The kiloton, which is used to measure the energy released in an atomic explosion, is equal to 4.2 ✕ 1012 J (approximately the energy released in the explosion of 1000 tons of TNT). Recalling that 1 kilocalorie of energy raises the temperature of 1 kg of water by 1°C and that 4184 joules is equal to 1 kilocalorie, calculate how many kilograms of water can be heated through 34°C by a 18 kiloton atomic bomb.
To solve this problem, we need to calculate the energy released by the 18 kiloton atomic bomb and then use the energy-water temperature relationship to determine the mass of water that can be heated.
1. Calculate the energy released by the atomic bomb:
Since 1 kiloton is equal to 4.2 ✕ 10^12 J, multiply the energy of 1 kiloton by 18 to find the total energy released by the 18 kiloton atomic bomb:
Total Energy = 4.2 ✕ 10^12 J/kiloton × 18 kilotons
Total Energy = 75.6 ✕ 10^12 J
2. Calculate the energy required to raise the temperature of the water by 34°C:
Since 1 kilocalorie is equal to 4184 J, the energy required to raise the temperature of 1 kg of water by 1°C is 4184 J.
Therefore, the energy required to raise the temperature of 1 kg of water by 34°C is:
Total Energy Required = 4184 J/°C × 34°C
3. Calculate the mass of water that can be heated:
To find the mass of water that can be heated, divide the total energy released by the atomic bomb by the energy required to raise the temperature of the water:
Mass of Water = Total Energy / Total Energy Required
Mass of Water = (75.6 × 10^12 J) / (4184 J/°C × 34°C)
Simplifying the equation, we have:
Mass of Water = (75.6 × 10^12 J) / (4184 J/°C × 34°C)
Mass of Water = 1.638 × 10^9 kg
Therefore, approximately 1.638 × 10^9 kilograms of water can be heated through 34°C by an 18 kiloton atomic bomb.