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Chapter 10: Problem 71

What change or changes in the state of a gas bring about each of the following effects? (a) The number of impacts per unit time on a given container wall increases. (b) The average energy of impact of molecules with the wall of the container decreases. (c) The average distance between gas molecules increases. (d) The average speed of molecules in the gas mixture is increased.

Short Answer

Expert verified
(a) Increase the pressure or decrease the volume to increase the number of impacts per unit time on a container wall. (b) Decrease the temperature to reduce the energy of impact of molecules with the container wall. (c) Increase the volume or decrease the pressure to increase the average distance between gas molecules. (d) Increase the temperature to increase the average speed of molecules in the gas mixture.

Step by step solution

01

(a) Increase in impacts per unit time on a container wall

To increase the number of impacts per unit time on a given container wall, we can do the following: 1. Increase the pressure: Higher pressure results in more frequent collisions between gas molecules and the container walls. 2. Decrease the volume: A smaller volume means that gas molecules have less space to move around, which leads to an increase in the collision frequency.
02

(b) Decrease in the average energy of impact

To decrease the average energy of impact of gas molecules with the container wall, we can lower the temperature of the gas. According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the temperature \( (KE \propto T) \). Hence, a decrease in temperature leads to a decrease in the average kinetic energy and the energy of impact on the container walls.
03

(c) Increase in the average distance between gas molecules

To increase the average distance between gas molecules, we can do the following: 1. Decrease the pressure: Lower pressure allows gas molecules to spread out. This results in a larger average distance between the molecules. 2. Increase the volume: A larger volume means gas molecules have more space to move around. This increases the average distance between molecules.
04

(d) Increase in the average speed of molecules in the gas mixture

To increase the average speed of gas molecules in the gas mixture, we can increase the temperature of the gas. According to the kinetic theory of gases, the average speed of gas molecules is related to the temperature \( (v \propto \sqrt{T}) \). Therefore, increasing the temperature will result in an increase in the average speed of the gas molecules.

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