Thermal Physics - Methane Fuel Cell

In summary, the conversation discusses a fuel cell that uses methane as fuel. The chemical reaction involved is CH4 + 2O2 = 2H2O + CO2 + energy. The conversation covers various aspects of the fuel cell, such as estimating the change in volume during the reaction, determining the change in entropy and Gibbs free energy, calculating the electrical work and waste heat for each mole of methane fuel, and discussing the theoretical maximum efficiency of the fuel cell. The conversation also explores the two simultaneous steps of the chemical reaction and calculates the electrical work per electron and the voltage of the fuel cell.
  • #1
phil ess
70
0
I think I got a and b, the rest I did my best on, and I could use some guidance! Thanks!

Homework Statement



1. [6] Methane (Natural Gas) Fuel Cell.
Consider a fuel cell that uses methane as fuel. The chemical reaction is

CH4 + 2O2 = 2H2O + CO2 + energy

(a) [0.5] Measurements reveal that deltaH for this reaction is -890 kJ for each mole of
methane processed, assuming standard temperature and pressure (T =298 K, P =100 kPa).
Ignoring the volume of the liquid H20, use the ideal gas law to estimate the change in
volume during this reaction, and thus determine the amount of energy we get for “free”
from the collapsing environment.

(b) [2.5] Using the appropriate table at the back of the textbook (or elsewhere), look up
the entropies of the various chemicals involved in the above reaction (at standard
temperature and pressure) and thus compute deltaS, the change in entropy for each mole of methane processed. Thus evaluate deltaG, the change in the Gibbs free energy (at
standard temperature and pressure) for each mole of methane processed.

(c) [0.5] Assuming ideal performance, how much electrical work can you get out of the
cell for each mole of methane fuel?

(d) [1] How much waste heat must be dumped into the environment for each mole of
methane fuel?

(e) [0.5] What is the theoretical maximum “efficiency" of this fuel cell?

(f) [1] In more detail, the above chemical reaction proceeds in two steps that are
happening simultaneously at the positive and negative electrodes of the fuel cell:

at - electrode CH4 + 2H2O = CO2 + 8H+ + 8e-

at + electrode 202 + 8H+ + 8e- = 4H2O

What this means is that for each methane molecule that reacts, eight electrons are pushed
around the circuit. It takes electrical work to do this. Considering the electrical work
computed in part (c), for one mole of methane, what is the electrical work per electron?
Express your answer in units of electron volts. Considering that 1 volt is the voltage
needed to give an electron 1 eV of energy, what is the voltage of the fuel cell?

Homework Equations



Lots

The Attempt at a Solution



a)

[tex]P \Delta V= \Delta n R T[/tex]

[tex]\Delta V = \Delta n R T / P[/tex]

We are going from 3 moles of gas to 1 mole:

[tex]\Delta V = -2 R T / P = -0.0496 L[/tex]

b)

[tex]\Delta S = \Delta S_{products} - \Delta S_{reactants} = [213.7+2(69.91)] - [2(205.1)+186.3] = -242.98 J/K[/tex]

I got the entropy values from my textbook

Then

[tex]\Delta G = \Delta H - T\Delta S = -890000 - 298(-242.98) = 817592 J[/tex]

c)

[tex]W = \Delta H = 890 kJ[/tex] ?

I'm just using the enthalpy of the reaction, which is the amount of heat released, so assuming it is all converted to useful work? Is this correct?

d)

Here I'm tempted to just use [tex]W = P \Delta V[/tex], since that is the amount of work the system does on the environment in expanding... ie the heat released to the environment?? Nevermind, I just saw that the volume is decreasing!

e)

If I can get the one before then this is easy:

[tex]e = workdone / heatsupplied = 1 - Qh / Qc[/tex]

right?

f)

Assuming c) is correct, then I just divide by 8 to get the work per electron, then convert to eV.
Thanks so much for any help you can offer!
 
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  • #2
Replying so that this thread isn't a no-reply, as per Greg's wishes.
If anyone has knowledge on this subject, feel free to reply.
 
  • #3
phil ess said:
I think I got a and b, the rest I did my best on, and I could use some guidance! Thanks!

Homework Statement



1. [6] Methane (Natural Gas) Fuel Cell.
Consider a fuel cell that uses methane as fuel. The chemical reaction is

CH4 + 2O2 = 2H2O + CO2 + energy

(a) [0.5] Measurements reveal that deltaH for this reaction is -890 kJ for each mole of
methane processed, assuming standard temperature and pressure (T =298 K, P =100 kPa).
Ignoring the volume of the liquid H20, use the ideal gas law to estimate the change in
volume during this reaction, and thus determine the amount of energy we get for “free”
from the collapsing environment.

(b) [2.5] Using the appropriate table at the back of the textbook (or elsewhere), look up
the entropies of the various chemicals involved in the above reaction (at standard
temperature and pressure) and thus compute deltaS, the change in entropy for each mole of methane processed. Thus evaluate deltaG, the change in the Gibbs free energy (at
standard temperature and pressure) for each mole of methane processed.

(c) [0.5] Assuming ideal performance, how much electrical work can you get out of the
cell for each mole of methane fuel?

(d) [1] How much waste heat must be dumped into the environment for each mole of
methane fuel?

(e) [0.5] What is the theoretical maximum “efficiency" of this fuel cell?

(f) [1] In more detail, the above chemical reaction proceeds in two steps that are
happening simultaneously at the positive and negative electrodes of the fuel cell:

at - electrode CH4 + 2H2O = CO2 + 8H+ + 8e-

at + electrode 202 + 8H+ + 8e- = 4H2O

What this means is that for each methane molecule that reacts, eight electrons are pushed
around the circuit. It takes electrical work to do this. Considering the electrical work
computed in part (c), for one mole of methane, what is the electrical work per electron?
Express your answer in units of electron volts. Considering that 1 volt is the voltage
needed to give an electron 1 eV of energy, what is the voltage of the fuel cell?

Homework Equations



Lots

The Attempt at a Solution



a)

[tex]P \Delta V= \Delta n R T[/tex]

[tex]\Delta V = \Delta n R T / P[/tex]

We are going from 3 moles of gas to 1 mole:

[tex]\Delta V = -2 R T / P = -0.0496 L[/tex]

b)

[tex]\Delta S = \Delta S_{products} - \Delta S_{reactants} = [213.7+2(69.91)] - [2(205.1)+186.3] = -242.98 J/K[/tex]

I got the entropy values from my textbook

Then

[tex]\Delta G = \Delta H - T\Delta S = -890000 - 298(-242.98) = 817592 J[/tex]
Your sign of ##\Delta G## is incorrect. It should be ##\Delta G=-817592\ J/mole##. This is minus the maximum amount of electrical work (non-PV work) that can be obtained from the cell per mole.
phil ess said:
c)

[tex]W = \Delta H = 890 kJ[/tex] ?

I'm just using the enthalpy of the reaction, which is the amount of heat released, so assuming it is all converted to useful work? Is this correct?
No. As I said, the maximum amount of electrical work per mole of methane is 818000 J/mole
 

1. What is a methane fuel cell and how does it work?

A methane fuel cell is a type of fuel cell that uses methane as its fuel source. It works by converting the chemical energy of methane into electrical energy through a process called electrochemical reaction. This involves the oxidation of methane at the anode, which releases electrons that then flow through an external circuit to produce electricity.

2. What are the advantages of using methane fuel cells?

One of the main advantages of methane fuel cells is that they produce significantly less emissions compared to traditional combustion engines. They also have a higher efficiency, meaning they can convert a greater percentage of the fuel's energy into electricity. Additionally, methane is a widely available and relatively inexpensive fuel source, making it a practical option for energy production.

3. How does thermal physics play a role in methane fuel cells?

Thermal physics is essential in understanding the behavior and efficiency of methane fuel cells. The electrochemical reactions that take place in the fuel cell are influenced by temperature, and the heat generated during these reactions must be managed to prevent damage to the cell. Additionally, the thermodynamics of the system must be carefully considered to maximize the efficiency of the fuel cell.

4. What are the limitations of methane fuel cells?

One of the main limitations of methane fuel cells is the need for a constant supply of oxygen to sustain the electrochemical reactions. This can be challenging to maintain in certain environments, such as in space or underwater. Additionally, methane is a flammable gas, so safety measures must be in place to prevent any potential hazards.

5. How are methane fuel cells being used in real-world applications?

Methane fuel cells are being used in a variety of applications, including transportation, power generation, and portable devices. They are commonly used in buses, forklifts, and other vehicles that require a reliable and efficient power source. They are also being integrated into renewable energy systems, such as solar and wind, to store excess energy for later use. In addition, portable methane fuel cells are being developed for use in remote or off-grid locations.

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