If oxygen isn't flammable, why do people care if people smoke around a person with respiratory oxygen therapy

Answer:
The oxygen itself will not burn, but the oxygen mask or cannula, clothing, skin, hair, and anything else that can act as a fuel WILL.

We have to be careful in the OR because it is a high oxygen environment, and things like surgical drapes and endotracheal tubes will combust if a laser or cautery ignites them. Airway fires can be awful, even deadly.

There is also the issue of not smoking around people with lung disease, so as to not further cripple their lungs, but that has nothing to do with flammability.

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