# Avg. kinetic energy

## Homework Statement

What is the ratio of the average speed of an atom of neon to another atom of neon at twice the temperature but the same pressure?

## Homework Equations

KE = 3/2 RT; v1/v2 = sqrt. m2/sqrt. m1

## The Attempt at a Solution

I first used KE = 3/2RT and substituted 1 and 2 for T and set them equal to each other. I ended up with a ratio of 1:2. Why is the answer 1:1.4?

Quantum Defect
Homework Helper
Gold Member

## Homework Statement

What is the ratio of the average speed of an atom of neon to another atom of neon at twice the temperature but the same pressure?

## Homework Equations

KE = 3/2 RT; v1/v2 = sqrt. m2/sqrt. m1

## The Attempt at a Solution

I first used KE = 3/2RT and substituted 1 and 2 for T and set them equal to each other. I ended up with a ratio of 1:2. Why is the answer 1:1.4?

Note that you are using equations that are appropriate for root-mean-squared speed. I would take "average" to be "mean", in which case the equations are slightly different. The functional form is the same.

v_mean = SQRT(8*RT/[pi*M]) ==> v2/v1 = ???

Hi, I do not understand what you wrote. I am trying to understand this from a KE=3/2RT and KE=1/2mv^2 point of view. I see that when I set these equal to each other, temp. and velocity are inversely related. T = v^2, thus taking the sqrt. of the temp. I do not know how to use Graham's law for something like this.

Quantum Defect
Homework Helper
Gold Member
Hi, I do not understand what you wrote. I am trying to understand this from a KE=3/2RT and KE=1/2mv^2 point of view. I see that when I set these equal to each other, temp. and velocity are inversely related. T = v^2, thus taking the sqrt. of the temp. I do not know how to use Graham's law for something like this.

You don't need to use Graham's Law.

v_mean = SQRT(8RT/[pi*M])

For the same gas at two different temperatures:

v_2/v_1 = SQRT(8RT_2/(pi*M))/SQRT(8RT_1/(pi*M)) ==> All constants cancel top and bottom ==> v_2/v_1 = SQRT(???)