Physical Chemistry Question

In summary, we calculated the electrical energy produced by burning 1 pound of coal to be 24139 W-hrs, assuming an efficiency of 41%. The estimated temperature at which the coal burns is 277°C.
  • #1
chrisama
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Homework Statement



The chemical reaction in which C and 02 (Dioxide) form Carbon dioxide produces 4.1 eV (Electron-Volts) of energy per Carbon atom. How much electrical energy, in W-hrs, is produced by burning a pound of coal? Here are all the conversions:

1kg.=2.2 pounds
1 mole of carbon= 12X10^-3 kg
1 mole=6X10^23 atoms
1eV=1.6X10^-19 J
1W/hr==3600J

Take the efficiency of conversion from chemical energy to electrical energy to be N=0.41(N represents efficiency). Compare your answer for the available energy to the one we found in class. Assuming that the cold reservoir for the particular heat engine used is at 20C, estimate the temperature at which the coal burns. Note that these calculations connect energy production in a coal plant all the way to fundamental chemistry and physics.

Homework Equations



E (generator)= η (total efficiency) x E (coal). But I'm almost sure that this is the wrong equation.


The Attempt at a Solution


I'm drawing a blank. Could someone please guide me?
 
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  • #2


Hello there,

First, let's start by converting the given information into SI units for easier calculation.

1 pound = 0.45359237 kg
1 mole of carbon = 12 x 10^-3 kg = 0.012 kg
1 mole = 6 x 10^23 atoms
1 eV = 1.6 x 10^-19 J
1 W-hr = 3600 J

Now, let's calculate the energy produced per kg of carbon burned:

4.1 eV/atom x 1.6 x 10^-19 J/eV x 6 x 10^23 atoms/mole x 0.012 kg/mole = 4.67 x 10^8 J/kg

Next, we need to calculate the total energy produced by burning 1 pound (0.45359237 kg) of coal:

4.67 x 10^8 J/kg x 0.45359237 kg = 2.12 x 10^8 J

Now, we can use the given efficiency (N = 0.41) to calculate the electrical energy produced:

E (generator) = N x E (coal)
E (generator) = 0.41 x 2.12 x 10^8 J = 8.69 x 10^7 J

To convert this into W-hrs, we divide by 3600 (since 1 W-hr = 3600 J):

8.69 x 10^7 J / 3600 = 24139 W-hrs

This is the electrical energy produced by burning 1 pound of coal. Now, let's compare it to the energy we found in class. I'm not sure what energy you found in class, so I'll just continue with the calculations assuming it is the same as what we found here.

Assuming the cold reservoir is at 20°C, we can use the Carnot efficiency formula to estimate the temperature at which the coal burns:

N = 1 - T_cold/T_hot
0.41 = 1 - (293 K / T_hot)
T_hot = 550 K = 277°C

This means that the coal is burning at a temperature of approximately 277°C.

I hope this helps guide you in solving the problem. Let me know if you have any further questions.
 
  • #3


I would approach this problem by first identifying the key information and equations needed to solve it. The given information includes the chemical reaction of C + O2 → CO2, the energy produced per Carbon atom (4.1 eV), and various conversion factors. The equation for converting electrical energy to power (W/hr) is also provided.

The first step would be to convert the given information into a form that can be used in the equation. This would involve converting the given energy per Carbon atom (4.1 eV) into Joules (J), as this is the unit used in the equation for electrical energy. Using the conversion factor of 1eV = 1.6x10^-19 J, we can calculate that 4.1 eV is equivalent to 6.56x10^-19 J.

Next, we need to determine the amount of Carbon atoms in a pound of coal. Using the given conversion factor of 1 mole = 6x10^23 atoms and the information that 1 mole of Carbon = 12x10^-3 kg, we can calculate that there are 1.83x10^23 atoms of Carbon in a pound of coal.

Now, we can use the equation E (generator) = η (total efficiency) x E (coal) to calculate the electrical energy produced by burning a pound of coal. The total efficiency (η) is given as 0.41, so we can plug in the values and solve for E (generator).

E (generator) = 0.41 x (1.83x10^23 atoms) x (6.56x10^-19 J) = 5.08x10^4 J

Next, we need to convert this energy value into power (W/hr). Using the given conversion factor of 1W/hr = 3600 J, we can calculate that 5.08x10^4 J is equivalent to 14.11 W/hr.

Finally, we are asked to estimate the temperature at which the coal burns, assuming a cold reservoir temperature of 20C. This can be done using the Carnot efficiency formula, η = 1 - (Tc/Th). Solving for Th (the hot reservoir temperature), we get Th = Tc/ (1-η) = (293 K)/ (1-0.41) = 497 K.

In conclusion, using the
 

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