Question

Calculate the minimum amount of energy, in joules, required to completely melt$\mathbf{\text{130g}}$of silver initially at$\mathbf{\text{15.0°C}}$.

Short answer

The minimum amount of energy required to completely melt 130 g of silver is$4.27\times {10}^4\text{J}$

Step-by-step solution

The given data

1. The mass of the silver is$m=130\text{gor}130\times {10}^{-3}\text{kg}$
2. The initial temperature of the silver is${\text{T}}_{\text{i}}{\text{=15.0}}^0\text{Cor288K}$

Understanding the concept of specific heat

A substance's specific heat capacity is the amount of energy required to raise its temperature by one degree Celsius. We can use the concept of specific heat of silver. The silver completely melts; hence, there is a change of phase.

Formula:

The heat energy required by a body,$Q=mc\Delta T$ …(i)

Where, m = mass

c = specific heat capacity

$\Delta T$= change in temperature

Q= required heat energy

The heat energy released or absorbed by the body, $Q=Lm$ …(ii)

Where, m= mass

L = specific latent heat

Calculation of the minimum energy required to melt silver

The melting point of silver is$1235K$ , hence final temperature of the silver is$T_f=1235K$In order to melt the silver completely, silver uses energy in two steps. First, it takes energy to increase the temperature from$288K$to$1235K$, and then, the energy used by the silver is given using equation (i) as:

$Q_1=cm(T_f-T_i)$ …(iii)

Whereis the specific heat of silver,$c=236\text{J/kg.K}$

When the silver melts completely, there is a phase change from solid to the liquid and heat of transformation is called heat of fusion. Then, this energy is calculated using equation (ii) as:

$Q_2=L_{F}m$ …(iv)

Where,is the heat of fusion of silver.$L_F=105\times {10}^3\text{J/kg}$

Using equation (iii) and equation (iv), the total heat energy required to melt the given amount of silver is given as:

$\begin{array}{c}Q=Q_1+Q_2\\ =[236\text{J/kg.K}\times 130\times {10}^{-3}\text{kg}\times (1235\text{K}-288\text{K})+105\times {10}^3\text{J/kg}\times 130\times {10}^{-3}\text{kg}]\\ =4.27\times {10}^4\text{J}\end{array}$

Therefore, the energy required to melt the silver is$4.27\times {10}^4\text{J}$