# Thermal and Statistical Physics [Optionals IAS Mains Physics]: Questions 1 - 7 of 21

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## Question 1

Appeared in Year: *2011 (IFS)*

### Write in Short

Short Answer▾Write down the expression for the Bose – Einstein distribution function and explain the meaning of the symbols used. (Paper-I) (Section - B)

## Question 2

Appeared in Year: *2012 (IFS)*

### Describe in Detail

Essay▾What are Einstein՚s A and B coefficients? Establish a relation between the. (Section A)

### Explanation

- There are three Einstein coefficients associated with any pair of energy levels. Of these three only one is independent. The other two dependent upon the coefficient taken to be independent, plus the frequency of the transition and the statistical weight of the two associated terms.

- “Coefficient of spontaneous em…

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## Question 3

Appeared in Year: *2011 (IFS)*

### Write in Short

Short Answer▾Write down the expression for the Bose – Einstein distribution function and explain the meaning of the symbols used. (Section - B)

## Question 4

Appeared in Year: *2002*

### Describe in Detail

Essay▾Describe Carnot cycle and show that efficiency is given by

Where the symbols have their usual meaning. (20 Marks)

### Explanation

- The Carnot cycle is accomplished in
__four steps__and the changes of the temperature and the entropy of the auxiliary system are plotted for each of these steps in figure 1. - The Carnot cycle is a thermodynamic cycle that gives the best efficiency possible. Given an amount of energy in form of heat, the Carnot cycle transforms heat put in to produce use…

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## Question 5

Appeared in Year: *2000*

### Describe in Detail

Essay▾What is the most probable distribution of speeds in a large number of molecules of a gas and indicate the steps for its derivation. (20 Marks)

### Explanation

- For the velocity distribution of molecules in a gas, we must choose a given direction and see how many molecules have particular components of velocity along it. We define the velocity distribution as the fraction of molecules with velocities, say the x direction b/w is . The velocity distribution function is proportional to the Boltzmann factor, …

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## Question 6

### Write in Short

Short Answer▾Prove that the value of is nearly Hence determine the Fermi temperature of a metal whose Fermi energy is .

## Question 7

Appeared in Year: *2011*

### Describe in Detail

Essay▾What led Vander Waals to modify the ideal gas equation? Using the concepts of critical temperature , pressure and volume , show that the critical constant for a real gas is (20 marks)

### Explanation

- The ideal gas equation is given by
Where is the number of moles or equivalently by

- Where is the molar volume (i.e. the volume occupied by 1 mole) .
- This equation of state leads to isotherms. However, real gas don՚t behave quite like this, particularly when the pressure is high and the volume is small. If you get a real gas cold enough it will lique…

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