Английский Этимологический словарь - exhaust (v.)

- 1533, "to draw off or out, to use up completely," from L. exhaustus, pp. exhaurire "draw off, take away, use up," from ex- "off" + haurire "to draw up" (as water), from PIE *aus- "to draw water." Sense of "waste gas" was originally from steam engines. Exhaustion "fatigue," first recorded 1646, from sense of "drawing off" of strength.