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Chapter 20: Problem 2

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

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

Step by step solution

01

Identify the known values

We know the mass of steam (m) is 6.00 g, the temperature (T) in 掳C is 100掳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掳C: 100掳C + 273.15 = 373.15 K.
02

Calculate the change in entropy

Using the formula for entropy change during a phase transition: 鈭哠 = mL/T, we can calculate the change in entropy as follows: 鈭哠 = (6.00 g)(2260 J/g) / (373.15 K)
03

Simplify and solve for 鈭哠

Simplify the expression and solve for 鈭哠: 鈭哠 = 6.00 * 2260 / 373.15 鈮� 36.3 J/K
04

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) \(36.3 \mathrm{~J} / \mathrm{K}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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掳C condenses to water at the same 100掳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掳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.

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Most popular questions from this chapter

Explain how it is possible for a heat pump like that in Example 20.2 to operate with a power of only \(6.28 \mathrm{~kW}\) and heat a house that is losing thermal energy at a rate of \(21.98 \mathrm{~kW}\).

A Carnot engine operates between a warmer reservoir at a temperature \(T_{1}\) and a cooler reservoir at a temperature \(T_{2}\). It is found that increasing the temperature of the warmer reservoir by a factor of 2 while keeping the same temperature for the cooler reservoir increases the efficiency of the Carnot engine by a factor of 2 as well. Find the efficiency of the engine and the ratio of the temperatures of the two reservoirs in their original form.

An ideal gas is enclosed in a cylinder with a movable piston at the top. The walls of the cylinder are insulated, so no heat can enter or exit. The gas initially occupies volume \(V_{1}\) and has pressure \(p_{1}\) and temperature \(T_{1}\). The piston is then moved very rapidly to a volume of \(V_{2}=3 V_{1}\). The process happens so rapidly that the enclosed gas does not do any work. Find \(p_{2}, T_{2},\) and the change in entropy of the gas.

You are given a beaker of water. What can you do to increase its entropy? What can you do to decrease its entropy?

A heat engine consists of a heat source that causes a monatomic gas to expand, pushing against a piston, thereby doing work. The gas begins at a pressure of \(300 . \mathrm{kPa}\), a volume of \(150 . \mathrm{cm}^{3}\), and room temperature, \(20.0^{\circ} \mathrm{C}\). On reaching a volume of \(450 . \mathrm{cm}^{3}\), the piston is locked in place, and the heat source is removed. At this point, the gas cools back to room temperature. Finally, the piston is unlocked and used to isothermally compress the gas back to its initial state. a) Sketch the cycle on a \(p V\) -diagram. b) Determine the work done on the gas and the heat flow out of the gas in each part of the cycle. c) Using the results of part (b), determine the efficiency of the engine.
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