Question

sample a
mass of each particle: 30 u
average particle speed: 1,400 m/s
compare the average kinetic energies of the particles in each sample. which sample has the higher temperature?
sample a
sample b
neither; the samples have the same temperature
sample b
mass of each particle: 46 u
average particle speed: 1,400 m/s

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $m$ is the mass and $v$ is the speed.

Step2: Calculate kinetic energy for sample A

Given $m_A=30\ u$ and $v = 1400\ m/s$. Substitute into the formula: $K_A=\frac{1}{2}\times30\times(1400)^{2}= 30\times\frac{(1400)^{2}}{2}$.

Step3: Calculate kinetic energy for sample B

Given $m_B = 46\ u$ and $v = 1400\ m/s$. Substitute into the formula: $K_B=\frac{1}{2}\times46\times(1400)^{2}=46\times\frac{(1400)^{2}}{2}$.

Step4: Compare kinetic energies

Since $\frac{(1400)^{2}}{2}$ is the same in both expressions and $46>30$, we have $K_B > K_A$.

Step5: Relate kinetic energy and temperature

The average kinetic energy of particles is directly proportional to the temperature of the sample. Higher average - kinetic energy means higher temperature.

Answer:

sample B