A 1 -kg piece of iron is heated to \(100^{\circ} \mathrm{C}\), and then submerged in \(1 \mathrm{~kg}\) of water initially at \(0^{\circ} \mathrm{C}\). The iron cools and the water warms until they are at the same temperature (in thermal equilibrium). Assuming there is no other transfer of heat involved, is the final temperature closer to \(0^{\circ} \mathrm{C}, 50^{\circ} \mathrm{C}\), or \(100^{\circ} \mathrm{C}\) ? Why?

Specific heat capacity, often simply called specific heat, is the amount of heat required to change the temperature of a substance by one degree Celsius. The interesting thing about specific heat is that it's different for each material. For instance, water has a high specific heat capacity, which means it needs a lot of heat to increase in temperature.

Using our exercise example, iron, which has a lower specific heat than water, will change temperature more quickly with the same amount of heat transfer. This property explains why, in situations involving thermal equilibrium, materials with lower specific heat will undergo larger temperature changes than those with higher specific heat. This core concept is vital in understanding why the water's temperature in our exercise did not rise significantly despite absorbing heat from the hot iron.

Heat transfer is the process of thermal energy moving from one object or material to another. It can occur in three ways: conduction, convection, and radiation. In the exercise, we are focusing on conduction, which is the transfer of heat through direct contact.

Understanding Thermal Equilibrium

Thermal equilibrium happens when two objects in contact reach the same temperature and heat no longer flows between them. For the piece of iron and water in our exercise, the heat transfers from the hot iron to the cooler water until both reach the same temperature. Because heat flows from the hotter object (iron) to the cooler one (water), we often observe the final temperature as closer to the substance with the higher specific heat-capacity—in this case, water.

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. This applies to heat energy during heat transfer scenarios.

In our textbook exercise, we illustrate this principle by demonstrating that the heat lost by the iron is equal to the heat gained by the water. This is the core behind setting up an energy balance equation.

Why Is the Final Temperature Important?

The final temperature tells us about the relation between the heat capacities and masses of the substances involved. Since energy is conserved, the energy given off by the iron equals the energy absorbed by the water, leading to a final temperature that reflects the capacity of each substance to store heat. The higher specific heat of water explains why, in our example, the final temperature is much closer to the temperature of the water than that of iron.