6.0 x 10³ / 0.31 = 19.35 x 10³ J
To solve this question, we need to use the formula for efficiency, which states that Efficiency = (Output Energy / Input Energy) x 100.
We know that the Output Energy is 6.0 × 10³ J, and we need to figure out the Input Energy. To find the Input Energy, we can rearrange the formula to Input Energy = (Output Energy / Efficiency) x 100.
Plugging in our values, we have Input Energy = (6.0 × 10³ J / 0.31) x 100 = 19.35 x 10³ J.
Therefore, the energy that must be added to the engine during one cycle in order for it to operate at 31 percent efficiency is 19.35 x 10³ J.