There are too many variables to give a definitive answer. When do you use water? How much? Are you out for 16 hours a day? Do you take a daily bath or just a quick shower? Do you use gas, electricity or oil to heat the water?

Your plumber has a good point but only if your hot water tank is very efficiently insulated. It takes a lot of energy to heat water and this will be lost if the water is allowed to cool.

You mention "on demand": if you actully have an on-demand heater then these can be very efficient because they only heat the water you need, as you need it. Similarly, boiling a kettle to do the dishes (for example) might be efficient in some households, but electricity is a more expensive way to heat water than using a good gas boiler.

I mainly agree with Pete and your physics classes. Your plumber needs to do a bit of arithmetic, unless he has invented a perfect insulator.It seems he is confusing the question of whether it takes more heat to heat cool water than hot water, with the question of whether you can keep it hot without spending heat all the time, or get it hot in the first place without spending just as much heat as heating it before use.

Consider:

You have a mass of water at low temperature. it takes say 5 MJ to heat it to your needs. No one gives you free hot water; you spend those 5MJ as a basic given, whther you do it yesterday or today.

OK?

Suppose you do it today,pretty quickly, and as the last Joule slots in, you get into your bath.

Cost: 5 MJ. (pretty near anyway!)

Or you heated it this morning and take your bath this evening. The water is perhaps 20 degrees cooler than this morning, so (ugh!) you first heat it again. Bill say an extra 3 MJ, that being how fast the heat got lost from morning to evening, but fastest in the morning, when the water was hot!

But, says plumber, you silly sausage you! You were wasting 3MJ just to heat up your water! Leave your geyser on in the morning and come home to free hot water! No three MJ!

What WOULD we do without these professionals to help us?

You are ahead of me aren't you? (I HOPE!)

Keeping the water warm required the same amount of heat as you lost anyway (unless your plumber had invented a geyser that doesn't lose heat while the electricity is switched on!)

Right?

PLUS...!!!

In fact, you wre losing heat throughout the day from HOT water, not water that on average was just warm!

Your evening bill will be a lot more than 3MJ!

I hope you get this; I see alarming symptoms that sggest that the system is acting up agian!

Q = cp.m.dT

Q = amount of heat (Joules or calories) What we're interested in ...

cp = specific heat capacity (of water in this case) Not relevant here ...

m = mass ... 1 gm/ml for pure water.

dT = temperature differenence between hot and cold side, i.e. inside the geyser and outside the geyser.

Taking a theoretical situation, let's say the inside temperature is set at 50C and the outside temperature is maintained at 20C. The difference therefore is 30C. The geyser is also a 100 ltr geyser (bit small, but possible).

I also prefer to use calories (I'm a bit old fashioned, OK!) ...

Situation 1: The geyser starts at its max then is switched off and left cooling for 16 hours before switching electricity on again. Let's say (theoretical) that cools right down to ambient temperature in that time. 100 000 gms of water has lost 30 degrees of heat. Energy to heat up to max is therefore 30 X 100 000 calories = 3000 Kcals.

Situation 2: The geyser starts at it's max, then is left switched on for the 16 hours. Every time it cools, say, 5 degrees below max, the thermostat switches on and heats it back up. Let's say this happens 5 times during the 16 hours (I've no clue what it would really do in real life, but this is just theory). So 5 times it is heated up by 5 degrees = 25. Energy required is therefore 25 X 100 000 calories = 2500 Kcals.

Situation 3: Assume that your insulation is not so effective and more heat is lost during the 16 hours than in Situation 2. The thermostat would come on more often then, say 8 times in the 16 hours. Same maths, result = 40 X 100 000 calories = 4000 Kcals.

So both you and your plumber are both correct! Solution is to get insulation for your geyser and lag any pipes, then you can leave the geyser switched on as much as you like, and not risk a cold bath/shower because you forgot to switch on when you got home from work.

I'm confused... my answer appeared twice... the subject was a fishpond... I answered about a geyser. UK slang for water heater.

In a similar situation... I had heard the suggestion to turn my electric water heater  off when I wasn't home from both the landlord and the electric company.

I installed an LED that indicated when the water heater was operating.

The idea was to know when it reached temperature, and went off, so the next person could begin their shower with a hot tankful.

Watching TV I would notice it come on and off.

It was 7 minutes out of every three hours!

Obviously not worth shutting it off in my opinion.

Saving a few pennies every three hours... and then not having hot water when I got home, or got up in the morning... please!

Then pay for, and wait to, heat the water from lukewarm as well.