Unsolved Questions

1. Derive the Clausius-Clapeyron equation from the third Maxwell’s relation, namely,
2. The latent heat of ice I is 3.34 X 10⁵ J/kg at 0° C and atmospheric pressure. If the change in specific volume on melting is -9.05 X 10^-5 m³/kg, then calculate the change of melting temperature due to change of pressure.
3. Prove that, during a first-order phase transition:
   1. The entropy of the entire system is linear function of the total volume.
   2. The change of internal energy is given by
4. In a second-order phase transition, s⁽ⁱ⁾ = s^(f) at (T, p), and s⁽ⁱ⁾ + ds⁽ⁱ⁾ = s^(f) + ds^(f) at (T + dT, p + dp).
   1. prove that
      In a second-order phase transition, at (T+dT, p+dp).
      
   2. prove that
      (Note: these are Ehrenfest’s equations)
5. For a two-phase system in equilibrium, is a function of only; therefore,
   for such a system show that
   
   regardless of the type of transition between the phases.
6. It is found that a certain liquid boils at a temperature of 95° C at the top of a hill, where as it boils at a temperature of 105° C at the bottom. The latent heat is 4.187 kJ/gmol. What is the approximate height of hill? Assume T₀ = 300 K
7. Calculate the latent heat of vaporization of steam formed by boiling water under a pressure of 101.325 kPa. At a pressure near this, a rise of temperature of 1 K causes an increase of vapour pressure of 3.62 kPa.
8. Using the Redlich-Kwong equation of state, develop expressions for the changes in entropy and internal energy of a gas in an isothermal process.
9. According to Berthelot, the temperature effect of the second virial coefficient is given by
   where a and b are constants. Show that according to Berthelot,
10. The following expressions for the equation of state and the specific heat are obeyed by a certain gas:
    
    where α, A, B, C are constants. obtain an expression for
    1. the Joule-Thomson coefficient, and
    2. the specific heat C_v
11. Determine the maximum Joule-Thomson inversion temperature in terms of critical temperature T_c predicted by
    1. van der Waals equation
    2. Redlich-Kwong equation
    3. Dieterici equation
12. To make baking soda (NaHCO₃), a concentrated aqueous solution Na₂CO₃ of is saturated with CO₂. The reaction is given as
    Thus Na⁺ ions and CO₃^- ions, H₂O, CO₂ and NaHCO₂ are present in arbitrary amounts, except that all the Na⁺ and CO₃^- are from Na₂CO₃. Find the number of degree of freedom of this system.
13. Determine the number of degree of freedom for the system at each lettered point and state the variables for a cadmium-bismuth system (Fig. 2.13)

    
    Fig. 2.13 Phase diagram of cadmium-bismuth system