Well PP, can you then please explain me, how a photosynthesis operates?? I believe H20 has no BTU, CO2 has no BTU, but green plants using catalyzer (chlorophyl) are able to make sugars with a lot of energy. It is all about chemical bonds not about your BRU. Thats why it is called chemistry - not algebra.
Your statement "1 BRU + 1 BRU must be 2 BRU" is useless here!