...assuming no heat is lost of course (all your energy goes into heating the cup)
how are you going to convert sound into heat other than the heat resulting from the vibrations?
I believe the answer stactically is 8 years (with no breaks) though I can't remember where I found that info.
Err, nevermind. I think I got that from one of the those fake value number of statistics are made up.
A detailed explaination:
http://www.physicscentral.com/explore/poster-coffee.cfm
says, to heat up a quarter liter of coffee 50 C it would take: 1 year, 7 months, 26 days, 20 hours, 26 minutes and 40 seconds
continuous yelling.....i think i would stop after 30 min max
I couldn't even get myself started on yelling but if I did, the most I could go for without a breath would be maybe just a little above 1 or 2 minutes.