Using the Maxwell’s relations, obtain the energy equations.
Maxwell's relations are a set of equalities among the partial derivatives of thermodynamic state functions. These relations are derived from the four fundamental thermodynamic potentials: internal energy (U), enthalpy (H), Helmholtz free energy (A), and Gibbs free energy (G). The relations are particularly useful in connecting different thermodynamic properties and providing additional insights into the behavior of _______ _____ _______ _____ ____ _______ ____.
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Write van der Waal’s equation of state and using this equation obtain critical constants.
Derive an expression for Planck’s law of black body radiation. Use this law to obtain Wien’s displacement law and Stefan’s law.
Define degree of freedom of a molecule. Write its general formula. Calculate the degree of freedom for a single atom.
What is a Gibbs paradox? How can it be resolved?
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.
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 .
What is adiabatic demagnetization? Explain the variation of entropy of a paramagnetic salt with temperature and magnetic field.