Define degree of freedom of a molecule. Write its general formula. Calculate the degree of freedom for a single atom.
In thermodynamics and statistical mechanics, the degree of freedom of a molecule refers to the number of independent ways it can move or store energy. For a classical monatomic gas molecule, the three translational degrees of freedom represent its ability to move in three spatial ____ _____ ____ ____ ___.
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Calculate the temperature at which the root mean square velocity of a chlorine molecule will be equal to its escape velocity from the earth’s gravitational field. Given that the radius of earth is 6400 km.
i) Intensive and Extensive variables,
ii) Quasistatic process,
iii) Isochoric process
iv) Adiabatic boundary,
v) Irreversible process
b) Prove that for a PVT system:
where = isobaric coefficient of volume expansion,
r = isothermal compressibility.
c) A resistor initially at 300 K has a heat capacity of 10 J K-1 . It is thermally insulated from its surrounding and is connected to a battery from which it takes 1200 J through an electric current. Calculate the change in entropy of (i) the resistor, (ii) the surroundings.
d) Calculate the work done during an adiabatic expansion of an ideal gas from volume Vi to Vf .
e) One gram mole of a monoatomic perfect gas at 27°C is adiabatically compressed from an initial pressure of 1 atm to final pressure of 50 atm. Calculate the resulting final temperature.
Derive an expression for Planck’s law of black body radiation. Use this law to obtain Wien’s displacement law and Stefan’s law.
What is a Gibbs paradox? How can it be resolved?
Write van der Waal’s equation of state and using this equation obtain critical constants.
Calculate the probability that the speed of a chlorine molecule will lie between 200 m s−1 and 220 m s-1 at 300 K. Given that mass of chlorine molecule = 70u, kB = 1.38 × 10-23 JK-1 and NA = 6.02 × 1026 kmol-1 .
For a given gas the coefficient of viscosity is 1.9 × 10-5 N s m-2 and the diffusion coefficient is 1.2 × 10-5 m2s -1 . Calculate the density and mean free path at average molecular velocity of 380 m s-1 .