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Data from Dohle et al. (2000).

Data from Dohle et al. (2000).

Consider methanol, a fuel that has been proposed for both internal combustion (IC) engines and fuel cells. Methanol can be derived from fossil fuels and also from biomass. Being liquid at RTP conditions, it is a convenient fuel for automobiles. It has reasonable reactivity in fuel cells.

In IC engines, methanol is first evaporated and then burned. The engine exhausts water vapor. In fuel cells, the methanol reacts in liquid form, but the product water is in vapor form.

1. What heat do you get by burning 1 kg of methanol in an IC engine?

2. How much electric energy will an ideal fuel cell (using methanol and air) produce per kg of fuel?

3. How much heat does the cell reject?

4. A practical Otto cycle engine has an efficiency of, say, 20%, while a practical methanol fuel cell may have an efficiency of 60% (this is the efficiency of the practical cell compared with that of the ideal cell). If a methanol fueled IC car has a highway performance of 10 km per liter, what is the performance of the fuel cell car assuming that all the other characteristics of the car are identical?

5. If you drive 2000 km per month and a gallon of methanol costs $1.20, how much do you save in fuel per year when you use the fuel cell version compared with the IC version? Can you think of other savings besides that in fuel?

6. You get a 10-year loan with yearly repayments of principal plus interest of 18% of the initial amount borrowed. By how much can the initial cost of the fuel-cell car exceed that of the IC car for you to break even? Assume that after 10 years the car is totally depreciated.

7. What is the open-circuit voltage of an ideal methanol fuel cell at RTP? To answer this question, you need to make an intelligent guess about the number of electrons freed per molecule of methanol.

In the above questions, assume 100% current efficiency and 100% efficiency of the electric motor.

9.5 You want to build a hydrogen manometer based on the dependence of the output voltage on the pressure of the reactants. Take an H2/O2 fuel cell at 298 K. Assume that it produces water vapor and and acts as an ideal cell. The oxygen pressure is maintained at a constant 0.1 MPa while the hydrogen pressure, pH2, is the quantity to be measured.

1. What is the output voltage when pH2 is 0.1 MPa?

2. What is the output voltage when pH2 is 1 MPa?

3. Develop an expression showing the rate of change of voltage with Ph2 . What is this rate of change when pH2 is 0.1 MPa?

4. The output voltage of the cell is sensitive to temperature. Assume that a ±10% uncertainty in pressure measurement can be tolerated (when the pressure is around 1 MPa). In other words, assume that when a voltage corresponding to 1 MPa and 298 K is read, the actual pressure is 0.9 MPa because the temperature of the gases is no longer 298 K. What is the maximum tolerable temperature variation?

9.6 A certain gas, at 105 Pa, has a specific heat given by the expression cp = a + bT + cT2

a = 27.7 kJK-1 kmole-1, b = 0.8 x 10-3 kJ K-2 kmole-1, c = 10-6 kJK-3 kmole-1.

At 298 K, the enthalpy of the gas is 0 and its entropy is 130.0 kJ K-1 kmole-1. What are H, G, and S of the gas (per kilomole) at T = 1000 K and p = 105 Pa? Please calculate with four significant figures.

9.7 A fuel cell has the reactions:

All data are at RTP.

The overall reaction, 2 A2 + B2 =2 A2B, releases 300 MJ per kmole of A2B in a calorimeter. The entropies of the different substances are:

A2 b2

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