No, it is not accurate to say that spraying 1 gallon of water on the roof of a house will result in 1 British Thermal Unit (BTU) of cooling. The claim you mentioned is a common misconception.
The evaporation of water does have a cooling effect due to the energy required to change water from a liquid to a vapor state. However, the actual cooling effect is more complex and influenced by various factors such as humidity, temperature, airflow, and surface area.
When water evaporates, it absorbs heat from the surrounding environment, which can lead to a localized cooling effect. However, the amount of cooling produced by the evaporation of 1 gallon of water is not equivalent to 1 BTU. The specific amount of cooling depends on multiple factors, including the initial temperature, relative humidity, and the rate of evaporation.
The cooling effect of water evaporation can be significant in some situations, such as in evaporative cooling systems or misting systems designed for outdoor areas. However, for general residential purposes like spraying water on a roof, the cooling effect will likely be minimal and temporary.
It's important to note that if you're interested in cooling your home efficiently, using proper insulation, ventilation, and an energy-efficient air conditioning system is typically more effective than relying on the evaporative cooling effect of water.