Section 4.7: Fuel Energy and Power
Fuel energy is the chemical potential energy stored in fuels, which is converted to mechanical work or electricity. Power is the rate at which this energy is used.
Energy from Fuel:
- Energy content is measured in joules (J) or calories (cal).
- Efficiency determines how much of the fuel's energy becomes useful work.
Power Generated:
\[ P = \frac{W_\text{useful}}{t} \]
where \( W_\text{useful} = \eta \times E_\text{fuel} \).
Example 1
A car engine consumes fuel releasing 5 × 10⁶ J of energy in 10 s. If the engine efficiency is 25%, find the power output.
Useful work: \( W_\text{useful} = 0.25 \times 5\times10^6 = 1.25\times10^6 \text{ J} \)
Power: \( P = \frac{1.25\times10^6}{10} = 1.25\times10^5 \text{ W} \)
Example 2
A generator uses 2 × 10⁷ J of fuel energy in 1 min with 40% efficiency. Calculate the electrical power output.
Useful work: \( W_\text{useful} = 0.4 \times 2\times10^7 = 8\times10^6 \text{ J} \)
Time: \( t = 60 \text{ s} \)
Power: \( P = \frac{8\times10^6}{60} \approx 1.33\times10^5 \text{ W} \)
Practice Problems
- A fuel contains 3 × 10⁶ J and engine efficiency is 20%. Find power output in 15 s.
- Generator consumes 1.2 × 10⁷ J of energy in 2 min at 35% efficiency. Find output power.
- A car travels using fuel releasing 4 × 10⁶ J in 20 s. Engine efficiency is 30%. Calculate useful power.
- A device converts 60% of fuel energy into work. If it uses 5 × 10⁵ J in 10 s, find output power.
- An engine outputs 2 × 10^5 W, fuel input 1 × 10^6 J in 8 s. Find efficiency.