Question

The $550{\text{ }}grams$ of copper at ${200^ \circ }C$ is put in a cavity in a large block of ice at ${0^ \circ }C$. Find the heat loss and the mass of ice melted into water. c of copper$ = .0930{\text{ }}\dfrac{{cal}}{{gm{.^ \circ }C}}$.

Answer 1

Hint: From the Law of Calorimetry, we will find the amount of heat that has been lost from the help of the given values assigned here. Then by using the formula of latent heat we will find out the mass of ice being melted into water. The latent heat of fusion is $80{\text{ }}\dfrac{{cal}}{{gm{.^ \circ }C}}$.

Complete step by step answer:
Specific heat of the material of a substance is defined as the amount of heat required to change the temperature of unit mass of a substance by ${1^ \circ }C$. From the Law of Calorimetry we know that the amount of heat lost or gained is expressed as the formula,
$Q = mc\Delta T - - - - \left( 1 \right)$
The variables are defined as-
$Q = $ amount of heat lost or gained.
$m = $ mass of the substance.
$c = $ specific heat of the substance.
$\Delta T = $ change in temperature.
The quantities that are already given in the question are-
$m = 550$, $c = 0.0930$ and $\Delta T = 200 - 0 = 200$
Substituting the values in equation $\left( 1 \right)$ we get,
$Q = 550 \times 0.0930 \times 200 = 10230$
So, the amount of heat lost by the copper is $10230{\text{ }}cal$.

Now, the amount of heat that is being lost by water is gained by ice.According to the formula of Latent Heat of fusion we get,
$Q = m{L_f} - - - - - - \left( 2 \right)$
The variables defined here are,
$Q = $ amount of heat lost or gained, $m = $ mass of the substance and ${L_f} = $ Latent heat of fusion.
The heat is being found which is $Q = 10230$, and the latent heat of fusion of water is $80{\text{ }}\dfrac{{cal}}{{gm{.^ \circ }C}}$.Substituting the values in equation $(2)$ we can find the mass,
$10230 = m \times 80$
Arranging the equation we get,
$\therefore m = \dfrac{{10230}}{{80}} = 127.875$

Hence, the amount of ice that has been melted into water is $127.875{\text{ }}grams$.

Note: The heat energy that is being lost by the copper due to its change in temperature while in the block of ice, is equal to the heat energy that is being gained by the ice to convert itself into water. As energy can neither be created nor destroyed, it just transforms. Latent heat of a substance is the amount of heat that is required to change the state of a substance at approximately the same temperature for example from solid to liquid or liquid to gas.