Gas Collisions in Containers: Comparing Ratios of Wall Collisions"

In summary: Or you could use the expression for the number of particles in terms of ##m## and ##M##.In summary, to find the ratio of collisions with the wall in two containers with the same pressure and different temperatures, we can use the equation PV=nRT and the expressions for Urms and collisions. We can also use the number of particles in terms of mass to solve this problem.
  • #1
Any Help
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Homework Statement


You have two samples of the same gas in the same size container, with the same pressure. The gas in the first container has a kelvin temperature four times that of the gas in the other container.

The ratio of number of collisions with the wall in the first container compared to that in the second is:
A) 1:1
B) 4:1
C) 1:4
D) 2:1
E) 1:2

Homework Equations


PV=nRT
Urms = sqrt(3.R.T/M)
collisions= m.Urms^2
Kinetic energy average= 3/2 RT

The Attempt at a Solution


I find that n2 = 4n1
but what I should do after that?
I tried relating the kinetic energy but it didn't work with me.
How we can approach to such problems? What rules should we use
 
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  • #2
Any Help said:

Homework Statement


You have two samples of the same gas in the same size container, with the same pressure. The gas in the first container has a kelvin temperature four times that of the gas in the other container.

The ratio of number of collisions with the wall in the first container compared to that in the second is:
A) 1:1
B) 4:1
C) 1:4
D) 2:1
E) 1:2

Homework Equations


PV=nRT
Urms = sqrt(3.R.T/M)
collisions= m.Urms^2
Kinetic energy average= 3/2 RT

The Attempt at a Solution


I find that n2 = 4n1
but what I should do after that?
I tried relating the kinetic energy but it didn't work with me.
How we can approach to such problems? What rules should we use

It is a bit difficult to help since you don't define the meaning of any variables. Some of them are maybe obvious. But, what is ##m## and ##M##?
if ##m## is the mass/particle and ##M## is the total you would have ##M/m=n##. However, I would start by putting the expressions for ##U_{\mathrm{rms}}## in the expression for "collisions", leading to an expression for "collisions" depending on ##m/M##.
 

FAQ: Gas Collisions in Containers: Comparing Ratios of Wall Collisions"

1. What is the purpose of studying gas collisions in containers?

The purpose of studying gas collisions in containers is to better understand the behavior of gases in confined spaces, such as in industrial or laboratory settings. This knowledge can then be applied to improve safety protocols, optimize gas storage and transportation, and develop new technologies.

2. How do gas collisions occur in containers?

Gas collisions in containers occur when gas molecules move around freely within the container and collide with the walls of the container. These collisions are a result of the random motion of gas molecules and are influenced by factors such as temperature, pressure, and the size and shape of the container.

3. How do scientists compare ratios of wall collisions in gas containers?

To compare ratios of wall collisions in gas containers, scientists use mathematical equations and models to calculate the number of collisions per unit area of the container's walls. This allows them to analyze and compare the behavior of different gases in different types of containers.

4. What are some factors that can affect the ratio of wall collisions in gas containers?

Some factors that can affect the ratio of wall collisions in gas containers include the size and shape of the container, the temperature and pressure of the gas, and the speed and size of the gas molecules. The presence of other substances in the container, such as impurities or other gases, can also impact the ratio of wall collisions.

5. How can studying gas collisions in containers benefit society?

Studying gas collisions in containers can benefit society in various ways. It can help improve safety measures in industries that deal with gases, leading to a decrease in accidents and injuries. It can also contribute to the development of more efficient and environmentally friendly technologies for gas storage and transportation. Additionally, a better understanding of gas collisions can aid in the advancement of scientific research in fields such as chemistry, physics, and engineering.

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