Question

1) Assume that the annual US power consumption is 2.5 1020 Joules. If this energy could be supplied by combining pure matter and antimatter estimate the total mass (antimatter + matter) that would be required to power the US for 1 year. Compare this with the mass of fuel in your car's gas tank (assume fuel has a density of 0.75 kg per litre)

Answer 1

Annual US power Consumption 2.5 times 10^20 joules In the Reaction of matter & antimatter (like electrons & positrons) all the mass Convert into energy & they will disappear. So according to Einstein formula n E = mc^2 we need E = 2.5 times 10^20 Joules for 1 year E = mc^2 2.5 times 10^20 = mc^2 m = 2.5 times 10^20/(3 times 10^8)^2 m = 2777.78 kg 1 litre Golo line given 34.5 MJ energy 1 like 0.75 kg (for Gaso line) 0.75 kg = 34.5 MJ 1kg = 34.5/0.75 MJ Rightarrow 46 MJ So total foel required E = 2.5 times 10^2 joel foel headed = 2.5 times 10^20/46 times 10^6 = 5434782608695 kg = 5434 times 10^9 kg (approx)