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# Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were –8 degree Celsius each? (Specific heat of ice is 2100J/kg/K and Latent heat of fusion of ice is $3.36 \times {10^5}J/kg$

Last updated date: 13th Jun 2024
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Hint: in this question we will use the relation between kinetic energy and initial velocity. Next we will use this relation to get the expression for latent heat and specific capacity. Now substituting the given values, will give us the required answer. Further we will discuss the basics of kinetic energy, potential energy and speed as well.
Formula used:
$K.{E_{\max }} = \dfrac{1}{2}\mu {v^2}$
$m{u^2} = (ms\Delta \theta + mL) \times 2$

As we know that the specific heat is defined as the amount of heat per unit mass required to raise the temperature by one degree Celsius.
We will first find the expression for initial velocity u, from the kinetic energy, which is given by:
$K.{E_{\max }} = \dfrac{1}{2}\mu {v^2}$
Substituting the values, we get:
\eqalign{& K.{E_{\max }} = \dfrac{1}{2}\left( {\dfrac{m}{2}} \right){(2u)^2} \cr & \Rightarrow K.{E_{\max }} = m{u^2} \cr}
Now, as we use relation between initial velocity, latent heat and specific capacity of ice:
$m{u^2} = (ms\Delta \theta + mL) \times 2$
Substituting the given values in above equation, we get:
\eqalign{& \Rightarrow u = \sqrt {2(2100 \times 8 + 336000)} \cr & \therefore u = 840m/s \cr}
Therefore, we get the required result, which gives the minimum speed required to make both the blocks melt completely i.e., 840m/s