Molten sodium chloride is to be used as a constant-temperature bath for a high-temperature chemical reactor. Two hundred kilograms of solid NaCl at 300K is charged into an insulated vessel, and a 3000kW electrical heater is turned on, raising the salt to its melting point of 1073K and melting it at a constant pressure of 1 atm.

(a) The heat capacity (Cp) of solid NaCl is 50.41 J/(mol ∙ K) at T = 300 K, and 53.94 J/(mol K) at T = 500 K, and the heat of fusion of NaCl at 1073K is 30.21 kJ/mol. Use these data to determine a linear expression for Cp(T) and to calculate ΔH (kJ/mol) for the transition of NaCl from a solid at 300K to a liquid at 1073 K.

(b) Write and solve the energy balance equation for this closed system isobaric process to determine the required heat input in kilojoules.

(c) If 85% of the full power of 3000 kW goes into heating and melting the salt, how long does the process take?