Efficient Hot & Cold water combination for bathing

[djsourabh]

Generally for bathing purpose, we heat water to higher temperature say T1 than the temperature at which body is comfortable say T0 (is T0 = 70 degree Celsius?) & add some quantity of cold water to it to have the temperature of water = T0. Is the process energy efficient?
What is the best combination of hot & cold water (quantities & temperature) so that least amount of energy is spent?
eg, say we require 10 litres of water at temp T0 for comfortable bathing.
So how do we do it, heat 7 litres of water to temp T1 & add 3 litres of cold water at temp T2 to get 10 litres of water at temp T0. But this may not be the energy efficient combination, we might heat 10 litres of water to T0 & spend lesser energy than the above case. So what are the equations & how to know which would be the best combination?

 

[Baluncore]

Energy losses are proportional to temperature. The basic principle here should be to generate water that is just hot enough for use without needing to dilute with cold water. This is especially true where hot water is stored for some time waiting for use. This also has the safety advantage of not scalding children.

The only reason to run at a higher temperature than needed is when the capacity of the storage is less than the volume of hot water immediately required.

I believe your mixing calculations should be based on the mass of water, not on volume.

 

[djsourabh]

Energy losses are proportional to temperature. The basic principle here should be to generate water that is just hot enough for use without needing to dilute with cold water This is especially true where hot water is stored for some time waiting for use. This also has the safety advantage of not scalding children.

The only reason to run at a higher temperature than needed is when the capacity of the storage is less than the volume of hot water immediately required.

I believe your mixing calculations should be based on the mass of water, not on volume.

Do you mean that we spend least energy in the case you mentioned? (The basic principle here should be to generate water that is just hot enough for use without needing to dilute with cold water) ?? It will be very helpful if I get equations to support that.

 

[Baluncore]

Yes, just warm enough is more efficient than hot.
It is probably best analysed from the lost energy viewpoint.

The hotter the water in the reservoir is, the faster it will lose heat. It will do that even if you do not use any water. That is a major inefficiency. Get better thermal insulation on the tank.

When you use hot water it passes along a pipe that absorbs heat and then radiates proportional to the elevation in temperature. Use low thermal capacity pipe material and insulate all hot water pipes.

If you use a greater volume of warm water, than if it were hotter, it will still only heat the pipe to a lower water temperature once. If small quantities of water are used often, pipe thermal loss will be significant. Put the hot water reservoir near the kitchen sink. The distance to a bath or shower can be greater since, more water is used, less often.