The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T₁ and T₂). Which temperature is greater? Explain.

Verified step by step guidance

1. Observe the graph showing the distribution of molecular velocities for the same molecule at two different temperatures, T1 (blue) and T2 (red).
2. Note that the x-axis represents molecular velocity (m/s) and the y-axis represents the relative number of molecules.
3. Understand that at higher temperatures, the distribution of molecular velocities broadens and shifts to higher velocities.
4. Compare the two curves: the red curve (T2) is broader and shifted to higher velocities compared to the blue curve (T1).
5. Conclude that T2 is the higher temperature because the distribution of molecular velocities is broader and shifted to higher velocities compared to T1.

Key Concepts

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that the temperature of a gas is directly related to the average kinetic energy of its molecules. As temperature increases, the average velocity of the molecules also increases, leading to a broader distribution of molecular speeds.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution describes the distribution of speeds among molecules in a gas. It shows that at higher temperatures, the distribution curve shifts to higher velocities, indicating that more molecules have higher kinetic energy. The peak of the curve represents the most probable speed of the molecules, which shifts to the right as temperature increases.

Temperature and Molecular Velocity

Temperature is a measure of the average kinetic energy of the molecules in a substance. In the context of the graph, the temperature associated with the red curve (T2) is greater than that of the blue curve (T1), as indicated by the broader distribution and higher average molecular velocities at T2. This relationship is crucial for understanding how temperature affects molecular motion.