Sure! Let's break down the problem step by step before drawing the Sankey Diagram.
1. Understand the Problem: We have an appliance with an efficiency of [tex]\( 75\% \)[/tex] and a total input energy of 100 Joules. We need to determine how much of this energy is converted into useful stores (useful energy) and how much is wasted.
2. Determining Useful Energy:
- Efficiency is defined as the ratio of useful output energy to total input energy, expressed as a percentage.
- Given efficiency ([tex]\( \eta \)[/tex]) = [tex]\( 75\% = 0.75 \)[/tex] (in decimal form).
- Total input energy = 100 Joules.
The useful energy ([tex]\( E_{\text{useful}} \)[/tex]) is calculated by multiplying the total input energy by the efficiency:
[tex]\[
E_{\text{useful}} = \text{Efficiency} \times \text{Total Input Energy} = 0.75 \times 100 = 75 \text{ Joules}
\][/tex]
3. Determining Wasted Energy:
- The wasted energy ([tex]\( E_{\text{wasted}} \)[/tex]) is the amount of energy not converted into useful work. It can be calculated by subtracting the useful energy from the total input energy:
[tex]\[
E_{\text{wasted}} = \text{Total Input Energy} - \text{Useful Energy} = 100 - 75 = 25 \text{ Joules}
\][/tex]
4. Sankey Diagram:
- A Sankey Diagram is a flow diagram where the width of the arrows is proportional to the flow rate of a resource. For our scenario:
- We start with an arrow representing 100 Joules of input energy.
- This arrow splits into two parts: one representing the useful energy (75 Joules) and the other representing the wasted energy (25 Joules).
Here is a simple representation of what the Sankey Diagram might look like:
```
Input Energy (100 Joules)
|
|
v
----------------------
| Useful Energy (75 J) |
----------------------
|
|
v
----------------------
| Wasted Energy (25 J) |
----------------------
```
So, based on this analysis, the total input energy is 100 Joules, out of which:
- 75 Joules go to useful stores.
- 25 Joules are wasted.
