1530s, "to draw off or out, to use up completely," from Latin exhaustus, past participle of exhaurire "draw off, take away, use up, empty," from ex "off" (see ex-) + haurire "to draw up" (as water), from PIE *heusio- "to scoop." Meaning "make weak or helpless, as by fatigue" is from 1630s. Related: Exhausted; exhausting; exhaustible.
"waste gas," 1848, originally from steam engines, from exhaust (v.). In reference to internal combustion engines by 1896. Exhaust pipe, which carries away waste gas or steam from an engine, is by 1849.