Question

A block of mass $2.5kg$ is heated to a temperature of ${500^0}C$ and placed on a large ice block. What is the maximum amount of ice that can melt (approx.) Specific heat for body $= 0.1$ Cal per gram.

Answer 1

Hint : Here, it is given that the block is heated at some temperature and placed on a large ice block and due to heat released by the block the ice melts. We have to find that amount of ice which have been melted by using the formula for heat released by the block as:
$Q = mc\Delta T$ ; $Q$ is the heat released, $m$ mass of the object, $c$ specific heat for the body and $\Delta T$ is the temperature change.

Complete Step By Step Answer:
According to the given data we have
Mass of the block is $m = 2.5kg$
Temperature at which the block is to be heated from ${T_1} = {0^0}C$ to ${T_2} = {500^0}C$
$c = 0.1 \times 1000calk{g^{ - 1}}$ … (Specific heat for body $= 0.1$ Cal per gram)
Now, we know the formula for the heat released by the block is given by:
$Q = mc\Delta T$
Now, on putting the given value from above, we get
$\Rightarrow Q = 2.5 \times 0.1 \times {10^3} \times \left( {500 - 0} \right)$
$\Rightarrow Q = 2.5 \times 0.1 \times {10^3} \times 500$
$\Rightarrow Q = 125 \times {10^3}$
$\Rightarrow Q = 125000cal$
Thus, the heat released by the block is $125000cal$
But we are also asked about the mass of ice that has been melted by the heat released and it is given by:
The formula for latent heat of fusion is used since here the melting of ice is considered as the fusion transformation of the body from one state to another. And the formula is:
$Q = mL$ …. ( $L$ is the latent heat for melting of ice)
The latent heat of fusion of ice is $33600J{K^{ - 1}}$ and the latent heat for fusion of ice is the amount of heat required to melt a unit mass of ice from the solid-state to the liquid state.
Therefore, the answer is obtained as
$\Rightarrow m = \dfrac{{125000cal}}{{33600J{K^{ - 1}}}}$
$\Rightarrow m = 1.57kg$
By solving the above equation we obtained the answer that the mass of ice melted is $1.57kg$ .

Note :
We have to change the units into SI systems and apply it in these equations and obtain the required answer. Latent heat formula is important to find the mass of the melted ice and the amount of heat to be required for melting of ice. Hence, we calculated the answer.