From the power plant, it took 100 kJ of coal to produce the 15 kJ of useful energy in your home.  What is the total efficiency?

Efficiency is calculated by dividing the useful output energy (or power) by the total input energy (or power). It's often expressed as a percentage.

Here's the step-by-step calculation:

1. Identify the Input and Output: In this case, the total input energy is 100 kJ (the energy from the coal) and the useful output energy is 15 kJ (the energy that ends up being used in your home).

2. Calculate Efficiency: Divide the useful output energy by the total input energy.

Efficiency = (Useful output energy / Total input energy) * 100%

3. Substitute the given values into the formula:

Efficiency = (15 kJ / 100 kJ) * 100%

4. Calculate the Result:

Efficiency = 15%

So, the total efficiency of the power plant in this case is 15%.