Question

The total volume of the Pacific Ocean is estimated to be 7.2 × 10⁸ km³. A medium-sized atomic bomb produces 1.0 × 10¹⁵ J of energy upon explosion. Calculate the number of atomic bombs needed to release enough energy to raise the temperature of the water in the Pacific Ocean by 1°C.

Answer 1

Approximately 3.01 × 10⁴ atomic bombs would be needed to raise the temperature of the Pacific Ocean by 1°C, using the specific heat capacity of water and the total mass of the ocean water.

Step-by-step explanation:

The student has asked to calculate the number of atomic bombs needed to raise the temperature of the water in the Pacific Ocean by 1°C, given that the ocean's volume is 7.2 × 10⁸ km³ and a medium-sized atomic bomb releases 1.0 × 10¹⁵ J of energy.

To answer this question, we need the specific heat capacity of water, which is approximately 4.186 J/g·°C. The mass of the ocean's water can be found by multiplying the volume by the density of water (1 g/cm³ or 1 kg/L). Given that 1 km³ equals 1 × 10¹⁵ L, we have:

Mass of ocean water = 7.2 × 10⁸ km³ × 1 × 10¹⁵ L/km³ × 1 kg/L = 7.2 × 10¹⁵ kg.