The Collaborative International Dictionary of English v.0.48:

Duty \Du"ty\, n.; pl. Duties. [From Due.]
   1. That which is due; payment. [Obs. as signifying a material
      thing.]
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            When thou receivest money for thy labor or ware,
            thou receivest thy duty.              --Tyndale.
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   2. That which a person is bound by moral obligation to do, or
      refrain from doing; that which one ought to do; service
      morally obligatory.
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            Forgetting his duty toward God, his sovereign lord,
            and his country.                      --Hallam.
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   3. Hence, any assigned service or business; as, the duties of
      a policeman, or a soldier; to be on duty.
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            With records sweet of duties done.    --Keble.
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            To employ him on the hardest and most imperative
            duty.                                 --Hallam.
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            Duty is a graver term than obligation. A duty hardly
            exists to do trivial things; but there may be an
            obligation to do them.                --C. J. Smith.
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   4. Specifically, obedience or submission due to parents and
      superiors. --Shak.
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   5. Respect; reverence; regard; act of respect; homage. "My
      duty to you." --Shak.
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   6. (Engin.) The efficiency of an engine, especially a steam
      pumping engine, as measured by work done by a certain
      quantity of fuel; usually, the number of pounds of water
      lifted one foot by one bushel of coal (94 lbs. old
      standard), or by 1 cwt. (112 lbs., England, or 100 lbs.,
      United States).
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   7. (Com.) Tax, toll, impost, or customs; excise; any sum of
      money required by government to be paid on the
      importation, exportation, or consumption of goods.
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   Note: An impost on land or other real estate, and on the
         stock of farmers, is not called a duty, but a direct
         tax. [U.S.]
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   Ad valorem duty, a duty which is graded according to the
      cost, or market value, of the article taxed. See Ad
      valorem.

   Specific duty, a duty of a specific sum assessed on an
      article without reference to its value or market.

   On duty, actually engaged in the performance of one's
      assigned task.
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Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "on duty":
   at it, at work, busy, employed, engaged, full of business,
   hard at it, hard at work, in harness, occupied, on the go,
   on the hop, on the job, on the jump, on the move, on the run,
   tied up, working