Calculate Engine Efficiency: 0.490 kJ of Heat for 0.120 kJ of Work

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SUMMARY

The efficiency of the engine is calculated as the ratio of useful work output to the total energy input. In this case, the engine releases 0.490 kJ of heat while performing 0.120 kJ of work. The correct formula for efficiency is useful work divided by the sum of useful work and waste heat, resulting in an efficiency of 0.211. The misunderstanding arose from incorrectly calculating the total energy input.

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An engine releases 0.490 kJ of heat for every 0.120 kJ of work it does. What is the efficiency of the engine?

I am having trouble with this problem.
I tried

Wnet/ heat input = efficiency
0.120/0.450 = 0.27
but it says it is the wrong answer. (correct answer is 0.21)
 
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The efficiency is the useful work divided by the total energy. What is the total energy in terms of the useful work and the waste heat generated?
 
thanks!

0.120/(0.450+0.120) = 0.211
 

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