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Question:

if i was to build a metal box and place a 40 gallon hot water tank with two 250 watt heat bulbs ?

i am tired of paying for hot water and lp gas. i am planning on bulding a shelf cantained box placing two 250 watt heat bulbs and a 40 gallon water tank in it what would happen

Answer:

The heat produced by 2 - 250 watt bulbs is miniscule if trying to heat water, plus electricity is normally more expensive than gas. As previously suggested you can bring the sun into play in order to temper the cold water before it enters your LP water heater. Thoroughly insulating your LP heater (don't interfere with the exhaust or burner areas) will diminish the heat lost from the unit, especially if it is located in a cold basement. Also insulating your hot water pipes will be helpful. There are high efficiency water heaters available but analyze such a purchase carefully as sometimes the added cost negates the energy saved.
I think you're on the wrong track if you're trying to save money on heating the water. Firstly, 40 gallons is a piddling amount of water for domestic use. Secondly, how much electricity will you be using at 250 watts times two, to heat water? Third; the bulbs will, I suspect, overheat in that confined space and the elements will blow. But I can see how you are thinking; it is the intial heating-up of the water from very cold that consumes the most energy, isn't it? That's common knowledge. So why don't you continue with your idea of a water tank. Paint it matt-black and site it somewhere to catch sunlight. The matt-black will absorb the heat and raise the temperature of the water, especially if the tank can be surrounded by glass (Greenhouse effect) to keep cooling winds off the tank. The eternal conundrum with most of those energy-saving schemes is the cost of building and installing the apparatus. By the time all of that is factored into the so-called saving, there IS no saving. Perhaps the cheapest way to save heat is to conserve it by lagging the water tank to keep the heat in. Since you've got a supply of LP gas, why don't you try running your car on LP gas? I do. Half the price, so what you save on car expenses, you can put towards heating your water.
build a heat exchanger for the hot water, [solar] or do like we did in the military hang a Black colored bag out side in the sun, let the sun heat it up a black plastic tank will do the same
I'd be glad to have LP Gas, or even Natural Gas, to have for my heat and hot water, at least based on the electric rates from our utility. If you want electric hot water, and your electric rates are cheap enough to compete with LP or natural gas, you need a hot water immersion storage tank, which will have two 240V 3KW heaters (usually with a stepped heating arrangement, where the top is heated to temperature first, then the bottom is allowed to heat. ) You can install a timer to control when it gets power to heat the water, to heat it only when you are scheduled to need it for laundry or dishes, or to heat on your cheap electric rate, for time-of-use billing. Depeding on code and practices, you could get point of use small volume electric water heaters as well.
This saves nothing, will not heat the water (500 watts from the 2 bulbs is a far cry from the needed minimal 2,000 watts to heat in any reasonable time), and it is inefficient. It is too bad that many who want to reduce energy costs are not technically trained. Because they are technically untrained, they cannot look beyond the initial concept to see if it is practical. Another problem often seen is that the costs for the materials and labor to make and install any such device is so high that it is in fact more costly than the current situation. For example, coal fired electricity costs about $0.07 / kw hr and solar or wind generated costs over $0.20 / kw hr. People are so hung up on the free fuel in sun and wind they do not understand there is no savings.

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