Technology connections has a good video on YouTube that shows the inside working.
Basically they reuse a lot of the water. First it pumps a little water and uses sprayers to get most of the food particles off. They have their own filter and can reuse most of the water. It also does the top and bottom separately so it needs less water total. The machine is also insulated to keep the water hot once it’s heated up. It only replaces the water for the final rinse and steam disinfection cycle. Honestly the heated dry part uses more energy than needed but still less than a water heater.
Compared to a sink which probably takes at least a dozen gallons of hot water to fill up. It takes a lot of energy to heat up that much water. Plus you have to use even more for rinsing. I think the average new dishwasher only uses like 4 gallons for a whole load. So that’s a lot less energy in heating and a lot less water.
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