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Chapter 19: Problem 29

How would each of the following changes affect the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c) change of state from liquid to gas?

Short Answer

Expert verified
(a) An increase in temperature results in an increase in the number of microstates, as particles can occupy a larger number of possible energy levels. (b) A decrease in volume leads to a decrease in the number of microstates, as the available space for particles is reduced, restricting their positions and energy levels. (c) A change of state from liquid to gas increases the number of microstates, as particles can move more freely and occupy a larger volume.

Step by step solution

01

(a) Effect of an increase in temperature on the number of microstates

An increase in temperature means that the system has more energy. With more energy, the particles in the system can occupy a larger number of possible energy levels. This leads to a higher number of possible configurations or microstates available to the system. Hence, an increase in temperature results in an increase in the number of microstates.
02

(b) Effect of a decrease in volume on the number of microstates

When the volume of a system decreases, the available space for the particles to move in becomes smaller. This reduction in space restricts the possible positions and energy levels that the particles can occupy. As a result, the number of possible configurations or microstates available to the system decreases. Therefore, a decrease in volume will result in a decrease in the number of microstates.
03

(c) Effect of a change of state from liquid to gas on the number of microstates

When a system changes from a liquid state to a gaseous state, the particles gain sufficient energy to overcome intermolecular forces and occupy a larger volume. As a result, the particles can move more freely in a gaseous state, leading to an increase in the possible configurations or microstates available to the system. Thus, a change in the state from liquid to gas results in an increase in the number of microstates.

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Most popular questions from this chapter

The crystalline hydrate \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s)\) loses water when placed in a large, closed, dry vessel: \(\mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{Cd}\left(\mathrm{NO}_{3}\right)_{2}(s)+4 \mathrm{H}_{2} \mathrm{O}(g)\) This process occurs even though it is endothermic; that is, \(\Delta H\) is positive. Is this process an exception to Bertholet's generalization? Explain.

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