Question

If a power plant burns coal at a rate of 3.00 Gigawatts and produces electricity at a rate of 1.00 billion watts, what is the fractional efficiency of the plant?

Option 1: 0.25
Option 2: 0.33
Option 3: 0.75
Option 4: 0.50

Answer 1

The fractional efficiency of the power plant burning coal is 0.33, meaning 33% of the input energy from coal is converted into electrical energy.

Step-by-step explanation:

To calculate the fractional efficiency of a power plant, we must divide the output energy by the input energy. Given that the power plant burns coal at a rate of 3.00 Gigawatts (which is 3.00 x 109 watts) and produces electricity at a rate of 1.00 billion watts (1.00 x 109 watts), the fractional efficiency can be found by the formula: Efficiency = (Output Power / Input Power), Efficiency = (1.00 x 109 W) / (3.00 x 109 W), Efficiency = 0.333... Therefore, the fractional efficiency of the plant is 0.33, which corresponds to Option 2. This means that the power plant converts 33% of the energy from coal into electrical energy, with the remainder being lost as heat.