Question

Steam at \(100^{\circ} \mathrm{C}\) passing through a radiator condenses to water and releases heat. If 1500 kcal of heat are released, how much energy is required to vaporize the water, at \(100^{\circ} \mathrm{C},\) to steam?

Short answer

The energy required to vaporize the water is 1500 kcal.

Step-by-step solution

Understanding the Concept

The problem involves the process of condensation and vaporization. When steam condenses, it releases heat. Conversely, when water vaporizes, it requires the same amount of energy in reverse. We need to calculate the energy required to vaporize water into steam using the same energy released during condensation.

Identifying Given Data

We are given that 1500 kcal of heat is released when steam at \(100^{\circ} \mathrm{C}\) condenses into water. This means the same amount of energy (1500 kcal) is needed to vaporize water back to steam at \(100^{\circ} \mathrm{C}\).

Applying the Energy Concept

According to the principle of energy conservation and the latent heat of vaporization of water, the energy required to vaporize a certain amount of water is equal to the energy released by the same amount of water when it condenses. Hence, the energy required to vaporize the water is 1500 kcal.

Key concepts

Energy Conservation: The Underlying Principle

The principle of energy conservation is fundamental to understanding many physical processes. It states that energy cannot be created or destroyed, only transformed from one form to another. Whenever energy is released or absorbed in a process, the total energy remains constant, just changing its form.
In our context with condensation and vaporization:

• The energy released when steam condenses into water is equal to the energy required to reverse that process, turning water back into steam.
• This means the energy lost by the system during condensation is exactly the energy needed for vaporization, which demonstrates energy conservation in action.

This is why understanding energy conservation helps us calculate the energy required for processes like vaporization based on the energy released during condensation.

Condensation: Heat Release

Condensation is the process where vapor turns into a liquid. It plays a critical role in many natural and industrial processes. When steam, or any vapor, changes its state back to liquid:

• It releases latent heat to the surroundings.
• This release of energy occurs because molecules in the vapor slow down, allowing them to bond into a liquid state.
• In our example, condensation releases 1500 kcal when steam condenses.

Understanding how condensation releases heat helps us appreciate the energy transformations in heating systems or in nature, like the formation of dew. This release of heat is responsible for warming the surroundings during condensation.

Vaporization: Energy Requirement

Vaporization is the opposite of condensation. It's the process where a liquid becomes a vapor. To achieve this state change:

• The system must absorb a significant amount of energy, known as latent heat of vaporization.
• The absorbed energy allows molecules to break free from their liquid bonds and become a gas.
• For water at its boiling point, this process requires 1500 kcal, exactly the same amount released during condensation with water returning to steam.

This "energy exchange" is crucial for many applications, from steam engines to power plants. It illustrates both the complexity and simplicity of energy transformations, emphasizing the recurring balance and symmetry found in physical processes.