Video: Applying Knowledge of the Relationship between Gas Temperature, Particle Speed, and Particle Kinetic Energy

For statements I and II, state for each if they are true or false. I As the temperature of a gas increases, the average kinetic energy of its molecules decreases. II The average speed of gas molecules increases as the temperature decreases. If both are true, state if II is a correct explanation for I.

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Video Transcript

For statements 1 and 2, state for each if they are true or false. 1) As the temperature of a gas increases, the average kinetic energy of its molecules decreases. 2) The average speed of gas molecules increases as the temperature decreases. If both are true, state if 2 is a correct explanation for 1.

Statement 1 is asking us about the relationship between temperature and the average kinetic energy. The average kinetic energy of a gas and its temperature are in fact intimately related. Namely, the average kinetic energy is equal to three-halves times the gas constant times the temperature. As we can see from this formula, the average kinetic energy and the temperature are directly proportional.

So, when the temperature increases, the average kinetic energy increases as well. Statement 1 says that when the temperature increases, the average kinetic energy decreases. As we’ve just seen, statement 1 must be false. When the temperature of a gas increases, the average kinetic energy of the gas increases as well because the average kinetic energy and temperature are directly proportional.

Statement 2 is asking us about the relationship between the average speed of gas molecules and their temperature. Well, we know that the average kinetic energy and speed are related since kinetic energy is equal to one-half times the mass times the velocity squared. This question is asking us about the average speed of the gas molecules and not just the speed of the molecules. Because in any given sample of gas, there will be a distribution of speeds that the molecules have.

This distribution will change with the temperature of the sample. But at any temperature, there will always be some molecules that are moving extremely quickly and some molecules that are moving extremely slow. But as we can see from our formula, if the speed of the gas molecules increases, it will be due to an increase in the average kinetic energy of this gas. And as we’ve previously discussed, kinetic energy and temperature are directly proportional. So, if the kinetic energy goes up, the temperature will go up as well.

Statement 2 says that the average speed of the gas molecules increases when the temperature decreases. So, as we just discussed, the statement must be false. When the average speed of the gas increases, the temperature increases as well. This is also something that we can see in the diagram that I’ve drawn. When the temperature is increased, the average speed for the distribution shifts to the right, so it increases. Since statement 1 and statement 2 were both false, we don’t have to state if 2 is a correct explanation for 1.

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