Final answer:
The efficiency of the engine is calculated by dividing the useful work output (2800 J) by the total heat absorbed (11700 J), which results in an efficiency of approximately 23.93%.
Step-by-step explanation:
To calculate the efficiency of a heat engine, you can use the formula:
Efficiency (η) = Useful Work Output / Heat Absorbed
In this case, the engine performs 2800 J of useful work and absorbs a total amount of heat which equals the sum of useful work and the wasted heat exhausted by the engine. Given that the engine exhausts 8900 J of heat, the total heat absorbed is 2800 J + 8900 J = 11700 J.
Now we can calculate efficiency:
η = Useful Work Output / Heat Absorbed = 2800 J / 11700 J ≈ 0.2393
The efficiency can also be expressed as a percentage by multiplying by 100:
η ≈ 23.93%
So, the efficiency of the engine is approximately 23.93%.