Consider a liquid metal (L phase) in a container (d phase). The melting point of the metal is Tm =1350 K, the molar entropy change of melting is ASM = Sy-S9 = 5.5 J mol-? K-1, and the molar volume (for both the liquid and solid phase) is VM = 9.6 x 10-6 m3/mol. Now, we supercool the liquid metal to T = 1000 K. Please answer the following questions. (a) What is the critical radius of homogeneous nucleation for solidification, if the interface energy bet- ween liquid (L) and solid (8) phase, Yl3 = 0.15 J/m2? (b) If the interfacial energy between the liquid and the container is yL8 = 0.10 J/m and that between the metal solid and the container is y8 = 0.175 J/m, what is the contact angle of the heterogeneous nucleus on the container wall? (c) What is the volume of the critical heterogeneous nucleus on the container wall