A typical house uses about 110 liters/day of hot water. An integrated rooftop solar water heater with a collector area of 3.0 m² and storage 270 liters supplies this amount at 60°C throughout the year (365 days) with about 40% supplementary electric heating. Such a solar heater costs about RM 3,800 to be installed. If 60% of the energy input for hot water comes from the sun, electricity costs the householder RM 0.27 per kWh and the water has to be heated from 25°C. Determine the amount of sponsorship to be collected to ensure payback time for installing this solar water heater is less than 3.5 years. Given the specific heat capacity of water is 4.2 kJ/kg·K and electricity to heat conversion efficiency of 0.8.
i. Energy required to heat the water (in MJ)
ii. Energy required to heat the water (in kWh)
iii. Cost of electricity if 100% usage by electricity (in RM)
iv. Cost of electricity if the required energy input comes from the sun (in RM)
v. Sponsorship needed (in RM)