Well, i'm a second year student also and applied for a few internships intending to get a 6 week placement. if it was a 6 week placement i wouldnt expect anything more than expenses paid for. but i have an interview for a year's placement in london which will be all a paid placement
so id say if you were going to a placement for a few weeks then i doubt you'd get paid, but if you were to do longer then you'd be more likely to be paid.
if you have an interview and make a good impression with your skills and portfolio etc it wont matter that your second year. it will depend on the length of the placement and company size alongside your skills.