A soft drink in a cup can be cooled without dilution using chilled plastic spheres that are 1.0 cm in diameter instead of ice. Assume that 300 mL of the spheres initially at −20°C are added to 300 mL of the soft drink initially at 25°C in a well-insulated cup. The relevant properties of the plastic material are thermal conductivity k = 0.20 W/m K, density ρ = 1,400 kg/m³, and heat capacity C^p = 1,800 J/kg K. Neglecting the heat transfer resistance outside the spheres and assuming that the soft drink is well mixed, determine:

(a) The lowest temperature to which the soft drink can be cooled for these conditions.

(b) The time required to cool the soft drink to within 10% of the lowest possible temperature.