5. Measuring the mechanical equivalent of heat is difficult because heat capacities are so large. (a) How much heat is required to raise the temperature of 2,000 kg of water from 10C to 45C? This is similar to a medium-sized Japanese family bathtub. (b) I wanted to generate this heat by working, and I know that a person can sustain about a 250 W power output. How long would it take me to heat the water? (c) If the heat capacity is so large, why can't we use the heat in the lake water to power the electrical fixtures in a house?