Just give it to them as a free account, I expect the account would be tied to the professors email address for a record.
I would print up some cool stickers of your logo and send them to the professor to handout to the students using your API.
Maybe give them a tutorial on ways to limit/cache API requests so they don't overload your servers.
Good will like this could go a long way leading them to recommending you when ever they can in the future.
Everyone loves stickers they will end up on their laptops and computers and will be a reminder to use your service in the future.