91Ó°ÊÓ

Specific heat is a term used to describe the amount of heat required to change the temperature of a given amount of a substance. In chemistry and physics, specific heat is crucial because it helps us understand how different materials react to heat. The specific heat of a material is defined as the amount of heat per unit mass required to raise the temperature by one degree Celsius.

For instance, in our example, the specific heat of copper is given as \(0.385 \mathrm{J/g \, ^\circ C}\). This means that it takes 0.385 joules of thermal energy to raise the temperature of 1 gram of copper by 1 degree Celsius. Knowing the specific heat allows us to calculate the amount of energy exchanged during temperature changes.

Thermal energy change is a concept closely related to specific heat. It measures the total energy change when a substance is heated or cooled. In the example problem, the copper undergoes cooling, which results in a negative thermal energy change.

The formula to calculate thermal energy change is:

• \( q = m \times c \times \Delta T \)

Here, \(q\) is the heat transfer (thermal energy change), \(m\) is the mass, \(c\) is the specific heat, and \(\Delta T\) is the change in temperature.

In the exercise, copper cools from \(35.0^{\circ}\mathrm{C}\) to \(15.0^{\circ}\mathrm{C}\), with a change in temperature (\(\Delta T\)) of \(-20.0^{\circ}\mathrm{C}\). By plugging these numbers into the formula, we get a thermal energy change of \(-271.37\, \mathrm{J}\), indicating the heat released during cooling.

The molar enthalpy of fusion refers to the amount of energy required to change a mole of a solid to a liquid at a constant temperature, which is also known as the melting point. This property is crucial for phase change calculations.

In the exercise, the molar enthalpy of fusion for ice is provided as \(6.01 \mathrm{kJ/mol}\). This means \(6.01\) kilojoules of energy are needed to melt one mole of ice. The example problem uses the thermal energy change resulting from cooling copper to calculate how much ice can be melted with that absorbed energy.

Phase change calculations involve determining the amount of substance that changes state due to heat transfer. In our example, the energy released when copper cools is used to melt ice.

To find the number of moles of ice melted, we use:

• \( q = n \times \Delta H \)

Where \(n\) is the number of moles, and \(\Delta H\) is the molar enthalpy of fusion. After converting the released energy to kilojoules (\(-0.27137 \mathrm{kJ}\)), we use the enthalpy of fusion of ice to find the number of moles.

Rearranging gives:

• \( n = \frac{q}{\Delta H} = \frac{-0.27137 \mathrm{kJ}}{6.01 \mathrm{kJ/mol}} = -0.04514 \mathrm{mol} \)

The negative sign here reaffirms that the energy released cools the metal, resulting in \(0.04514 \mathrm{mol}\) of ice melting.