Question

Does the amount of heat absorbed as \(1 \mathrm{~kg}\) of saturated liquid water boils at \(100^{\circ} \mathrm{C}\) have to be equal to the amount of heat released as \(1 \mathrm{~kg}\) of saturated water vapor condenses at \(100^{\circ} \mathrm{C}\) ?

Short answer

Answer: Yes, the amount of heat absorbed during boiling of 1 kg of saturated liquid water and the heat released during condensation of the same amount of saturated water vapor are equal (approximately 2.26 * 10^6 Joules).

Step-by-step solution

Calculate the heat absorbed during boiling

We can calculate the heat absorbed during boiling using the latent heat of vaporization formula, which is: Q= m * L_v Where: Q = Heat absorbed during boiling in Joules m = mass of saturated liquid water (1 kg) L_v = latent heat of vaporization of water (approximately \(2.26\times10^6\) J/kg) Now we can plug in the values and calculate Q: Q = (1 kg) * (2.26 *10^6 J/kg) Q = 2.26 * 10^6 Joules So, the heat absorbed during boiling is approximately \(2.26\times10^6\) Joules.

Calculate the heat released during condensation

We can calculate the heat released during condensation using the latent heat of condensation formula, which is: Q = m * L_c Where: Q = Heat released during condensation in Joules m = mass of saturated water vapor (1 kg) L_c = latent heat of condensation of water (approximately \(2.26\times10^6\) J/kg, which is equal to latent heat of vaporization) Now we can plug in the values and calculate Q: Q = (1 kg) * (2.26 * 10^6 J/kg) Q = 2.26 * 10^6 Joules So, the heat released during condensation is approximately \(2.26\times10^6\) Joules.

Compare the two heat values

Now that we have calculated both heat values, we can compare them: Heat absorbed during boiling: 2.26 * 10^6 Joules Heat released during condensation: 2.26 * 10^6 Joules As we can see, the heat absorbed during the boiling of \(1 \mathrm{~kg}\) of saturated liquid water and the heat released during condensation of the same amount of saturated water vapor are equal. So yes, the amount of heat absorbed as \(1 \mathrm{~kg}\) of saturated liquid water boils at \(100^{\circ} \mathrm{C}\) has to be equal to the amount of heat released as \(1 \mathrm{~kg}\) of saturated water vapor condenses at \(100^{\circ} \mathrm{C}\).

Key concepts

Heat Transfer

Heat transfer refers to the movement of thermal energy from one object or substance to another. It happens because of a temperature difference. When two substances are at different temperatures, heat will transfer from the hotter substance to the cooler one until thermal equilibrium is reached.

There are three primary modes of heat transfer:

• Conduction: This occurs in solids where heat is transferred through direct contact. Heat moves through the material itself from the hot section to the cooler section.
• Convection: This takes place in fluids (liquids and gases) where heated fluid particles move and transfer heat. This process often occurs in the atmosphere and oceans.
• Radiation: Unlike conduction and convection, radiation doesn't need a medium to transfer heat. It occurs through electromagnetic waves and can happen in a vacuum, such as heat from the sun reaching Earth.

Understanding these modes helps in analyzing complex heat exchange in natural and engineering processes. In the context of the exercise, heat is transferred during the phase changes of water primarily through convection and conduction.

Phase Change

Phase change refers to the process where a substance changes from one state of matter to another. This occurs when energy, in the form of heat, is added or removed. The most common phase changes include melting, freezing, condensation, vaporization, sublimation, and deposition.

During these transformations:

• Vaporization (boiling): This is when a liquid turns into a gas. It requires heat, known as the latent heat of vaporization. For water at 100°C, approximately 2.26×10⁶ J of energy per kg is needed.
• Condensation: In this process, a gas changes back into a liquid. It releases heat equivalent to the latent heat of vaporization because energy is freed back into the system.

In the exercise, the phase change of water involves boiling and condensation. The latent heat is the same for both processes, highlighting the conservation of energy, since what is absorbed during boiling is released during condensation.

Thermodynamics

Thermodynamics is the study of heat and its transformation to different energy forms. It consists of principles that explain how energy is transferred and utilized within physical systems. The exercise focuses on a fundamental concept of thermodynamics—the conservation of energy.

Key principles of thermodynamics include:

• First Law of Thermodynamics (Law of Energy Conservation): This law states that energy cannot be created or destroyed, only transformed from one form to another. This concept is demonstrated in the exercise as the energy absorbed during the boiling of water is exactly equal to the energy released during its condensation.
• Second Law of Thermodynamics: It explains that heat naturally flows from a hot object to a cold one, not the other way around. This law also suggests that energy transformations are never 100% efficient.

Understanding these laws helps us analyze heat exchange processes across various systems, ensuring that concepts like latent heat and phase changes are consistent with natural energy laws.