My hot water system maintains a volume of 130 litres of water, which it heats to a maximum temperature of 60C in a cylindrical tank 1.5 metres tall. It works by drawing in cold (temperature 10C) water at the base of the tank, where the heating element is located. Hot water leaves through a pipe at the top of the system. If the tank is full of water at 60C, the manufacturer guarantees that it will produce 260 litres of water at or above 50C in the first hour of use. Temperature diffusion (as per the heat equation) in water has a diffusion coefficient of around 1.510^-7 m²/s. What is the minimum rate at which the element must heat the water (in C/litre/minute), to meet the manufacturer's guarantee?