Hot water heaters. Wouldn't make more sense to keep the temp higher than 120 degrees?

Due to insulating properties of water (and those of the water heater) wouldn't it be more energy efficient to keep the temperature of the water heater at around 150 degrees or more? When you take a bath or shower you be using less hot water since you would increase the ratio of cold/hot water to reach the same... show more Due to insulating properties of water (and those of the water heater) wouldn't it be more energy efficient to keep the temperature of the water heater at around 150 degrees or more? When you take a bath or shower you be using less hot water since you would increase the ratio of cold/hot water to reach the same temperature. For example you would use more hot water to achieve an overall water temp of 105 degrees it your water heater was set at 120 degrees. I realize that it would take more energy to initially heat the water to a higher temp, but keeping water at say 150 degrees wouldn't take considerably more heat than keeping it at 120 degrees. Also since you wouldn't be using quite a much hot water, the heater wouldn't be having to heat up as much cold water to replace the hot water that was used. I'd be interested in hearing about the maths and science involved in this. And the reason why 120 degrees is considered the better option. I'm not interested in the safety aspects of it, just the scientific reasoning. Thanks.
Update: Edit: I see what you are saying, but water retains heat much better than air. I would think that this property would allow it to retain heat better, even if the difference between ambient temp and water is higher
2 answers 2