In our university there's a posted sign that encourages students to take the stairs instead of the elevator to save the university electricity during the hot NYC summers.
When you climb the stairs you generate something like 8x your mechanical energy in metabolism which is dissipated as heat and must be cooled by the air conditioning in our cooled stairwells.
What are plausible assumptions about the energy efficiency limits of air conditioning and mechanical lifting of an elevator? What (fundamental) limits are there that prevent 100% efficiency in the elevator case? Are there other important factors for this analysis?
Is it plausible that the university is wrong? Should we take the elevator instead of the stairs to save the university energy? Do the humans of an energy-efficient future look like Wall-E?
The source of this question is a bathroom physics problem posted above university physics department toilets near grad offices. Problems are submitted by department members. To the best of my knowledge, none of these were ever homework questions. This question is adapted by my toilet memory from a problem that was provided by Andrei Gruzinov.