One coal sample was analyzed and showed 90% C, 8% hydrogen, and 2% ash. 2.0 gof this coal sample was burned in a bomb calorimeter and the temperature of 2.5Kg water was increased from 25 to 35°C. Calculate the GCV and NCV of coal. Given:Water equivalents the instrument and the latent heat of vaporization are 1500 gand 580 cal/g, respectively.
Question
One coal sample was analyzed and showed 90% C, 8% hydrogen, and 2% ash. 2.0 gof this coal sample was burned in a bomb calorimeter and the temperature of 2.5Kg water was increased from 25 to 35°C. Calculate the GCV and NCV of coal. Given:Water equivalents the instrument and the latent heat of vaporization are 1500 gand 580 cal/g, respectively.
Solution
To calculate the Gross Calorific Value (GCV) and Net Calorific Value (NCV) of the coal, we first need to find the heat absorbed by the water and the calorimeter, and then calculate the heat produced by the coal.
Step 1: Calculate the heat absorbed by the water The heat absorbed by the water can be calculated using the formula Q = m * c * ΔT, where m is the mass of the water, c is the specific heat capacity of water (1 cal/g°C), and ΔT is the change in temperature.
Q = 2.5 kg * 1 cal/g°C * (35°C - 25°C) = 2500 g * 1 cal/g°C * 10°C = 25000 cal
Step 2: Calculate the heat absorbed by the calorimeter The heat absorbed by the calorimeter is calculated using the formula Q = m * ΔT, where m is the water equivalent of the calorimeter and ΔT is the change in temperature.
Q = 1500 g * (35°C - 25°C) = 1500 g * 10°C = 15000 cal
Step 3: Calculate the total heat absorbed The total heat absorbed is the sum of the heat absorbed by the water and the calorimeter.
Q_total = 25000 cal + 15000 cal = 40000 cal
Step 4: Calculate the GCV of the coal The GCV of the coal is the total heat absorbed divided by the mass of the coal burned.
GCV = Q_total / m_coal = 40000 cal / 2.0 g = 20000 cal/g
Step 5: Calculate the NCV of the coal The NCV of the coal is the GCV minus the heat of vaporization of the water formed during combustion. The amount of water formed can be calculated from the percentage of hydrogen in the coal, as each gram of hydrogen forms 9 grams of water.
Water formed = 8% * 2.0 g = 0.16 g Heat of vaporization = 0.16 g * 580 cal/g = 92.8 cal
NCV = GCV - Heat of vaporization = 20000 cal/g - 92.8 cal/g = 19907.2 cal/g
So, the GCV of the coal is 20000 cal/g and the NCV is 19907.2 cal/g.
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