If the overall efficiency of the electrical grid is 30% determine how much energy worth of coal would be needed to produce 15.5kWh worth of end-use energy?

To determine how much energy worth of coal would be needed to produce 15.5 kWh of end-use energy given an overall grid efficiency of 30%, we can use the following steps:

1. **Understand the relationship between input energy and output energy**:
   - The overall efficiency \( \eta \) of the electrical grid is given by:
     \[
     \eta = \frac{\text{Output Energy}}{\text{Input Energy}}
     \]
   - Rearranging the equation to find the input energy:
     \[
     \text{Input Energy} = \frac{\text{Output Energy}}{\eta}
     \]

2. **Substitute the given values**:
   - Output Energy (end-use energy) = 15.5 kWh
   - Efficiency \( \eta \) = 30% = 0.30

   Now, plug these values into the equation:
   \[
   \text{Input Energy} = \frac{15.5 \text{ kWh}}{0.30}
   \]

3. **Calculate the input energy**:
   \[
   \text{Input Energy} = \frac{15.5 \text{ kWh}}{0.30} = 51.67 \text{ kWh}
   \]

So, to produce 15.5 kWh of end-use energy, **51.67 kWh** worth of energy from coal would be needed, considering the grid's 30% efficiency.

Would you like more details or have any questions? Here are some related questions to consider:

1. How is the efficiency of a power plant typically measured?
2. What factors contribute to the loss of efficiency in an electrical grid?
3. How much coal (in terms of mass) would be needed to generate 51.67 kWh of energy?
4. How can the efficiency of the electrical grid be improved?
5. What are the environmental impacts of using coal to generate electricity?

**Tip:** Efficiency can vary depending on the type of power plant and technology used; improving efficiency reduces the amount of fuel needed for the same energy output.

If the overall efficiency of the electrical grid is 30%, determine how much energy worth of coal would be needed to produce 15.5 kWh worth of end-use energy?

Determine the amount of coal energy needed to produce 15.5 kWh of end-use energy with a grid efficiency of 30%. This problem involves key concepts of energy efficiency and proportional relationships, making it suitable for high school students in Grades 10-12.

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