the diagrams below show two pure samples of gas in identical closed containers. each particle in sample a…

the diagrams below show two pure samples of gas in identical closed containers. each particle in sample a has less mass than each particle in sample b. all of the particles are moving at the same average speed. which sample has the higher temperature?

the diagrams below show two pure samples of gas in identical closed containers. each particle in sample a has less mass than each particle in sample b. all of the particles are moving at the same average speed. which sample has the higher temperature?

Answer

Explanation:

Step1: Recall kinetic - energy formula

The average kinetic energy of gas particles is given by $\overline{K.E.}=\frac{3}{2}kT$, and also $\overline{K.E.}=\frac{1}{2}m\overline{v^{2}}$. Since all particles have the same average speed $\overline{v}$, and particles in sample B have more mass $m$.

Step2: Compare kinetic - energies

Using $\overline{K.E.}=\frac{1}{2}m\overline{v^{2}}$, with $\overline{v}$ constant, a larger mass $m$ means a larger average kinetic energy $\overline{K.E.}$ for particles in sample B.

Step3: Relate kinetic - energy to temperature

Since $\overline{K.E.}=\frac{3}{2}kT$ (where $k$ is the Boltzmann constant), a larger average kinetic energy $\overline{K.E.}$ corresponds to a higher temperature $T$. So sample B has a higher temperature.

Answer:

Sample B