Molecular Physics | Thermodynamics Answers

How many lattice vibration modes are there in each branch of the Brillouin zone, if a solid contains (a) 100 and (b) 1000000 primitive cells?

A mole of gas has a volume of 10 m3 and a temperature of 300 K. At condition when pressure and temperature are constant, work has been done to compress the gas so that the volume is 5 m3. calculate the temperature and pressure of the gas at the end of the process.

Obtain an expression for the entropy of an assembly of photons. Using this expression, show that the equation for the adiabate of a photon gas is given by pV4/3= constant.

Derive an expression for the partition function of an ideal monoatomic gas. Hence obtain an expression for its entropy.

Write the van der Waal's equation of state for a real gas. Obtain the expressions for critical volume, critical pressure and critical temperature for this gas. Calculate the critical
temperature of He if the critical pressure is
2.5 atm and critical density is 0.069 g cm -3.

What is Brownian motion ? Give at least three examples of such a motion. Using Einstein's theory, obtain an expression for the mean square displacement of a Brownian particle.

For a heat engine working between tem peratures T1 and T2, show all the steps of Carrot cycle on a T-S diagram. Hence calculate the efficiency of the engine.

Derive Clausius — Clapeyron equation. On the basis of this equation, explain why mountaineers find it difficult to cook their food at high altitudes.

State Kelvin — Planck and Clausius statements of the second law of thermodynamics. Show by deduction that both the statements are equivalent.

With the help of a neat and labelled diagram, explain the working of a constant volume gas therm ometer.