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The Work-Energy Theorem of Newtonian Mechanics [should not be] confused
with the First Law of Thermodynamics. Given the situation (as I read you):
R is the constant net force on the object as it "loses" K (kinetic energy)
over a displacement x (in the direction of R), then K and R*x are numerically
equal - and rigorously so, by Newton's laws of motion. This is a purely
mechanical (dynamics) question, and stands quite apart from any conservation
of energy postulate or thermodynamic considerations.