Estimate how much energy can be produced in an ideal (i.e. loss-less) fuel cell

Question

Estimate how much energy can be produced in an ideal (i.e. loss-less) fuel cell per 1 kg of Hydrogen gas used. (The potential of the fuel cell is 1.23 V and the molecular weight of H2 is 2 g/mol) a) b) Notice how the energy produced per weight of fuel in this case compare to the battery above -this is a major advantage of Hydrogen. The Tesla model S electric car is running on batteries that carry 76 KWh when fully charged. If we were to replace the battery pack with a Hydrogen fuel cell, how much fuel would we need to provide the same amount of energy? c) d) At atmospheric pressure, the density of hydrogen gas is 0.08 g/L. Convert your calculation in (c) to volume. If this was included in a spherical balloon, what would be the radius of the balloon? (This is why we need pressurized Hydrogen tanks!) e) The density of liquid Hydrogen is 0.07 g/cm3. How much volume of liquid Hydrogen do we need to power our Tesla? (This is why liquified Hydrogen is one of the ways to store it as a fuel!) Disclaimer: the units of density have not been changed deliberately to confuse you. They are given in the commonly used units of g/L for gases and g/cm3 for liquids.

Explanation / Answer

a. for the ginve fuel cell

V = 1.23 V

charge on 2 protons = 2e

hence

work done inmoving the protons = 2eV

hence

work per unit fuel mass = 2eV/M

M = 2 g / mol = 2*10^-3 kg/6.022*10^23 molecules

hence

specific work

Ws = 118.51296 MJ / kg

b. this specific energy, theoretical of the fule cell is too much as compared to energy density inside the b atery ( like Li ionbattery has battery energy density of 432 J per g = 0.432 MJ per kg)

c. tesla battery

E = 76 kWh = 76*100W*3600 s= 273.6 MJ

for the same energy stored in fuel cell

mass of fuel required = 273.6/118.51296 = 2.3086 kg

d. rho = 0.08 g/L

volume of baloon = V

rho = m/V

V = m/rho = 2.3086*1000/0.08 = 28857.603 l

e. rho = 0.07 g/cm^3

V = 32980 cm^3 = 32.98 l

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