Introduction:
The thermal efficiency of a heat engine is a measure of how effectively it converts heat energy into mechanical work. It is given by the ratio of the work output to the heat input.

Given:
- Heat supply at 1000 K (T1)
- Heat supply at 500 K (T2)
- Heat rejection to sink at 300 K (T3)

Formula:
The maximum possible thermal efficiency (η) of a heat engine is given by the Carnot efficiency formula:

η = 1 - (T3 / T1)

Calculation:
1. Find the Carnot efficiency using the given temperatures:
η = 1 - (300 / 1000)
η = 1 - 0.3
η = 0.7

Explanation:
The Carnot efficiency is the maximum possible thermal efficiency for any heat engine operating between the given temperatures. It represents the ideal case where no energy is wasted.

In this case, the heat engine is supplied with half of its heat at 1000 K and the other half at 500 K. It rejects heat to a sink at 300 K. The Carnot efficiency is calculated using the formula η = 1 - (T3 / T1), where T1 is the higher temperature, T3 is the lower temperature, and η is the efficiency.

The maximum possible thermal efficiency of the heat engine is found to be 0.7 or 70%. This means that the engine can convert 70% of the input heat energy into useful work, while the remaining 30% is rejected to the sink.

It is important to note that this calculation assumes an idealized scenario and does not take into account any losses or inefficiencies that may occur in a real heat engine. In practice, the actual thermal efficiency of a heat engine is often lower than the Carnot efficiency due to factors such as friction, heat losses, and imperfect heat transfer processes.