A sample of anthracite has a moisture content of 5% when mined and an energy density of 35 kJg-1 when completely dried.
Assuming that during combustion, the temperature of the water in the un-dried coal is raised from 20.0oC to 100.oC, and then vaporized at 100.oC, estimate the energy density of the coal when it is mined.
(HINTS: i. use a 100.g sample of coal; ii. find energy needed to vaporize the water in that sample; iii. make sure to keep the units consistent; you’ll need the calorimetry equation, and the latent heat of vaporization for coal.)
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To estimate the energy density of the coal when it is mined, we need to consider the energy required to raise the temperature of the water in the coal to 100°C and then vaporize it.
First, let's calculate the energy needed to raise the temperature of the water in a 100 g sample of coal from 20°C to 100°C. We can use the specific heat capacity equation:
Q = m * c * ΔT
Where:
Q = energy (in joules)
m = mass of the water (in grams)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (100 - 20 = 80°C)
Q = 100 g * 4.18 J/g°C * 80°C = 33440 J
Next, we need to determine the energy required to vaporize the water in the coal. We can use the latent heat of vaporization equation:
Q = m * Lv
Where:
Q = energy (in joules)
m = mass of the water (in grams)
Lv = latent heat of vaporization for coal (specific to anthracite)
The latent heat of vaporization for anthracite coal can typically be found in reference books or online sources. Let's assume a hypothetical value of 2.5 kJ/g (2500 J/g) for Lv.
Q = 100 g * 2500 J/g = 250000 J
Now, let's add the energy required to raise the temperature and vaporize the water in the coal:
Total energy = 33440 J + 250000 J = 283440 J
Finally, we can calculate the energy density of the coal when it is mined. Given that the sample is 100 g and the total energy is 283440 J:
Energy density = Total energy / Mass of coal
Energy density = 283440 J / 100 g = 2834.4 J/g
Therefore, the estimated energy density of the coal when it is mined is approximately 2834.4 J/g.