Question

A sample of an ideal gas is heated and its Kelvin temperature doubles. What happens to the average speed of the molecules in the sample?

A) It does not change.
B) It doubles.
C) It halves.
D) It is sqrt(1/ 2) times smaller.
E) It is sqrt(2) times as large.

Answer 1

If the Kelvin temperature of an ideal gas doubles, the average speed of its molecules becomes sqrt(2) times as large, due to the proportional relationship between temperature and the square of the speed.

Step-by-step explanation:

When a sample of an ideal gas is heated and its Kelvin temperature doubles, the average kinetic energy of the gas molecules also doubles. According to physical principles, the typical speed of gas molecules (root mean square speed, or Urms) is proportional to the square root of the Kelvin temperature. Since the average kinetic energy is related to the square of the speed, when the temperature doubles, the average speed increases by a factor of the square root of two. Therefore, if the Kelvin temperature of an ideal gas doubles, the correct answer is E) It is sqrt(2) times as large.