Hawthorne Season 2 Episode 1 (Hawthorne s02e01) with title “No Excuses” airs on Tuesday, June 22nd 2010 at 09:00 pm via TNT Network.
Here is summary for Hawthorne Season 2 Premiere :

The hospital drama opens its second season. With Richmond Trinity out of business, numerous staff members land employment at a decaying hospital in a run-down neighborhood.

Few hours after original series aired on TV, online streaming video for Hawthorne Season 2 Episode 1 usually available on Net and of course, if video available, as soon as possible will show you where you can watch this episode for free.