sample a\nmass of each particle: 36 u\naverage particle speed: 1,300 m/s\nwhich sample has the higher…

sample a\nmass of each particle: 36 u\naverage particle speed: 1,300 m/s\nwhich sample has the higher temperature?\nsample a\nsample b\nneither; the samples have the same temperature\nwhich sample has the higher gas pressure?\nsample a\nsample b\nneither; the samples have the same gas pressure\nsample b\nmass of each particle: 36 u\naverage particle speed: 1,300 m/s

sample a\nmass of each particle: 36 u\naverage particle speed: 1,300 m/s\nwhich sample has the higher temperature?\nsample a\nsample b\nneither; the samples have the same temperature\nwhich sample has the higher gas pressure?\nsample a\nsample b\nneither; the samples have the same gas pressure\nsample b\nmass of each particle: 36 u\naverage particle speed: 1,300 m/s

Answer

Explanation:

Step1: Recall temperature - speed relation

Temperature of a gas is related to the average kinetic energy of its particles. The average kinetic energy formula is $K_{avg}=\frac{3}{2}kT$, and also $K_{avg}=\frac{1}{2}mv^2$. Since mass and average particle speed are the same for both samples A and B, their average kinetic energies are the same. So, their temperatures are the same.

Step2: Recall pressure - speed relation

Gas pressure is given by $P = \frac{2}{3}n\frac{1}{2}mv^2$ (where $n$ is the number density of particles). Without information about the number - density of particles in each sample, we cannot determine the pressure. But if we assume the samples are in the same volume and have the same number of particles (not given explicitly but if we consider a fair comparison), since mass, speed are the same, pressure is also the same.

Answer:

  • Which sample has the higher temperature? neither; the samples have the same temperature
  • Which sample has the higher gas pressure? neither; the samples have the same gas pressure