Molecular Physics | Thermodynamics Answers

What do you understand by mean free path of gas molecules? Derive an expression for the law of distribution of free paths.

What do you understand by first order phase transition? Derive Clausius-Clapeyron equation to explain variation of temperature with pressure in such a transition. Can we use this equation for transitions of order higher than one? Explain.

Show that the difference of heat capacities for a substance is given by the relation:

Cp-Cv= -T(¶V/¶T)^2 p x(¶p/¶V)T?

A certain mass of a gas at 273 K temperature and one atmospheric pressure is expanded
to 3 times its original volume under adiabatic conditions. Calculate the resulting
temperature and pressure. (Take the value of γ= 1.4)

Explain the working of a constant volume gas thermometer with the help of a neat and
labelled diagram

A block of copper whose expansivity, β, is 48.0 x 10^-6 k^-1 and isothermal elasticity, ET ,
is 1.30 x 10^11 Nm^-2 is at atmospheric pressure and a temperature of 0°C. Its temperature is
raised to 10°C. Calculate the final pressure when volume is kept constant. Express your
answer in units of atmospheric pressure (atm).

Derive an equation of state pVγ = constant for an adiabatic process and show that an
adiabat is steeper than an isotherm.

i) Write an expression for Planck’s law for energy density of photons in a cavity and
calculate total energy density, u. ii) Consider sun as a black body whose interior consists
of photons gas at T=3x 10^6 K Calculate the energy density of the solar radiations.
Take σ=7.56x 10^-16 Jm^-3 k^-4

What is Bose-Einstein condensation? Show that Bose-Einstein condensation temperature is given by Tc=h^2/2πmkB x [N / 2.612V]^2/3

What is meant by root mean square speed of a gas? Express it in terms of temperature and molecular weight of gas. Calculate Vrms for He atoms at 300 K. (Take mHe= 6.67x10^-27kg.)