Chapter 14, Problem 24P

How much heat is needed to melt 23.50 kg of silver that is initially at 25^CC?

To determine

The heat needed to melt the silver.

Answer to Problem 24P

Solution: $76.71\times {\text{ 10}}^5\text{ J}$

Explanation of Solution

Consider the melting point of silver, $T_m\text{ = 961}\text{.78}°\text{C}$ .

Latent heat of fusion, $L=111000\text{ J/kg}$

Specific heat capacity, $c\text{ = 230 J/kg}°\text{C}$

Given: Mass of the silver, $m=\text{ 23}\text{.5 kg }$

Formula used:$Q=mc\Delta t+mL$

Where, “ Q ” heat is needed to melt the silver.

“ m ” is the mass of the silver

“c” is the specific heat capacity

$"\Delta t"$ is the change in temperature

“ L” is the latent heat of fusion

Calculation:

The heat needed to melt the silver:

$\begin{array}{l}Q=mc\Delta t+mL\\ Q\text{ = 23}\text{.5 }\times \text{230 }\times \text{ (961}{\text{.78-25}}^0)+23.5\times 111000\\ Q=\text{7671795}\text{.9 J}\\ Q\text{ = 7671 }\times {\text{ 10}}^5\text{J}\end{array}$

Conclusion: The heat needed to melt 23.5 kg of silver is $76.71\times {10}^5\text{J}$ .