Question

What is the magnitude of the change in entropy when \(6.00 \mathrm{~g}\) of steam at \(100{ }^{\circ} \mathrm{C}\) is condensed to water at \(100{ }^{\circ} \mathrm{C} ?\) a) \(46.6 \mathrm{~J} / \mathrm{K}\) c) \(36.3 \mathrm{~J} / \mathrm{K}\) b) \(52.4 \mathrm{~J} / \mathrm{K}\) d) \(34.2 \mathrm{~J} / \mathrm{K}\)

Short answer

Answer: c) \(36.3 \mathrm{~J} / \mathrm{K}\)

Step-by-step solution

Identify the known values

We know the mass of steam (m) is 6.00 g, the temperature (T) in °C is 100°C, and the latent heat of vaporization for water (L) is 2260 J/g. First, we need to convert the temperature to Kelvin by adding 273.15 to 100°C: 100°C + 273.15 = 373.15 K.

Calculate the change in entropy

Using the formula for entropy change during a phase transition: ∆S = mL/T, we can calculate the change in entropy as follows: ∆S = (6.00 g)(2260 J/g) / (373.15 K)

Simplify and solve for ∆S

Simplify the expression and solve for ∆S: ∆S = 6.00 * 2260 / 373.15 ≈ 36.3 J/K

Compare the result to the given options

Our calculated change in entropy is approximately 36.3 J/K, which corresponds to option c. Therefore, the correct answer is: c) \(36.3 \mathrm{~J} / \mathrm{K}\)

Key concepts

Phase Transition

When a substance changes from one state of matter to another, such as from liquid to gas or vice versa, it undergoes a phase transition. These transitions occur due to energy changes within the substance that affect its physical properties, like volume and density.
The process of condensing steam into water is an example of a phase transition from gas to liquid. During such transitions, the temperature of the substance remains constant. For instance, steam at 100°C condenses to water at the same 100°C, ensuring that the energy involved goes solely into changing the state rather than altering the temperature.
To understand phase transitions further, it's important to note:

• Energy is absorbed or released, in the form of heat, to facilitate the transition.
• This energy exchange does not change the temperature, maintaining it constant until the transition completes.
• Phase transitions are integral to numerous natural and industrial processes, such as heating, cooling, and refrigeration systems.

Latent Heat of Vaporization

The latent heat of vaporization is the specific amount of heat required to convert a unit mass of a liquid into vapor without a temperature change. In simpler terms, it's the energy needed for a liquid to break its intermolecular forces to become a gas at the same temperature.
In the context of the exercise, the latent heat of vaporization of water is given as 2260 J/g. This is the energy needed to change 1 gram of water to 1 gram of steam or vice-versa, at 100°C with no temperature change.

• This process absorbs energy if water is heated to become steam and releases energy when steam condenses into water.
• The amount of energy depends directly on the mass of the water or steam involved. Hence, in our problem, for 6 grams, it's a simple scaling of the latent heat by the mass.
• Understanding latent heat is crucial for processes like climatic phenomena, industrial heating/cooling, and even in culinary practices.

Thermodynamics

Thermodynamics is the field of physics concerned with heat, temperature, and energy flow. In this problem, we're looking at how these principles apply to phase transitions and calculating changes in entropy when energy is exchanged.
Entropy, a key concept in thermodynamics, measures the degree of disorder or randomness in a system. When steam condenses into water, the system's entropy decreases as the molecules become more ordered.
Key points to understand thermodynamics in this context:

• Energy conservation: Energy lost as heat by one part of the system is gained by another, keeping the total energy constant.
• Entropy change: During phase transitions like condensation, calculating entropy can reflect changes in particle arrangement.
• Application of formulas: The equation \( \Delta S = \frac{mL}{T} \) is used to find entropy change, linking mass, latent heat, and temperature for the transition.

By grasping these basics, you'll have a solid foundation for understanding various physical processes in both natural and technological scenarios.