Remove the belt (you may find it's tricky as I think it takes a special torx tool to release the tensioner) then rotate the pulley by hand to feel if it turns smooth without grabbing, then use a screw driver to inspect the clutch - check youtube videos. May also give the pulley a kick, it should keep turning 2-3 turns without stopping too quickly, should have some inertia. But it's the clutch that would go bad first. I think the alternator is tricky to remove from the turbo engine, maybe it has to come out by the headlight hole after removing the headlight .
But while there also inspect the tensioner and especially the A/C pulley bearing - turn it by hand and feel for roughness/dry noise. At 110K miles I would rather look into the tensioner and A/C pulley bearing, the alternator pulley should be good to go up to 120-130k miles at least.