Question

Short answer

The amount of heat needed is \(7.1 \times {106}\;{\rm{J}}\).

Step-by-step solution

Given data

The mass is\(m = 23.50\;{\rm{kg}}\).

The temperature is \(T = 25\circ {\rm{C}}\).

Understanding heat transfer

To find the heat required to melt the silver, use the relation of heat transfer along with latent heat.

Calculation of the amount of heat required

The relation to find the amount of heat required is given by:

\(\begin{array}{l}Q = {Q_{\rm{h}}} + {Q_{\rm{m}}}\\Q = mc\Delta T + mL\end{array}\)

Here,\(L\)is the latent heat, cis the specific heat, and\(\Delta T\)is the change in temperature.

On plugging the values in the above relation, you get:

\(\begin{array}{l}Q = \left[ {\left( {23.50\;{\rm{kg}}} \right)\left( {230\;{\rm{J/kg}} \cdot \circ {\rm{C}}} \right)\left( {961\circ {\rm{C}} - {\rm{25}}\circ {\rm{C}}} \right) + \left( {23.50\;{\rm{kg}}} \right)\left( {0.88 \times {{10}5}\;{\rm{J/kg}}} \right)} \right]\\Q = 7.1 \times {106}\;{\rm{J}}\end{array}\)

Thus, \(Q = 7.1 \times {106}\;{\rm{J}}\) is the required amount of heat.