Question

A farmer has a herd of 100 cows, and wishes to use their waste to produce methane (a gaseous fuel) and then generate some can be converted into electricity for the farm. Assume each cow generates 2 kg waste per day, which yields 1.5 mA3 of methane. The energy content in methane is 40 MJ/mA3. Assume 25% of the energy can be converted into electricity, how much electricity energy (j) can be generated in one day? What is average power (W) of the electricity generation?

Answer 1

from the waste of each cow 1.5m³ of methane can be obtained, that means you have 100(1.5)=150m³ of methane, now we multiply that with the energy content to obtain the total energy obtained in a day; energy obtained=40(150)=6,000 MJ (note volume units cancel out).

If we mutiply the efficiency factor we obtain the real enery generated; 0.25(6000)=1500MJ or 1,500,000,000 J , that's the energy you get in a day.

the average power can be calculated like this: J/t when J is energy and t is the time interval (a day has 86,400 seconds) so the average power will be: 1500/86400 which is 0.017MW or 17,000 W