A \(2000 \mathrm{ft}^{2}\) house in Boston is being designed with NLC-12,000 Btu/F-day and \(150 \mathrm{ft}^{2}\) of direct gain. The direct gain system includes double glazing, nighttime insulation, and \(30 \mathrm{Btu} / \mathrm{ft}^{2} \mathrm{~F}\) thermal storage capacity. Using the LCR method, determine

(a) the annual auxiliary heating energy needed by this design 

(b) the storage mass and dimensions required.