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

• 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…

• 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, …

• 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…

• 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…

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 …

• 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 …