Final answer:
The missing 2000 J of energy was used to do work by the system, reflecting the First Law of Thermodynamics, where energy supplied either increases internal energy or does work.
Step-by-step explanation:
When a gas burner applied 6000 J of thermal energy to a system and the internal energy of the system increased by 4000 J, the missing 2000 J of energy likely accounts for work done by the system.
According to the First Law of Thermodynamics, the energy in a system can either increase its internal energy or do work on its surroundings, or a combination of both.
In this case, when the system's internal energy increased by less than the amount of energy supplied, the difference is usually the energy that was used to do work on the surroundings.