# Thermal and Statistical Physics-Thermodynamics [Optionals IAS Mains Physics]: Questions 1 - 6 of 16

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## Question 1

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 2

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 3

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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## Question 4

Appeared in Year: *2009*

### Describe in Detail

Essay▾Derive an expression for the specific heat of a solid on the basis of Debye՚s model. Show that it converges to Dulong and Petit՚s law at high temperature. (25 Marks)

### Explanation

- The Debye Approximation:- If the interatomic 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 co…

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## Question 5

Appeared in Year: *2014*

### Describe in Detail

Essay▾The velocity of sound in gold and copper is and respectively of the Debye temperature of copper is , then determine the Debye temperature of gold. Taking the densities of gold and copper as and respectively.

### Explanation

The Debye temperature is defined as

Where is the Debye frequency and is given by the relation

Here is the no. of atoms present in volume of the crystal and and represent the longitudinal and transverse velocities of sound waves in the crystal respectively.

Replacing and by the mean velocity of sound

We get

Considering one mole of atoms,

We can …

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## Question 6

Appeared in Year: *2012*

### Describe in Detail

Essay▾The Einstein theory of specific heat of solids gives the expression

Where with as the Einstein temperature.

(ii) Give schematic plot of V/S and common on the validity of expressions in (i) in comparison with experiments.

### Explanation

- A theoretical plot of V/S using given equation for diamond using is shown below. Some experimental points are also shown for comparison. It is seen that the Einstein curve fits the experimental points well over a wide range of temperature except for very low (liquid helium) temperatures where it falls more rapidly than the observed decrease in …

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