(a) Define specific heat capacity and specific latent heat of fusion, stating the SI unit of each. (4 marks) (b) Calculate the heat required to raise the temperature of $2$ kg of water from $20\ ^\circ$C to $80\ ^\circ$C. (Specific heat capacity of water $= 4200$ J kg$^{-1}$ K$^{-1}$.) (3 marks) (c) A block of ice of mass $0.5$ kg at $0\ ^\circ$C is completely melted and the resulting water is heated to $30\ ^\circ$C. Calculate the total heat supplied. (Specific latent heat of fusion of ice $= 336000$ J kg$^{-1}$; specific heat capacity of water $= 4200$ J kg$^{-1}$ K$^{-1}$.) (6 marks) (d) Explain why the temperature of the ice does not rise while it is melting. (2 marks)