The plant producing aluminium drinks cans generates about 19 tonnes of paper and cardboard waste a year. This goes to a waste-to-energy power station, which has an overall efficiency of 28%. If the heat of combustion of the paper and cardboard is 12.0 MJ kg-1, calculate the amount of useful electrical energy generated each year by burning the waste. *Explain your working and give your answer in units of MJ to two significant figures*.

To calculate the amount of useful electrical energy generated by burning the waste, we'll break the problem into steps.

### Given Data:
1. **Amount of waste**: 19 tonnes of paper and cardboard waste per year
   - Convert tonnes to kilograms: 
     \[
     1 \text{ tonne} = 1000 \text{ kg}, \quad 19 \text{ tonnes} = 19,000 \text{ kg}
     \]
2. **Heat of combustion**: 12.0 MJ per kg of paper and cardboard
3. **Efficiency of the power station**: 28% (which is 0.28 in decimal)

### Step 1: Calculate the total energy released by burning the waste

The total energy released by burning all the waste is the product of the mass of the waste and the heat of combustion:
\[
\text{Total energy released} = \text{mass} \times \text{heat of combustion}
\]
\[
\text{Total energy released} = 19,000 \text{ kg} \times 12.0 \text{ MJ/kg} = 228,000 \text{ MJ}
\]

### Step 2: Calculate the useful electrical energy

The useful electrical energy is obtained by multiplying the total energy released by the efficiency of the power station:
\[
\text{Useful energy} = \text{Total energy released} \times \text{efficiency}
\]
\[
\text{Useful energy} = 228,000 \text{ MJ} \times 0.28 = 63,840 \text{ MJ}
\]

### Step 3: Round to two significant figures

Rounding 63,840 MJ to two significant figures gives:
\[
\text{Useful energy} \approx 64,000 \text{ MJ}
\]

### Final Answer:
The amount of useful electrical energy generated each year by burning the waste is **64,000 MJ**.

---

Would you like more details or have any questions? Here are 5 related questions for further exploration:

1. How would the useful energy change if the efficiency of the power station increased to 35%?
2. What is the total energy released if only half of the waste is burned?
3. How would different heat of combustion values (e.g., for different types of waste) affect the energy output?
4. How can the plant reduce its overall waste production to lessen environmental impact?
5. How does the efficiency of this waste-to-energy process compare to other forms of energy generation?

**Tip**: Always ensure that the units are consistent throughout the calculation to avoid errors.

The plant producing aluminium drinks cans generates about 19 tonnes of paper and cardboard waste a year. This goes to a waste-to-energy power station, which has an overall efficiency of 28%. If the heat of combustion of the paper and cardboard is 12.0 MJ kg-1, calculate the amount of useful electrical energy generated each year by burning the waste. Explain your working and give your answer in units of MJ to two significant figures.

Calculate the useful electrical energy generated from 19 tonnes of paper and cardboard waste in a waste-to-energy power station with 28% efficiency. Learn how to use heat of combustion and efficiency formulas to determine the energy output, with a detailed step-by-step solution. Suitable for Grades 10-12.

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