A piano teacher can use the technique portion of a lesson to explore emotions or moods. The student can be instructed to play an arpeggio or scale in a tender way, or with “anger,” “happiness,” etc.
I prefer this type of technique-framed mood exploration to an enlistment of Baroque, Classic or Romantic era repertoire for the same purpose.
In the video below, I play a C Major arpeggio with various emotional prompts to myself, demonstrating how this approach might be applied to lessons.
P.S. Some piano teachers, might oppose applying emotional tags to music, preferring a more abstract frame of reference.
Some suggested routines with arpeggios: