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Not at all likely. A heat loss analysis would have to be done for a definitive answer. When a water heater is used for space heating typically nothing smaller than a 75 or 80 gallon unit is used.
Yes, a 40 gallon water heater is just big enough for DHW. No way it can also heat a 774 sq ft space at the same time.
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It depends on the conditions onsite. If there is space heating piping and the existing unit is smaller the cost can be more. Cost also depends on how the heater is vented. A power vented unit (exhaust fan on top) will be several hundred more than one that vents into a chimney. In the Boston area a typical replacement of the same sized chimney vented 75 gallon gas fired heater runs around $2000.