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
^{2 } - (C) γT
^{3 } - (D) γT
^{4}

**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
^{-1}K^{-1 } - (B) 0.19 kJmol
^{-1}K^{-1} - (C) 1.9 kJmol
^{-1}K^{-1 } - (D) 12 kJmol
^{-1}K^{-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/m ^{3}) is**

- (A) 3.65 x 10
^{-19}n^{2/3}eV - (B) 3.65 x 10
^{19}n^{2}eV - (C) 3.65 x 10
^{19}n^{1/3}eV - (D) 3.65 x 10
^{19 }n^{3/2}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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NOTE:- If you need anything else like e-books, video lectures, syllabus, etc. regarding your Preparation / Examination then do 📌 mention it in the Comment Section below. |

*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (B) | 06. | (C) | 11. | (C) |

02. | (C) | 07. | (D) | 12. | (D) |

03. | (A) | 08. | (C) | 13. | (B) |

04. | (A) | 09. | (D) | 14. | (A) |

05. | (C) | 10. | (A) | 15. | (C) |