An engine with an output of 233.0 W has an efficiency of 36.0 %. It works at 8.00 cycles/s. How much heat is rejected each cycle?

* I found that work done per cycle is 29.1 J. Im not sure what to do next

To find out how much heat is rejected each cycle, we can begin by calculating the work done per cycle, as you have already found it to be 29.1 J.

The efficiency of the engine can be expressed as:

efficiency = (useful output energy) / (input energy)

In this case, the useful output energy is the work done per cycle, which is 29.1 J. The input energy can be expressed as the sum of the work done per cycle and the rejected heat energy per cycle, denoted as Q.

Therefore, we have:

efficiency = 29.1 J / (29.1 J + Q)

The efficiency of the engine is given as 36%, which can be expressed as 0.36 in decimal form. Substituting this value into the equation, we get:

0.36 = 29.1 J / (29.1 J + Q)

To solve for Q, we can rearrange the equation:

0.36(29.1 J + Q) = 29.1 J

Now we can solve for Q:

10.476 J + 0.36Q = 29.1 J

Subtracting 10.476 J from both sides, we get:

0.36Q = 18.624 J

Finally, dividing both sides by 0.36, we find:

Q ≈ 51.733 J

So, each cycle of the engine rejects approximately 51.733 J of heat.