Problem 33 - Chemistry: The Central Science

Question

Would each of the following changes increase, decrease, or have no effect on the number of microstates available to a system: (a) increase in temperature, (b) decrease in volume, (c) change of state from liquid to gas?

Step-by-Step Solution

Answer

(a) An increase in temperature would increase the number of microstates available to a system, as more energy levels become accessible to the particles. (b) A decrease in volume would decrease the number of microstates available to a system, as there are fewer spatial arrangements of particles possible in the system. (c) A change of state from liquid to gas would increase the number of microstates available to a system, as the particles gain more freedom to move and occupy larger volumes.

Step 1: Scenario A: Increase in Temperature

When the temperature of a system increases, the kinetic energy of its particles also increases. This means that more energy levels become accessible to the particles. As more energy levels become accessible, the number of possible arrangements of particles among these energy levels increases, which results in an increase in the number of microstates. Therefore, an increase in temperature would increase the number of microstates available to a system.

Step 2: Scenario B: Decrease in Volume

When the volume of a system decreases while the number of particles remains constant, the particles become more confined in space. This leads to fewer spatial arrangements of particles possible in the system. As there are fewer spatial arrangements, the number of microstates available to the system decreases. Therefore, a decrease in volume would decrease the number of microstates available to a system.

Step 3: Scenario C: Change of State from Liquid to Gas

When a system undergoes a phase transition from liquid to gas, the particles within the system gain more freedom to move and occupy larger volumes. This increased freedom of movement allows for more spatial arrangements of particles among various energy levels. As a result, the number of microstates available to the system increases. Therefore, a change of state from liquid to gas would increase the number of microstates available to a system.