Final answer:
The root mean square (rms) speed of the x component of a gas particle's velocity in a monatomic gas at an absolute temperature is given by the equation u_rms = sqrt(3kBT/m), where kB is the Boltzmann constant, T is the temperature, and m is the mass of the gas particle.
Step-by-step explanation:
Root Mean Square (RMS) Speed of a Gas Particle
The question pertains to the root mean square (rms) speed of the x component of a gas particle's velocity in a monatomic gas at a given absolute temperature. According to Kinetic Molecular Theory (KMT), the rms speed, denoted as urms, is the square root of the average of the squares of the speeds across n particles. Expressing the mass m in kilograms and the rms speed in meters per second, we can relate the average kinetic energy to the temperature (T) of the gas using the Boltzmann constant (kB). The rms speed is given by:
urms = √(3kBT/m)
This equation shows that the rms speed is proportional to the square root of the temperature and inversely proportional to the square root of the particle's mass. The use of rms speed provides a measure of the average speed for a group of particles, which is useful in understanding the properties of gases at the standard conditions of temperature and pressure (STP), which impacts their behavior under different conditions.