Entry is not granted to your passport, but to you, the human being. You are permitted to spend 90 in 180 days as a tourist in the Schengen Area.

The Schengen authorities may link your old passport number to your new passport number, or they may not. Nonetheless, you should not break the law.

By the way, not all EU countries are in Schengen, and not all Schengen countries are in the EU.