What is the ruling on raising the volume of the Quran in a place filled with clamor and chatter, or leaving it playing loudly in a closed, empty room?

The first thing is for your friend to coordinate with his companions, consult them, and encourage them to listen to the Qur'an. If they agree, he may play it; otherwise, he should wait until they finish their conversation. If there is no coordination, it could lead to discord among them or some of them being alienated from the Qur'an. As for playing the Qur'an when people are present, there is no منع (prohibition) as long as there isn't a sleeper who would be disturbed by the sound, or someone praying, or someone else reciting the Qur'an. It is Sunnah (definition) (recommended) for those present to listen when the Qur'an is played, but it is not obligatory. This is the view of the majority of scholars, while the Hanafis consider it obligatory. As for playing a cassette in a room where no one is present, there is no harm in it, as it may help in expelling devils from the house.