Ch.19 - Chemical Thermodynamics

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.19 - Chemical Thermodynamics

Problem 17b

Chapter 19, Problem 17b

Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from 300 K to 200 K. (b) Is this process isothermal?

Verified step by step guidance

insert step 1: Understand the definition of an isothermal process. An isothermal process is one in which the temperature of the system remains constant throughout the process.

insert step 2: Identify the initial and final temperatures of the gas in the given problem. The temperature changes from 300 K to 200 K.

insert step 3: Compare the initial and final temperatures. Since the temperature changes from 300 K to 200 K, there is a change in temperature.

insert step 4: Determine if the process is isothermal. Since the temperature changes, the process is not isothermal.

insert step 5: Conclude that the process is not isothermal because the temperature does not remain constant.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. Understanding this law is crucial for analyzing gas behavior during thermodynamic processes.

Isothermal Process

An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout the process. For an ideal gas, this means that any heat added to the system is used to do work, rather than changing the internal energy. In the context of the question, since the temperature changes from 300 K to 200 K, the process cannot be classified as isothermal.

Thermodynamic States

Thermodynamic states refer to the specific conditions of a system, characterized by properties such as temperature, pressure, and volume. Changes in these properties define the transition from one state to another. In the given question, the transition from state 1 at 300 K to state 2 at 200 K indicates a change in temperature, which is a key factor in determining the nature of the process.

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Textbook Question

A system goes from state 1 to state 2 and back to state 1. (c) Suppose the changes in state are reversible processes. Is the work done by the system upon going from state 1 to state 2 the same or different as compared to that upon going from state 2 back to state 1?

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Textbook Question

Indicate whether each statement is true or false. (a) ΔS is a state function. (b) If a system undergoes a reversible change, the entropy of the universe increases. (c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.

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Consider the vaporization of liquid water to steam at a pressure of 1 atm. (d) At what temperature are the two phases in equilibrium?

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Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly?

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The normal freezing point of n-octane (C₈H₁₈) is -57 °C. (b) In what temperature range is the freezing of n-octane a spontaneous process?

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Textbook Question

Consider a process in which an ideal gas changes from state 1 to state 2 in such a way that its temperature changes from 300 K to 200 K. (a) Does the temperature change depend on whether the process is reversible or irreversible?

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