Question

A sample of copper absorbs 43.6 kJ of heat, resulting in a temperature rise of 75.0 °C, determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g°C.

Answer 1

Concept and reason

The concept used is to calculate the mass of copper using the specific heat capacity.

Fundamentals

According to the first law of thermodynamics, energy can neither be created nor destroyed. The total energy is a constant but energy changes from one form to another.

Specific heat capacity is the amount of heat required to increase the temperature of one gram of a substance by $1^\circ {\rm{C}}$ .

It is represented as ${C_p}$ .

Enthalpy is the heat content of a system. Enthalpy changes for a reaction may be exothermic or endothermic.

The enthalpy change for the reaction is the amount of energy gained or lost during the reaction. It is represented as $\Delta H^\circ$ .

The enthalpy change is calculated as follows:

$\Delta H^\circ = m{C_p}\Delta T$

Here, m is the mass, ${C_p}$ is the specific heat capacity and $\Delta T$ is the change in temperature $\left( {{\rm{Final}} - {\rm{Initial}}} \right)$ .

Given,

Specific heat of copper $\left( {{C_p}} \right)$ = $0.385{\rm{ J/g}}{\rm{.^\circ C}}$

${\rm{Change in temperature}}\left( {\Delta T} \right) = 75{\rm{^\circ C}}$

Amount of heat absorbed by copper = $43.6{\rm{ kJ}}$

Convert kJ to J.

$\begin{array}{c}\\43.6{\rm{ kJ}} = 43.6{\rm{ kJ}} \times \frac{{1000{\rm{ J}}}}{{1{\rm{ kJ}}}}\\\\ = 43.6 \times {10^3}{\rm{ J}}\\\end{array}$

Substitute these values in the formula for enthalpy change and calculate the mass as follows:

$\begin{array}{l}\\\Delta H^\circ = m{C_p}\Delta T\\\\43.6 \times {10^3}{\rm{ J}} = m\left( {0.385{\rm{ J/g}}{\rm{.^\circ C}}} \right)\left( {75^\circ {\rm{C}}} \right)\\\\m = \frac{{43.6 \times {{10}^3}{\rm{ J}}}}{{\left( {0.385{\rm{ J/g}}{\rm{.^\circ C}}} \right)\left( {75^\circ {\rm{C}}} \right)}}\\\\ = 1510{\rm{ g}}\\\end{array}$

Mass of copper = $1510{\rm{ g}}$

Convert g to kg as follows:

$\begin{array}{c}\\1510{\rm{ g}} = 1510{\rm{ g}} \times \frac{{1{\rm{ kg}}}}{{1000{\rm{ g}}}}\\\\ = 1.51{\rm{ kg}}\\\end{array}$

Ans:

The mass of copper is $1.51{\rm{ kg}}$ .