Sarah,

You could define the emotions through physical and/or psychological effects.

Colour, composition and form are the tools that painters use. Have a look at the still life paintings of Georgio Morandi. Bottles and vases to be sure, but he manages to convey subtle nuances of feeling and emotion within the apparent simplicity of his work.

Ask an artist, get an artistic answer. Ask a chemist, get a chemistry answer etc.

If someone does not know what an emotion is then I would think that you would need to define an emotion in easily measurable and observable phenomenon - physical and behavioural seems the best bet.