Which of the following graphs represents a system with the lowest temperature?

• A. A graph showing particles with the highest average kinetic energy.
• B. A graph where the peak of the distribution is at a higher speed.
• C. A graph where the distribution of particle speeds is shifted toward higher values.
• D. A graph showing particles with the lowest average kinetic energy.

Answer: (D)

Verified step by step guidance

1. Recall that temperature in a system is directly related to the average kinetic energy of its particles. The higher the average kinetic energy, the higher the temperature.
2. Understand that the kinetic energy of a particle is given by the formula \(KE = \frac{1}{2}mv^2\), where \(m\) is the mass and \(v\) is the speed of the particle.
3. Recognize that a graph showing particles with higher average kinetic energy means particles are moving faster on average, indicating a higher temperature.
4. Identify that the peak of the distribution on a speed graph corresponds to the most probable speed of particles; a peak at higher speed means higher temperature.
5. Conclude that the graph representing the system with the lowest temperature will be the one where particles have the lowest average kinetic energy, which corresponds to lower speeds and a peak shifted toward lower values.