Question

sample a
mass of each particle: 32 u
average particle speed: 1,100 m/s
which sample has the higher temperature?
sample a
sample b
neither; the samples have the same temperature
which sample has the higher gas pressure?
sample a
sample b
neither; the samples have the same gas pressure
sample b
mass of each particle: 32 u
average particle speed: 1,300 m/s

Explanation:

Step1: Recall kinetic - theory relation

The average kinetic energy of gas particles is given by $\overline{K}=\frac{3}{2}kT$, and $\overline{K}=\frac{1}{2}m\overline{v^{2}}$. Since $m$ is the same for both samples, the sample with higher average particle speed $\overline{v}$ has higher average kinetic energy $\overline{K}$, and thus higher temperature $T$.

Step2: Compare speeds

Sample A has an average particle speed of $1100\ m/s$ and sample B has an average particle speed of $1300\ m/s$. Since $1300> 1100$, sample B has higher average kinetic energy and higher temperature.

Step3: Recall pressure - kinetic theory relation

The pressure of a gas is related to the average kinetic energy of its particles and the number of collisions with the container walls. Higher - speed particles (higher kinetic energy) result in more forceful and more frequent collisions, leading to higher pressure. Since sample B has higher - speed particles, it has higher gas pressure.

Answer:

Which sample has the higher temperature?
B. sample B
Which sample has the higher gas pressure?
B. sample B