CALCU-The assay of particular coal from Illinois i

Solution by Steps

step 1

To find the higher heating value (HHV) of the coal, we use the formula:

\text{HHV} = 33.94 \times \text{C} + 144.45 \times (\text{H} - \frac{\text{O}}{8}) + 9.16 \times \text{S}

where C, H, O, and S are the mass percentages of carbon, hydrogen, oxygen, and sulfur, respectively

step 2

Substitute the given values into the formula:

\text{C} = 67.40\%, \text{H} = 5.31\%, \text{O} = 15.11\%, \text{S} = 2.36\%

\text{HHV} = 33.94 \times 67.40 + 144.45 \times (5.31 - \frac{15.11}{8}) + 9.16 \times 2.36

step 3

Calculate the intermediate values:

33.94 \times 67.40 = 2287.196

144.45 \times (5.31 - 1.88875) = 144.45 \times 3.42125 = 494.073

9.16 \times 2.36 = 21.6176

step 4

Sum the intermediate values to find the HHV:

\text{HHV} = 2287.196 + 494.073 + 21.6176 = 2802.8866 \, \text{kJ/kg}

step 5

To find the lower heating value (LHV), we use the formula:

\text{LHV} = \text{HHV} - 2.447 \times \text{H}

Substitute the values:

\text{LHV} = 2802.8866 - 2.447 \times 5.31

\text{LHV} = 2802.8866 - 12.99357 = 2789.89303 \, \text{kJ/kg}

Answer

The higher heating value (HHV) of the coal is approximately 2802.89 kJ/kg, and the lower heating value (LHV) is approximately 2789.89 kJ/kg.

Key Concept

Higher and Lower Heating Values

Explanation

The higher heating value (HHV) represents the total energy released when the coal is burned, including the latent heat of vaporization of water. The lower heating value (LHV) excludes this latent heat, providing a measure of the usable energy.

Solution by Steps

step 1

Calculate the annual electricity consumption difference between the old and new refrigerators:

1500 \, \text{kWh} - 375 \, \text{kWh} = 1125 \, \text{kWh}

step 2

Calculate the annual cost savings by multiplying the difference in electricity consumption by the cost per kWh:

1125 \, \text{kWh} \times 0.12 \, \text{RM/kWh} = 135 \, \text{RM}

step 3

Calculate the annual CO₂ emissions avoided by multiplying the difference in electricity consumption by the CO₂ emission factor:

1125 \, \text{kWh} \times 0.7 \, \text{kg/kWh} = 787.5 \, \text{kg}

Answer

The household will save 135 RM per year and avoid 787.5 kg of CO₂ emissions per year.

Key Concept

Energy savings and CO₂ emissions reduction

Explanation

By replacing an old refrigerator with a more energy-efficient model, the household reduces its electricity consumption, leading to cost savings and a reduction in CO₂ emissions.

Generated Graph

Solution by Steps

step 1

To determine the simple payback period, we divide the initial cost of the solar collector by the annual savings

step 2

The initial cost is RM650 and the annual savings are RM375. Therefore, the simple payback period is calculated as follows:

\text{Simple Payback Period} = \frac{650}{375} = 1.7333 \text{ years}

step 3

To determine the discounted payback period, we need to account for the interest rate of 7%. The formula for the discounted payback period is:

\text{Discounted Payback Period} = \frac{\text{Initial Cost}}{\text{Annual Savings} - (\text{Interest Rate} \times \text{Initial Cost})}

step 4

Plugging in the values, we get:

\text{Discounted Payback Period} = \frac{650}{375 - (0.07 \times 650)} = \frac{650}{375 - 45.5} = \frac{650}{329.5} \approx 1.973 \text{ years}

Answer

The simple payback period is approximately 1.7333 years, and the discounted payback period is approximately 1.973 years.

Key Concept

Payback Period Calculation

Explanation

The simple payback period is calculated by dividing the initial cost by the annual savings. The discounted payback period accounts for the interest rate, adjusting the annual savings accordingly.

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