Avg. Kinetic Energy: Neon Ratio @ Diff. Temps

In summary, the ratio of the average speed of an atom of neon to another atom of neon at twice the temperature but the same pressure is 1:1.4.
  • #1

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?
 
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  • #2
brake4country said:

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 = ?
 
  • #3
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.
 
  • #4
brake4country said:
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(?)

[Look at the difference between your answer and the book's answer]
 
  • #5


The ratio of the average speed of an atom of neon to another atom of neon at twice the temperature but the same pressure is not 1:1.4. The correct ratio is 1:1. This is because the kinetic energy of a gas particle is directly proportional to its temperature, and the mass of the particles does not affect this relationship. Therefore, at twice the temperature, the ratio of the average speed of the particles will still be 1:1, regardless of the mass of the particles. The equation you used, v1/v2 = sqrt. m2/sqrt. m1, is used to calculate the ratio of the speeds of two different particles with different masses at the same temperature. In this case, we are looking at the same type of particle (neon atoms) at different temperatures, so this equation is not applicable. Instead, the correct equation to use is KE = 3/2RT, which you have already correctly used in your attempt at a solution. Therefore, the ratio of the average speed of an atom of neon to another atom of neon at twice the temperature but the same pressure is 1:1.
 

What is average kinetic energy?

Average kinetic energy refers to the average amount of energy that a group of particles possess as they move. It is a measure of the motion of particles in a system, and is related to temperature.

What is the neon ratio at different temperatures?

The neon ratio at different temperatures refers to the ratio of the average kinetic energy of neon particles at various temperatures. This ratio can be used to understand the behavior of neon particles as the temperature changes.

How is average kinetic energy related to temperature?

Average kinetic energy and temperature are directly proportional. This means that as the temperature increases, the average kinetic energy of particles in a system also increases, and vice versa.

What is the significance of studying the average kinetic energy of neon particles at different temperatures?

Studying the average kinetic energy of neon particles at different temperatures can provide insights into the behavior of gases and how they interact with one another. It can also help in understanding the properties of neon and how it behaves under different conditions.

How is the average kinetic energy of neon particles calculated?

The average kinetic energy of neon particles can be calculated by using the formula KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass of the particle and v is the velocity of the particle. This formula can be applied to a group of particles to find the average kinetic energy.

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