What is the formula for average kinetic energy (KE) of a molecule in a fluid?

What is the formula for average kinetic energy (KE) of a molecule in a fluid?

• A. KE = 2kT
• B. KE = (1/3)kT
• C. KE = (3/2)kT
• D. KE = kT

Answer: (C)

The average kinetic energy (KE) of a molecule in a fluid is given by the formula KE = (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin. This relationship emerges from statistical mechanics, where temperature is directly related to the average kinetic energy of particles. At a fundamental level, the factor of (3/2) arises when considering the three dimensions of motion (x, y, and z) that molecules experience. Each degree of freedom contributes 1/2 kT to the average kinetic energy, and since there are three translational degrees of freedom for a simple molecule, we multiply by three to obtain the total average energy. Thus, as the temperature increases, the kinetic energy of the molecules also increases, reflecting the principle that temperature is a measure of the average energy of particles in a substance. In this context, the other options do not represent the correct relationship between kinetic energy and temperature in an ideal gas or fluid scenario.

The average kinetic energy (KE) of a molecule in a fluid is given by the formula KE = (3/2)kT, where k is the Boltzmann constant and T is the temperature in Kelvin. This relationship emerges from statistical mechanics, where temperature is directly related to the average kinetic energy of particles.

At a fundamental level, the factor of (3/2) arises when considering the three dimensions of motion (x, y, and z) that molecules experience. Each degree of freedom contributes 1/2 kT to the average kinetic energy, and since there are three translational degrees of freedom for a simple molecule, we multiply by three to obtain the total average energy.

Thus, as the temperature increases, the kinetic energy of the molecules also increases, reflecting the principle that temperature is a measure of the average energy of particles in a substance. In this context, the other options do not represent the correct relationship between kinetic energy and temperature in an ideal gas or fluid scenario.