A certain heat engine takes in 300 J of energy from a hot source and then transfers 200 J of that energy to a colder object. What is the efficiency of the heat engine

The efficiency is 0.33, or 33%.

Explanation:

From the thermodynamics equations, we know that the formula for the efficiency of a heat engine is:

Where η is the efficiency of the engine, Q_1 is the heat energy taken from the hot source and Q_2 is the heat energy given to the cold object. So, plugging the given values in the formula, we obtain:

This means that the efficiency of the heat engine is 0.33, or 33% (The efficiency of an engine is dimensionless).