K and 170K, respectively. At room temperature, if the specific heat for copper is 1.5 kJmol^-1K^-1, the specific heat for gold is about:

• (A) 1.2 kJmol-1K-1
• (B) 0.19 kJmol-1K-1
• (C) 1.9 kJmol-1K-1
• (D) 12 kJmol-1K-1

Q8. The Fermi energy ε in metals depends on the number density n of mobile electrons, which may be thought of as a free Fermi gas. If n of one metal is larger by a factor of 1000 compared to another, then in comparison, its Fermi energy is

• (A) 1000 times larger
• (B) smaller by a factor of 1/100
• (C) 100 times larger
• (D) 10 times larger

Q9. Flow of electron is affected by which of the following:

• (A) thermal vibration
• (B) only impurity atom
• (C) only crystal defects
• (D) only all of (a), (b) & (c)

Q10. Fermi energy level for intrinsic semiconductors lies:

• (A) at the middle of the band gap
• (B) close to the conduction band
• (C) close to valence band
• inside valence band

Q11. The Fermi energy of silver is 5.51 electron volt. The average energy of the free electrons in silver at 0 °K is given by

• (A) 0.864 eV
• (B) 0.864 eV
• (C) 4.205 eV
• (D) 3.306 eV

Q12. Which of the following statements concerning the electrical conductivities at room temperature of apure copper sample and a pure silicon sample is NOT true ?

• (A) If the temperature of the copper sample is increased, its conductivity will decrease
• (B) If the temperature of the silicon sample is increased, its conductivity will increase
• (C) The addition of an impurity in the copper sample always decreases its conductivity
• (D) The addition of an impurity in the silicon always decreases its conductivity

Q13. In the Kronig-Penney model, electrons are assumed to be moving in

• (A) one-dimensional square well potential
• (B) one-dimensional square well periodic potential
• (C) a periodic harmonic potential
• (D) three-dimensional coulomb potential

Q14. The general expression for the Fermi energy of a metal at 0°K (if n is the number of free electrons/m3) is

• (A) 3.65 x 10-19 n2/3 eV
• (B) 3.65 x 1019 n2 eV
• (C) 3.65 x 1019 n1/3 eV
• (D) 3.65 x 1019 n3/2 eV

Q15. Fermi level represents the energy level with probability of its occupation of

• (A) 0%
• (B) 25%
• (C) 50%
• (D) 100%

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