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The work function is the energy required to remove an electron from a solid to a point outside, it is a single value. Why is it called a function, instead of a single value? The word function suggests it is a function of some variable x.
.. is a function of ..
I'm sorry if I appear to lack sympathy while presenting the counterargument.As Baluncore doesn't seem to have much sympathy for your complaint,
I did some further googling. The term work function seems to have been introduced by Richardson in 1914.(link) He proposed that the emission law should have the mathematical form ##J = A T^2 \mathrm{e}^{- W \over k T}##, where W is the 'work function'. A comment on Richardson's work says: "a common error in the application of equation to thermionic emission is the assumption that the true work function W is a constant."(link) W not being constant would explain why it is called a function, instead of a value.