Question

80g of water at $30{}^\circ C$ is poured on a large block of ice at $0{}^\circ C$. The mass of ice that melts is:
A. 30g
B. 80g
C. 1600g
D.150g

Answer 1

The situation given in the question could be related to the concept of mixing of liquids at different temperatures. In that case, the liquid at high temperature loose heat and the other gain heat so as to reach the equilibrium temperature. Here, the heat gained by ice used for the process of fusion and hence find the answer accordingly.

Formula used:
Heat lost by water,
$\Delta {{H}_{w}}=ms\Delta T$
Heat gained by ice,
$\Delta {{H}_{i}}=m{{L}_{f}}$

Complete answer:
In the question we are given 80g of water at $30{}^\circ C$and it is poured over an ice block of temperature $0{}^\circ C$. We are supposed to find the mass of the ice that melts.
We could use the same concept used for the mixing of two liquids which are at different temperatures.
We know that when substances of two different temperatures are mixed the substance at high temperature loses heat and substance at low temperature gains heat and both of them thus attain the same equilibrium temperature.
So, as per this concept, the heat lost by water will be equal to the heat gained by the ice block, that is,
$\Delta {{H}_{w}}=-\Delta {{H}_{i}}$
Here, the equilibrium temperature is $0{}^\circ C$ and the heat gained by the ice is used for its conversion to water.
So heat lost by water could be given by,
$\Delta {{H}_{w}}=ms\Delta T$
Mass of water is give as,
$m=80g$
$\Delta T=30-0=30{}^\circ$
Specific heat capacity s of water is known to be,
$s=1cal/g{}^\circ C$
So,
$\Delta {{H}_{w}}=80\times 1\times 30=2400cal$…………………………………………. (1)
Heat gain by ice is given by,
$\Delta {{H}_{i}}=m{{L}_{f}}$
Where, m is the mass of ice melted and ${{L}_{f}}$ is the latent heat of fusion. We know the value of latent heat of fusion of water to be, $80cal/g$, so,
$\Delta {{H}_{i}}=m\times 80$…………………………… (2)
Now we could equate (1) and (2) to get,
$80m=2400$
$\Rightarrow m=\dfrac{2400}{80}$
$\therefore m=30g$
Therefore, we found the mass of ice that melts to be 30g.

Hence, option A is found to be the correct answer.

Note:
We should note here that the heat gained by ice is not used for increase in temperature of ice but for its fusion process. The process by which the ice is converted to water is called fusion. Latent heat of fusion could be defined as the enthalpy change for a given amount of substance when undergoing the fusion process, that is, when it converted from solid form to liquid form.