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Chapter 17: Problem 4

The average speed of the molecules in a gas increases with increasing temperature. What about the average velocity?

Short Answer

Expert verified
While the average speed of gas molecules increases with increasing temperature due to increased kinetic energy, the average velocity remains zero due to the random and equally probable direction of molecular movement in the gas.

Step by step solution

01

Understanding Speed and Velocity

Firstly, differentiate between speed and velocity. Speed is a scalar quantity that refers to 'how fast an object is moving' whereas velocity is a vector quantity that refers to 'the speed of an object in a particular direction'.
02

Describing Molecular Gas Theory

Secondly, according to the molecular kinetic theory, particles of a gas are in constant, random motion and collide with each other and the walls of their container. The speed of these molecules indeed increases when the temperature rises. This causes the gas to expand or increase pressure.
03

Relate Random Direction of Molecules to Velocity

Thirdly, since the direction of the molecules is random and equally probable in all directions, the average of the directional speeds will approach zero, irrespective of temperature, as there is an equal tendency of the molecules to move in one direction as in any other. This gives the average velocity of the molecules, which remains zero.
04

Conclusion

While the average speed of gas molecules increases as temperature increases, due to the random movement of the molecules in all directions, the average velocity remains zero irrespective of the temperature.

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