Two pieces of ice, of equal mass and moving towards each other with the same velocity, collide head on and are vaporised due to this collision. Find out the minimum initial velocity of the pieces of ice. Given, initial temperature, specific heat and latent heat of fusion of ice are `-12^(@)C, 0.5 cal cdot g^(-1) cdot^(@)C^(-1)` and `80cal cdot^(@)g^(-1)` respectively, latent heat of steam is `540 cal cdot g^(-1)`.

Explanation

Let m = mass of each piece of ice, v = minimum initial velocity.
Here, work done due to collision, W
= loss in kinetic energy = `2 xx 1/2 mv^(2) = mv^(2)`
Heat produced , H
`=2 [m xx 0.5 xx 12 + m xx 80 + m xx 1 xx 100 + m xx 540]`
`= 1452 m cal`
`W = JH or, mv^(2) = J xx 1452 m`
or, `v^(2) = (4.2 xx 10^(7)) xx 1452 = 6.1 xx 10^(10)`
So, `v = 2.47 xx 10^(5) cm cdot s^(-1) = 2.47km cdot s^(-1)`.