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 38°C by a 19 kiloton atomic bomb.
heat=masswater*specificheatwater*38
but heat=19kiloton*4.2E12J/kiloton
so if you set them equal, and for c use units of J/kgC, solve for mass.
To calculate the number of kilograms of water that can be heated through 38°C by a 19 kiloton atomic bomb, we can use the following steps:
Step 1: Calculate the total energy released by the 19 kiloton atomic bomb.
The given kiloton value is equal to 4.2 ✕ 10^12 J. Therefore, multiplying this value by 19 will give us the energy released by the 19 kiloton atomic bomb.
Total energy released = (4.2 ✕ 10^12 J) × 19
Step 2: Convert the total energy released to kilocalories.
Since we know that 4184 joules is equal to 1 kilocalorie, we can divide the total energy released (in joules) by 4184 to convert it to kilocalories.
Total energy in kilocalories = (Total energy released) / 4184
Step 3: Calculate the amount of water that can be heated.
Given that 1 kilocalorie of energy raises the temperature of 1 kg of water by 1°C, the total energy in kilocalories calculated in Step 2 represents the amount of heat required to raise the temperature of the water.
Amount of water = Total energy in kilocalories / 38
Let's plug in the values:
Total energy released = (4.2 ✕ 10^12 J) × 19
Total energy in kilocalories = (Total energy released) / 4184
Amount of water = Total energy in kilocalories / 38
By performing these calculations, we can determine the number of kilograms of water that can be heated through 38°C by a 19 kiloton atomic bomb.