According to the kinetic theory of matter, which of the following statements is true?

According to the kinetic theory of matter, which of the following statements is true?

• A. The average kinetic energy is inversely proportional to the mass of the particles
• B. The average kinetic energy is directly proportional to the square of the average velocity of the particles
• C. The average kinetic energy is equal to the temperature of the particles
• D. The average kinetic energy is independent of the temperature

Answer: (B)

The correct answer highlights a fundamental aspect of the kinetic theory of matter, which relates the average kinetic energy of particles in a substance to their motion. According to this theory, the average kinetic energy of gas particles is indeed directly proportional to the square of their average velocity. This relationship is rooted in the formula for kinetic energy, which is expressed as \( KE = \frac{1}{2} mv^2 \), where \( m \) is mass and \( v \) is velocity. As temperature increases, so does the average kinetic energy of the particles. Since velocity is a component of kinetic energy, understanding that kinetic energy relates to the square of the velocity is crucial. Thus, when the average velocity of particles increases—often due to an increase in temperature—this leads directly to an increase in the average kinetic energy. The other statements fail to accurately describe the relationship established by the kinetic theory. The first option mixes mass with kinetic energy inaccurately; kinetic energy does not decrease with increasing mass when velocity is constant. The third option misstates that average kinetic energy equals temperature; in fact, temperature is a measure related to the average kinetic energy, but they are not equal. Lastly, the assertion that average kinetic energy is independent of temperature

The correct answer highlights a fundamental aspect of the kinetic theory of matter, which relates the average kinetic energy of particles in a substance to their motion. According to this theory, the average kinetic energy of gas particles is indeed directly proportional to the square of their average velocity. This relationship is rooted in the formula for kinetic energy, which is expressed as ( KE = \frac{1}{2} mv^2 ), where ( m ) is mass and ( v ) is velocity.

As temperature increases, so does the average kinetic energy of the particles. Since velocity is a component of kinetic energy, understanding that kinetic energy relates to the square of the velocity is crucial. Thus, when the average velocity of particles increases—often due to an increase in temperature—this leads directly to an increase in the average kinetic energy.

The other statements fail to accurately describe the relationship established by the kinetic theory. The first option mixes mass with kinetic energy inaccurately; kinetic energy does not decrease with increasing mass when velocity is constant. The third option misstates that average kinetic energy equals temperature; in fact, temperature is a measure related to the average kinetic energy, but they are not equal. Lastly, the assertion that average kinetic energy is independent of temperature