Final answer:
The D-D fusion energy available in 1 kg of water could provide the energy needs of a house with an average power consumption of 10 kW for approximately 1.33 years.
Step-by-step explanation:
To estimate the available D-D fusion energy in 1 kg of water, we need to understand that water contains deuterium (D), a stable isotope of hydrogen with a natural abundance of approximately 0.0115%, or about 1 part in 6,500 of hydrogen in water. For 1 kg of water, this would be roughly 0.000115 kg or 115 mg of deuterium. Deuterium-deuterium (D-D) fusion releases an energy of approximately 3.65 x 1014 joules per kilogram of deuterium fused.
Therefore, the amount of energy available from D-D fusion in 115 mg of deuterium would be:
Energy = 115 mg / 1,000,000 mg/kg * 3.65 x 1014 J/kg = 4.1975 x 1010 J
If all this energy is converted to electricity with 100% efficiency, a house with an average power consumption of 10 kW (or 10,000 watts) would use energy at the rate of:
Energy consumption rate = Power consumption * Time
Energy = 10 kW * 3,600 s/h = 36,000 kJ/h
To find out how long the D-D fusion energy would last, we divide the total energy by the consumption rate:
Duration = Total energy / Energy consumption rate
Duration = 4.1975 x 1010 J / (10 kW * 3,600 s/h)
Duration = 4.1975 x 107 seconds
Converting seconds to hours:
Duration = 4.1975 x 107 s / 3,600 s/h = 11,660 hours
Finally, converting hours to years (using 8,760 hours per year as an approximation for a non-leap year):
Duration = 11,660 hours / 8,760 hours/year = approximately 1.33 years
Thus, 1 kg of water, through complete D-D fusion, could power a house with a 10 kW average power consumption for about 1.33 years.