Final answer:
The system's thermal energy increases by 500 J when 750 J of heat energy is transferred to it and it does 250 J of work.
Step-by-step explanation:
The system's thermal energy changes based on the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat energy transferred to the system minus the work done by the system. In this scenario, the system is receiving 750 J of heat energy and doing 250 J of work. To calculate the change in thermal energy, you subtract the work done from the heat added to the system:
Change in thermal energy = Heat energy transferred to the system - Work done by the system
Change in thermal energy = 750 J - 250 J
Change in thermal energy = 500 J
So, the system's thermal energy increases by 500 J.