Question

A lava flow is threatening to engulf a small town. A 400-m-wide, 35-cm-thick tongue of 1200°C lava is advancing at the rate of 1.0 m per minute. The mayor devises a plan to stop the lava in its tracks by flying in large quantities of 20°C water and dousing it. The lava has density 2500 kg/m3, specific heat 1100 J/kg K, melting temperature 800°C, and heat of fusion 4.0 * 105 J/kg. How many liters of water per minute, at a minimum, will be needed to save the town?

Short answer

The per litre is 11325 litre comes per minute

Step-by-step solution

Defination of boiling point 

At high rate of temperature of water, water turns into vapoure. it is the boiling point of water

Finding of volume 

$Q=m(c∆T+L_e)$

The heat is latent heat temperature

Now at a freeze heat temperature

$Q={\rho }_{w}F(c∆T+L_f)$

therefore, $Q=Wh{\rho }_{l}m(c∆t+L_f)$

Now similar to two-equation

${\rho }_{w}F(c∆T+L_f)=Wh{\rho }_{l}m(c∆t+L_f)$

Applying all values

$$\begin{gathered} {\rho }_{w}F(c∆T+L_f)=Wh{\rho }_{l}m(c∆t+L_f) \\ F=\frac{Wh{\rho }_{l}m(c∆t+L_f)}{(c∆T+L_f){\mathit{\rho }}_{\mathbf{w}}}=\frac{400\times 0.35\times 1\times 2500(1100+\times 400+400000)}{1000\times \left(4200\times 80+2.26\times {10}^6\right)}=11.325m^3/min=11325litre \end{gathered}$$