Final answer:
For an expanding and heating hot air balloon, heat is being added to the system (q > 0) and work is done by the system on its surroundings (w < 0), making option B (q > 0; w < 0) the correct answer.
Step-by-step explanation:
If a hot air balloon is expanding and its temperature is increasing, this implies that heat is being added to the system, so q > 0. When a system expands, it does work on its surroundings because the gas inside the balloon needs to push outwards against the pressure of the atmosphere. Therefore, work done by the system is w < 0, because energy is leaving the system in the form of work. The correct answer is B. q > 0; w < 0, which corresponds to the system gaining heat and the system doing work on its surroundings.