The brief
The owner had been hearing a high-pitched squeal on cold starts for a couple of weeks. It would die away once the engine warmed up. That's the classic ageing-belt signature: cold rubber goes hard and slips, warm rubber softens and grips. He brought the C180 in before the slip became a stretch and the stretch became a snap, because a belt that lets go takes the alternator, the water pump and the steering with it.
The accessory belt is the single ribbed belt that drives the alternator, the aircon compressor and the water pump off the crankshaft. A spring-loaded tensioner keeps it tight, idler pulleys guide it. When the belt glazes and the tensioner spring weakens, the belt can't hold under load, so it slips, and slipping rubber is what you hear.
The diagnosis
With the belt off the engine, the rib face was glazed shiny and showing fine surface cracking, well past the point of replacing. The tensioner spring was still loaded, but the bearing had developed a small wobble, so it wasn't running true any more. The idler spun smoother but it's on the same age clock as the rest.
So this was a whole-set job: the belt, the tensioner and the idler all together. Fitting a new belt onto a tired tensioner just gives you the same noise again in a few months, and leaves the wobbling bearing waiting to seize.
The work
Belt tension was released, the old belt and the failed tensioner came off, and new Mercedes-spec parts went on, including a fresh idler pulley. The new belt was routed correctly through the accessory drive, since a misrouted belt is its own kind of noise, and tensioned to spec.
Then the engine was run through a warm-up cycle with the aircon and other loads switched on to confirm the belt drive ran silent, cold and hot, under load.
The outcome
No squeal on cold start, no slip when the aircon and alternator both pull, and a silent belt drive right across the rev range.
The C180 went home with the front of the engine quiet again and the slip path cut off. Doing the belt drive as a set, belt and tensioner and idler together, is the right way to do it: it stays fixed, and it heads off the worst case, a belt failure that strips the charging, the cooling and the steering all at once.