Consider the concept of a thermal battery where a Carnot cycle is used to exchange heat between a cold reservoir where ice and water are in equilibrium and a hot reservoir where water and steam are in equilibrium, each at 1 bar. The Carnot cycle runs as a heat pump transferring energy from the cold to the hot reservoir. (a) What is the coefficient of performance for this process? (b) How much ice is created and how much water is boiled per kWh of input energy