If the temperature of an ideal gas is increased from 20°C to 40°C,by what percent does the speed of the molecules increase?
A)3%
B)30%
C)70%
D)100%

Question

Quizplus · Accepted Answer

The speed of molecules in an ideal gas is related to the temperature by the equation for the root-mean-square speed, $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature in Kelvin, and $m$ is the mass of a molecule. The percentage increase in speed can be calculated using the temperatures in Kelvin (293K for 20°C and 313K for 40°C). The increase in speed is approximately 3%, as the relationship between temperature and speed is square root, and the increase in temperature from 293K to 313K does not double the speed.

If the Temperature of an Ideal Gas Is Increased from 20°C