Question

Calculate the quantity of heat required to convert \[1.5{\text{ }}kg\] of ice at \[0^\circ C\] to water at $15^\circ C$.(\[{L_{{\text{ice}}}} = 3.34 \times {10^5}J/kg,{C_{water}} = 4180J/kg/^\circ C\])
A) 597000 J
B) 596685J
C) 595000 J
D) None of these

Answer 1

Hint: In this solution, we will calculate the heat required by different processes in converting the given amount of ice into water. We will first convert the ice into water and then heat the water up again to $15^\circ C$.
Formula used: In this solution, we will use the following formula:
-$Q = mL$ where $m$ is the mass of ice to be converted and $L$ is the constant of latent heat to convert ice into water
-$Q = mc\Delta T$ where $Q$ is the energy needed to heat up a liquid by $\Delta T$ temperature difference and $C$ is the specific heat capacity of the liquid

Complete step by step answer:
We want to find the amount of heat required to convert \[1.5{\text{ }}kg\] of ice at \[0^\circ C\] to water at $15^\circ C$. This will be a two-step process where we first heat the ice to convert it into the water and then we will heat the water up to $15^\circ C$.
So, to convert \[1.5{\text{ }}kg\] of ice into water, the amount of latent heat required can be calculated as
${Q_1} = mL$
Substituting the value of \[m = 1.5{\text{ }}kg\] and ${L_{{\text{ice}}}} = 3.34 \times {10^5}\,J/kg$, we get
${Q_1} = 1.5 \times 3.34 \times {10^5}$
$ \Rightarrow {Q_1} = 5.01 \times {10^5}\,{\text{J}}$
Now the heat energy required to raise the temperature of water will be
${Q_2} = mC\Delta T$
Substituting the value of $C = 4180\,J/kg/^\circ C$ and $\Delta T = (15 - 0) = 15^\circ C$, we get
${Q_2} = 1.5 \times 4180 \times 15$
$ \Rightarrow {Q_2} = 0.94 \times {10^5}\,{\text{J}}$
Hence the total amount of heat required will be
$Q = {Q_1} + {Q_2}$
$ \Rightarrow Q = 5.95 \times {10^5}\,J\,{\text{or }}595000J$

So, the correct choice is option (C).

Note: In such questions, we must be careful not to directly use the formula of specific heat to calculate the energy required in our process. This is because the energy required to convert ice into water must be taken into account.