Maxwell Distribution of speeds

In summary, the conversation discusses the use of the Maxwell distribution of speeds to determine the fraction of carbon dioxide molecules with a kinetic energy in the range of 1.0 eV to 1.1 eV at 1000 K and 3000 K. The individual suggests converting the energy to Joules and using the equation KE=1/2mv^2 to calculate the velocity, and then using the Maxwell distribution of speeds to find the desired fraction. They also mention comparing the result to the integral from 0 to infinity.
  • #1
zeshkani
29
0

Homework Statement


4. Use the Maxwell distribution of speeds to determine the following:
What fraction of carbon dioxide molecules has a kinetic energy in the range 1.0 eV to 1.1 eV at 1000 K and 3000 K?



Homework Equations


i just don't see how the kinetic energy can be used in the maxwell distribution of speeds?


The Attempt at a Solution


ok i tired a few things and this is what i came up with
i think this is the only way to solve it, but iam not sure

so i converted 1.0eV - 1.1eV to Jouls and i used KE=1/2mv^2 to calculate velocity

so (V1)= square root{(1.60218e-19J)(2)/(44.01MM)}
V1= 8.532e-11 m/s

and V2= square root{(1.76239411e-19)(2)/(44.01)}
V2= 8.94936e-11 m/s

does this seem to be the right way on doing this
and now since i have velocity i can use the maxwell distribution of speeds ?
 
Physics news on Phys.org
  • #2
You do the integral from 1.0 to 1.1

Then do the integral from 0 to inf, and compare.
 

FAQ: Maxwell Distribution of speeds

What is the Maxwell Distribution of speeds?

The Maxwell Distribution of speeds is a mathematical model that describes the distribution of speeds of particles in a gas at a given temperature. It is named after physicist James Clerk Maxwell, who first derived it in the 19th century.

How is the Maxwell Distribution of speeds related to kinetic theory?

The Maxwell Distribution of speeds is a fundamental part of kinetic theory, which explains the behavior of gases at a molecular level. It states that the average kinetic energy of gas particles is directly proportional to the temperature of the gas.

What factors affect the shape of the Maxwell Distribution of speeds?

The shape of the Maxwell Distribution of speeds is affected by three main factors: temperature, molecular mass, and the type of gas. Higher temperatures result in a broader distribution with a higher average speed, while heavier molecules have a lower average speed and a narrower distribution.

How is the Maxwell Distribution of speeds different from the Boltzmann Distribution?

The Maxwell Distribution of speeds is a special case of the Boltzmann Distribution, which describes the distribution of speeds of particles in a gas at a given temperature and pressure. The Maxwell Distribution specifically refers to an ideal gas with no intermolecular forces, while the Boltzmann Distribution can be applied to gases with varying degrees of intermolecular interactions.

How is the Maxwell Distribution of speeds used in practical applications?

The Maxwell Distribution of speeds is used in many practical applications, such as in the design of gas turbines and in the study of atmospheric gases. It is also used in the field of thermodynamics to calculate the average kinetic energy of gas particles and to understand the behavior of gases in different conditions.

Back
Top