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 is from 1889.