An engine does 15kJ of work while rejecting 37 kJ to the cold reservoir. What is the efficiency of the engine?

To calculate the efficiency of an engine, you need to know both the work done and the heat rejected by the engine.

The efficiency of an engine is given by the formula:

Efficiency = (Work Done / Heat Input)

In this case, the work done by the engine is 15 kJ, and the heat rejected to the cold reservoir is 37 kJ.

Plugging in the values, we get:

Efficiency = (15 kJ / 37 kJ)

Simplifying this expression, we find:

Efficiency ≈ 0.4054 or 40.54%

Therefore, the efficiency of the engine is approximately 40.54%.