Thermal and Statistical Physics-Thermodynamics [IAS (Admin.) Mains Physics]: Questions 7 - 11 of 31

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Question 7

Appeared in Year: 2012

Describe in Detail Subjective▾

The Einstein theory of specific heat of solids gives the expression

Where with as the Einstein temperature.

(i) Mention Einstein՚s assumption in deriving it. Also obtain low-and high- temperature limiting expressions for it.

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Explanation

  • Classical theory of lattice heat capacity. A crystal consists of atoms which are arranged in a periodic manner and are behind together by strong binding forces. Each atom is free to vibrate about its equilibrium position and constitutes a three – dimensional harmonic oscillator. The effect of imparting thermal energy to a solid is to increase its i…

… (340 more equations) …

Question 8

Appeared in Year: 2016

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Explain the principle of (I) induced absorption (II) spontaneous emission and (II) stimulated emission. Show the ratio of Einstein՚s coefficients is given by .

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Explanation

  • An atomic system is characterized by discrete energy states, and usually the atoms occupy the lowest energy state, known as the ground state. An atom in a lower energy state may be excited to a higher energy state through a number of processes, one process being absorption of electromagnetic radiation of proper frequency. On the other hand, an atom…

… (619 more equations, 18 figures) …

Question 9

Appeared in Year: 2016

Describe in Detail Subjective▾

Write down the salient features of the Einstein՚s theory of lattice heat capacity. Further write down the expression for specific heat in Einstein՚s theory and explain it՚s high and low temperature limits.

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Explanation

  • The salient features of the Einstein՚s theory are listed below:
    1. A crystal consists of atoms which may be regarded as identical and independent harmonic oscillators.
    2. A solid consisting of atoms is equivalent to one dimensional harmonic oscillators.
    3. All the oscillators vibrate with the same natural frequency due to the id…

… (524 more equations) …

Question 10

Appeared in Year: 2010

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Distinguish between Einstein and Debye models of specific heats of solids. Obtain an expression for the specific heat of a solid on the basis of Debye model. Discuss the results for high and low temperature ranges.

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Explanation

The salient features of the Einstein theory are listed below:

  1. A crystal consists of atom which may be regarded identical and independent harmonic oscillations.
  2. A solid consisting of N atoms is equivalent to 3N one-dimensional harmonic oscillations.
  3. All the oscillations vibrate with same natural frequency due to the identical environment of each.
  4. The os…

… (2575 more equations) …

Question 11

Appeared in Year: 2018

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Derive an expression for lattice specific heat in Debye model. Find its low temperature limit (Debye ) (Paper -II)

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Explanation

If the inter atomic distance is small as compared to the wavelength of elastic waves, the crystal can be regarded as a continuum from the point of view of the wave. Based on this idea, Debye assumed that the continuum model is applicable to all possible vibrational modes of the crystal. Further the fact that the crystal consists of a finite no. (N)…

… (783 more equations, 39 figures) …