Here are some units that can
never represent work:
-- kilogram
-- meter
-- second
-- volt
-- newton
-- light-year
-- mile
-- Pascal
-- lumen
-- Smoot
-- fortnight
-- Hertz
-- inch
-- week
-- ohm
-- quart
-- pound
-- ampere
-- furlong
-- pint
-- dollar
-- acre
-- bushel
-- horsepower
-- gallon
-- liter
-- yard
-- Watt
-- month
-- dram
-- hectare
-- farad
-- Ångstrom
-- shekel
-- decibel
-- radian
-- Scoville