combustion of municipal solid waste in a waste-to-energy facility Given heat released (Q_fuel) = 326,400 kJ; mass of fuel burned (m_fuel) = 312.0 kg, determine the higher heating value (HHV) in kJ/kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except HHV is given, so isolate HHV symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for HHV:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 326,400 kJ, mass of fuel burned (m_fuel) = 312.0 kg.

4. Step 4 — Substitute the given values:

   $$HHV = \dfrac{326400}{312.0}$$

5. Step 5 — Evaluate:

   $$HHV = 1046\ \text{kJ/kg}$$

6. Step 6 — Check: returning HHV = 1,046 kJ/kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,092 — kept a factor of two that cancels in the correct rearrangement.
• 523.1 — dropped that same factor in the other direction.
• 1,151 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion heating value calculation for a fuel sample Given mass of fuel burned (m_fuel) = 901.0 kg; higher heating value (HHV) = 37,990 kJ/kg, determine the heat released (Q_fuel) in kJ.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except Q_fuel is given, so isolate Q_fuel symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for Q_fuel:

   $$Q_{fuel} = HHV\,m_{fuel}$$

3. Step 3 — List the givens: mass of fuel burned (m_fuel) = 901.0 kg, higher heating value (HHV) = 37,990 kJ/kg.

4. Step 4 — Substitute the given values:

   $$Q_{fuel} = 37990\,901.0$$

5. Step 5 — Evaluate:

   $$Q_{fuel} = 34228990\ \text{kJ}$$

6. Step 6 — Check: returning Q_fuel = 34,228,990 kJ to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 68,457,980 — kept a factor of two that cancels in the correct rearrangement.
• 17,114,495 — dropped that same factor in the other direction.
• 37,651,889 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion energy release computed from fuel mass and heating value Given heat released (Q_fuel) = 1,994,400 kJ; higher heating value (HHV) = 25,450 kJ/kg, determine the mass of fuel burned (m_fuel) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except m_fuel is given, so isolate m_fuel symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for m_fuel:

   $$m_{fuel} = \dfrac{Q_{fuel}}{HHV}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 1,994,400 kJ, higher heating value (HHV) = 25,450 kJ/kg.

4. Step 4 — Substitute the given values:

   $$m_{fuel} = \dfrac{1994400}{25450}$$

5. Step 5 — Evaluate:

   $$m_{fuel} = 78.3654\ \text{kg}$$

6. Step 6 — Check: returning m_fuel = 78.3654 kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 156.7 — kept a factor of two that cancels in the correct rearrangement.
• 39.1827 — dropped that same factor in the other direction.
• 86.2020 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion of municipal solid waste in a waste-to-energy facility Given heat released (Q_fuel) = 3,555,600 kJ; mass of fuel burned (m_fuel) = 646.0 kg, determine the higher heating value (HHV) in kJ/kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except HHV is given, so isolate HHV symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for HHV:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 3,555,600 kJ, mass of fuel burned (m_fuel) = 646.0 kg.

4. Step 4 — Substitute the given values:

   $$HHV = \dfrac{3555600}{646.0}$$

5. Step 5 — Evaluate:

   $$HHV = 5504\ \text{kJ/kg}$$

6. Step 6 — Check: returning HHV = 5,504 kJ/kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 11,008 — kept a factor of two that cancels in the correct rearrangement.
• 2,752 — dropped that same factor in the other direction.
• 6,054 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion heating value calculation for a fuel sample Given mass of fuel burned (m_fuel) = 710.0 kg; higher heating value (HHV) = 28,590 kJ/kg, determine the heat released (Q_fuel) in kJ.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except Q_fuel is given, so isolate Q_fuel symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for Q_fuel:

   $$Q_{fuel} = HHV\,m_{fuel}$$

3. Step 3 — List the givens: mass of fuel burned (m_fuel) = 710.0 kg, higher heating value (HHV) = 28,590 kJ/kg.

4. Step 4 — Substitute the given values:

   $$Q_{fuel} = 28590\,710.0$$

5. Step 5 — Evaluate:

   $$Q_{fuel} = 20298900\ \text{kJ}$$

6. Step 6 — Check: returning Q_fuel = 20,298,900 kJ to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 40,597,800 — kept a factor of two that cancels in the correct rearrangement.
• 10,149,450 — dropped that same factor in the other direction.
• 22,328,790 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion energy release computed from fuel mass and heating value Given heat released (Q_fuel) = 4,998,000 kJ; higher heating value (HHV) = 41,070 kJ/kg, determine the mass of fuel burned (m_fuel) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except m_fuel is given, so isolate m_fuel symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for m_fuel:

   $$m_{fuel} = \dfrac{Q_{fuel}}{HHV}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 4,998,000 kJ, higher heating value (HHV) = 41,070 kJ/kg.

4. Step 4 — Substitute the given values:

   $$m_{fuel} = \dfrac{4998000}{41070}$$

5. Step 5 — Evaluate:

   $$m_{fuel} = 121.7\ \text{kg}$$

6. Step 6 — Check: returning m_fuel = 121.7 kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 243.4 — kept a factor of two that cancels in the correct rearrangement.
• 60.8473 — dropped that same factor in the other direction.
• 133.9 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion of municipal solid waste in a waste-to-energy facility Given heat released (Q_fuel) = 3,857,700 kJ; mass of fuel burned (m_fuel) = 500.0 kg, determine the higher heating value (HHV) in kJ/kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except HHV is given, so isolate HHV symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for HHV:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 3,857,700 kJ, mass of fuel burned (m_fuel) = 500.0 kg.

4. Step 4 — Substitute the given values:

   $$HHV = \dfrac{3857700}{500.0}$$

5. Step 5 — Evaluate:

   $$HHV = 7715\ \text{kJ/kg}$$

6. Step 6 — Check: returning HHV = 7,715 kJ/kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 15,431 — kept a factor of two that cancels in the correct rearrangement.
• 3,858 — dropped that same factor in the other direction.
• 8,487 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion heating value calculation for a fuel sample Given mass of fuel burned (m_fuel) = 527.0 kg; higher heating value (HHV) = 44,840 kJ/kg, determine the heat released (Q_fuel) in kJ.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except Q_fuel is given, so isolate Q_fuel symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for Q_fuel:

   $$Q_{fuel} = HHV\,m_{fuel}$$

3. Step 3 — List the givens: mass of fuel burned (m_fuel) = 527.0 kg, higher heating value (HHV) = 44,840 kJ/kg.

4. Step 4 — Substitute the given values:

   $$Q_{fuel} = 44840\,527.0$$

5. Step 5 — Evaluate:

   $$Q_{fuel} = 23630680\ \text{kJ}$$

6. Step 6 — Check: returning Q_fuel = 23,630,680 kJ to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 47,261,360 — kept a factor of two that cancels in the correct rearrangement.
• 11,815,340 — dropped that same factor in the other direction.
• 25,993,748 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion energy release computed from fuel mass and heating value Given heat released (Q_fuel) = 567,200 kJ; higher heating value (HHV) = 10,220 kJ/kg, determine the mass of fuel burned (m_fuel) in kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except m_fuel is given, so isolate m_fuel symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for m_fuel:

   $$m_{fuel} = \dfrac{Q_{fuel}}{HHV}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 567,200 kJ, higher heating value (HHV) = 10,220 kJ/kg.

4. Step 4 — Substitute the given values:

   $$m_{fuel} = \dfrac{567200}{10220}$$

5. Step 5 — Evaluate:

   $$m_{fuel} = 55.4990\ \text{kg}$$

6. Step 6 — Check: returning m_fuel = 55.4990 kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 111.0 — kept a factor of two that cancels in the correct rearrangement.
• 27.7495 — dropped that same factor in the other direction.
• 61.0489 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion

combustion of municipal solid waste in a waste-to-energy facility Given heat released (Q_fuel) = 2,621,300 kJ; mass of fuel burned (m_fuel) = 971.0 kg, determine the higher heating value (HHV) in kJ/kg.

Start with the thinking

• The governing relation printed in this handbook section is Combustion.
• Everything except HHV is given, so isolate HHV symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Combustion of solid waste or fuel releases heat quantified by the higher heating value per unit mass of fuel.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

2. Step 2 — Rearrange symbolically for HHV:

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

3. Step 3 — List the givens: heat released (Q_fuel) = 2,621,300 kJ, mass of fuel burned (m_fuel) = 971.0 kg.

4. Step 4 — Substitute the given values:

   $$HHV = \dfrac{2621300}{971.0}$$

5. Step 5 — Evaluate:

   $$HHV = 2700\ \text{kJ/kg}$$

6. Step 6 — Check: returning HHV = 2,700 kJ/kg to

   $$HHV = \dfrac{Q_{fuel}}{m_{fuel}}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5,399 — kept a factor of two that cancels in the correct rearrangement.
• 1,350 — dropped that same factor in the other direction.
• 2,970 — rounded an intermediate value before the final step.

Reference: FE Handbook — Combustion