Read the comments on the link posted above. You have to send the current passport to get the second one, so you can’t send for the visa until you get the second passport. It recommends to expedite the second. Second catch-22 is that you can’t get the expedited one unless you have immediate need for travel, and if he’s not going until July…?
If you live in a city with an expediting office, I’d head there with everything you can think of - rules for the study abroad visa, schedule for summer travel (tickets?), the passport you have, etc.
I’ve been really lucky and run into some passport clerks who were very helpful and figured out what I needed to do. ID, pics, money (lots of money), passport, application filled out and each item I was using to prove that spot on the application (ID, old passport, for my kids their birth certificates and other papers).