Randall D. Knight — Work, Heat, and the First Law of Thermodynamics: Problem 79

A lava flow is threatening to engulf a small town. A 400-m-wide, 35-cm-thick tongue of \(1200^{\circ}\text{C}\) lava is advancing at the rate of \(1.0\text{ m per minute}\). The mayor devises a plan to stop the lava in its tracks by flying in large quantities of \(20^{\circ}\text{C}\) water and dousing it. The lava has density \(2500\text{ kg/m}^3\), specific heat \(1100\text{ J/kg K}\), melting temperature \(800^{\circ}\text{C}\), and heat of fusion \(4.0 \times 10^5\text{ J/kg}\). How many liters of water per minute, at a minimum, will be needed to save the town?