Question

A silver block, initially at 58.2 ?C, is submerged into 100.0 g of water at 25.0 ?C, in an insulated container. The final temperature of the mixture upon reaching thermal equilibrium is 27.6 ?C.

-What is the mass of the silver block?

Answer 1

Concepts and reason

The given problem is based on the principle of heat exchange between two systems. The mass of the silver block needs to be calculated which is submerged into the given mass of water. The mixture reached thermal equilibrium at temperature $27.6^\circ {\rm{C}}$ therefore, by equating the heat loss by one system and gained by the other system, calculate the mass of silver block.

Fundamentals

Heat capacity can be defined as the amount of heat released or absorbed to change the temperature of the compound. Mathematically, it can be represented as follow:

$q = m{\rm{.c}}{\rm{.}}\Delta T$

Here,

$\begin{array}{c}\\q = {\rm{Amount}}\,{\rm{of}}\,{\rm{heat}}\\\\m = {\rm{Mass of substance}}\\\\{\rm{c}} = {\rm{specific}}\,{\rm{heat}}\,{\rm{capacity}}\\\\\Delta T = {\rm{temperature}}\,{\rm{change}}\\\end{array}$

Use the following equation to calculate the heat gain by $100\,{\rm{g}}$ of water when the temperature of water is raised from $25\,^\circ {\rm{C}}$ to $27.6\,^\circ {\rm{C}}$ as shown below:

$\begin{array}{c}\\{q_1}\,\left( {{\rm{Heat}}\,{\rm{gain}}\,{\rm{by}}\,{\rm{water}}\,{\rm{system}}} \right) = m{\rm{.c}}{\rm{.}}\Delta T\\\\ = 100.0\,{\rm{g}} \times 4.186{\rm{ J}}/{\rm{g}}\,^\circ {\rm{C}} \times \left( {27.6\,^\circ {\rm{C}} - 25\,^\circ {\rm{C}}} \right)\\\\ = 1088.36{\rm{ J}}\\\end{array}$

Calculate the mass of silver block as shown below:

$\begin{array}{c}\\ - {q_2}\left( {{\rm{Heat}}\,{\rm{loss}}\,{\rm{by}}\,{\rm{silver}}\,{\rm{system}}} \right) = {m_{silver}}{\rm{.}}{{\rm{c}}_{silver}}{\rm{.}}\Delta T\\\\ - 1088.36{\rm{ J}} = {m_{silver}} \times 0.239{\rm{ J}}/{\rm{g}}\,^\circ {\rm{C}} \times \left( {27.2\,^\circ {\rm{C}} - 58.2\,^\circ {\rm{C}}} \right)\\\\{m_{silver}} = \frac{{1088.36{\rm{ J}}}}{{7.41\,{\rm{J}}/{\rm{g}}}} = 148.8\,{\rm{g}}\\\end{array}$

Ans:

Hence, the mass of the silver block is calculated as $148.8\,{\rm{g}}$ .