Thermal speed

A gas for which pressure, temperature, and volume are steady and constant has a Maxwellian distribution of particle speeds. Knowing how many particles there are at any speed allows us to find the average thermal speed, which is the speed of a particle with average kinetic energy given by equation (23.5). This equation (repeated below) is derived directly from the Maxwellian distribution. Read the text aloud Show What are degrees of freedom?
E= 3 2 k B T
E  = energy (J)
kB  = Boltzmann’s constant = 1.38×10−23 J/K
T  = absolute temperature (K)
Thermal energy
per atom
We determine the average thermal speed vth for a particle in a gas by setting the kinetic energy equal to the average thermal energy from equation (23.5): 1 2 m v th 2 = 3 2 k B T Solving this for the average thermal speed leads to the following equation. Read the text aloud
(23.13) v th = 3 k B T m
vth  = thermal speed of particles (m/s)
kB  = Boltzmann’s constant = 1.38×10−23 J/K
T  = temperature (K)
m  = mass (kg)
Thermal speed
Argon is a monatomic gas that makes up about 1% of Earth’s atmosphere. Slightly heavier than oxygen or nitrogen, argon has an atomic mass of 40 g/mol. For argon gas at room temperature of 293 K (20ºC) the average thermal speed is 427 m/s, or 956 mph! As argon heats up, the average speed of the particles becomes even greater, reaching 1,765 m/s when the temperature is 5,000 kelvin! Read the text aloud Maxwellian distribution of speeds for argon gas at three different temperatures
The thermal speed of air is higher than that of argon because the thermal speed varies as the inverse square root of the particle mass. The average molecular mass of air (29 g/mol) is smaller than that for argon; therefore, the thermal speed of air is higher. At 293 K the average thermal speed of air is 502 m/s or 1,120 mph. The speed of sound is related to the thermal speed because sound waves move through collisions between air molecules. In air, the speed of sound at 20ºC is 343 m/s and increases as the square root of the temperature, in agreement with the formula for the thermal speed. Read the text aloud
Two different gases are at the same temperature. One is helium, which has an atomic mass of 4 g/mol. The other gas is neon, which has an atomic mass of 20 g/mol. Which of the following statements is true?
  1. Helium atoms move faster because they have less mass and the same energy.
  2. Atoms of both helium and neon have about the same average speed because they have the same temperature.
  3. Helium atoms move slower because their mass is lower and therefore their energy is also lower.
  4. Neon atoms move faster because they have higher energy proportional to their higher mass.
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