Chapter 23, Problem 23A

Calculate the energy needed to melt 100 grams of $0°C$ ice and then heat it to $30°C$.

To determine

The energy released to melt $100\text{g}$ at $30°\text{C}$ ice.

Answer to Problem 23A

  $\text{45958 J}$

Explanation of Solution

Given info:

The mass of ice, $m=100\text{g}$

Temperature difference of ice, $T=30\text{°C}=303\text{K}$

Formula used:

The energy released is calculated as :

  $Q=mL+mc\Delta T$

Here, L is the latent heat of fusion of ice in J/g.

  $L=334\text{J/g}$

c is the specific heat of water = $\text{4}.\text{186 J}/\text{g}$ .

Calculation:

Substituting the given values,

  $Q=mL+mC\Delta T$

Substitute the values in the above expressions.

  $\begin{array}{c}Q=100\times 334+100\times 4.186\times (30-0)\\ =33400+12558=45958\text{J}\end{array}$

Conclusion:

The energy released to melt $100\text{g}$ ice at $30°\text{C}$ is $\text{45958 J}$ .