What Car? Q&A - Why do diesels smoke?
A: A little puff of black smoke when accelerating hard isn't anything to worry about. A lot of smoke is something to worry about, though - it indicates incomplete combustion (i.e. partially unburnt fuel is being blown out of the exhaust). Diesel fuel contains a higher level of carbon than petrol, so if it's unburnt it often appears as a thick, black smoke.
This is more than likely the issue with your son's Passat. There's no need to panic – chances are it's a relatively minor problem, such as a clogged air filter or faulty injector. However, there is a possibility it could be something more serious.
Take the car to your local VW dealer or to a diesel specialist and ask them to investigate the problem.
Different coloured smoke would indicate other problems. If it's blue, engine oil is being burnt, which points to worn valve guides or piston rings. If it's white, the 'smoke' is probably actually steam, which could suggest a blown head gasket.