Question

the diagrams below show two pure samples of gas in identical closed, rigid containers. each colored ball represents one gas particle. both samples have the same number of particles. compare the average kinetic energies of the particles in each sample. which sample has the higher temperature?

Explanation:

Step1: Recall the formula for average kinetic energy

The average kinetic energy of gas particles is given by \(K.E.=\frac{1}{2}mv^{2}\), where \(m\) is the mass of a particle and \(v\) is the average speed of the particles.

Step2: Analyze the given data

For both Sample A and Sample B, the mass of each particle \(m = 36u\) and the average particle speed \(v=1300m/s\).

Step3: Calculate the average kinetic energy for both samples

Since \(K.E.=\frac{1}{2}mv^{2}\), and \(m\) and \(v\) are the same for both samples, the average kinetic energy of the particles in Sample A and Sample B is the same.

Step4: Recall the relationship between average kinetic energy and temperature

According to the kinetic - molecular theory of gases, the average kinetic energy of gas particles is directly proportional to the absolute temperature (\(K.E.\propto T\)). If the average kinetic energies are the same, then the temperatures are the same.

Answer:

Neither, the samples have the same temperature.