(a) [6 marks] When lead is melted at atmospheric pressure, the melting point is 327.0C, the density decreases from 1.101x104 to 1.065104 kg/m and the latent heat is 24.5 kJ/kg. Esti- mate the melting point of lead at pressure of 100 atm. (b) [5 marks] The first law of thermodynamics for an elastic rod of length L and subjected to a tension f is dU = TdS + fdL. By consideration of free energy F = U - TS show that I (051) (c) [7 marks] Using the result from (b), and the reciprocity theorem, show that as L T OL = af (F) L TAETaf CL 9 where A is the cross-sectional area of the rod, Er is the Young's modulus at constant tempera- ture, af is the coefficient of thermal expansion at constant tension, and C is the heat capacity at constant length