# KE of Gases

#### hansen44

10+ Year Member
7+ Year Member
Ok so there was a problem I did while practicing that explained this but I have literally thousands of problems and I cant find that specific one, so bear with me. I cant exactly remember if the gases were in mixture or separated, for the 1st scenario lets say they were a mixture of non ideal gases at the same temperature, if gas A is heavier than gas B which one will have the greater kinetic energy? I know that Gas B will have a higher average speed than A but will A have a higher Kinetic Energy because of its larger mass? Or will B have a higher Kinetic energy due to the relation of KE=1/2mv^2 since V will be much higher in B? In the 2nd scenario lets say the non ideal gases were separated how do my questions apply to this case. I would really appreciate anyones helps, I know in non ideal gases it might depend on what the gases are and how different the speeds are but in general would you think the heavier mass would have a higher KE or the lighter gas would? Thanks

#### physics junkie

10+ Year Member
5+ Year Member
The internal energy of an ideal gas is solely a function of temperature.

update: wait. realized you are asking about real gases. My guess would be that the same holds for real gases. Temperature is defined as a measure of an object's tendency to give off energy(I didn't make that up). Oh, now that I just looked through wikipedia to double check my definition of temperature I came across "In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy." I can't think of an assumption of the ideal gas model that if removed would make the situation any different for a real gas.

#### Kaustikos

##### Archerize It
Gold Donor
10+ Year Member
The internal energy of an ideal gas is solely a function of temperature.

update: wait. realized you are asking about real gases. My guess would be that the same holds for real gases. Temperature is defined as a measure of an object's tendency to give off energy(I didn't make that up). Oh, now that I just looked through wikipedia to double check my definition of temperature I came across "In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy." I can't think of an assumption of the ideal gas model that if removed would make the situation any different for a real gas.
ditto. Energy is not based on mass, only velocity. That's all you really need to know in regards to the MCAT. Non-ideal gases will only be tested in regards to their pressure and volume affects, not velocity or kinetic energy.

I mean that in regards to the question you asked. IF they were to ask something about velocity or KE, you would always assume ideal. If they were to talk about real gases in that, they would probably explain it in the passage.

#### RSAgator

##### Junior Member
10+ Year Member
5+ Year Member
I suspect that if you were in fact supposed to differentiate the two you'd be given each of their masses/velocities. It would likely be very clear where you had to go with it.

#### hansen44

10+ Year Member
7+ Year Member
The internal energy of an ideal gas is solely a function of temperature.

update: wait. realized you are asking about real gases. My guess would be that the same holds for real gases. Temperature is defined as a measure of an object's tendency to give off energy(I didn't make that up). Oh, now that I just looked through wikipedia to double check my definition of temperature I came across "In a mixture of particles of various mass, the heaviest particles will move more slowly than lighter counterparts, but will still have the same average energy." I can't think of an assumption of the ideal gas model that if removed would make the situation any different for a real gas.
Thanks for the help everybody, this is exactly what im looking for, but how valid does everyone think this quote from Wikipedia is about the the the heavier gas having the same energy as the light gas even though their masses are different?

#### RPedigo

Moderator Emeritus
10+ Year Member
They both have identical energy because they have identical temperature. Temperature is a measure of average kinetic energy. Let's say they both have, oh I don't know, 1000 joules of energy.

Kinetic energy is 1/2mv^2

So you should see if 1000 = 1/2mv^2
The heavier gas will have a lower velocity by virtue of having higher mass. The lighter gas will have a higher velocity by virtue of having a lower mass. They have the same energy, they're just traveling at different speeds.

Let's say that Gas A weighs "20kg"... keep in mind these are arbitrary numbers and would be nowhere near what's real, but I'm doing it to just simplify my explanation
1000 = 1/2mv^2
2000 = mv^2
2000 = (20)v^2
100 = v^2
v = 10m/s

Let's say that Gas B weighs "2kg"... keep in mind these are arbitrary numbers and would be nowhere near what's real, but I'm doing it to just simplify my explanation
1000 = 1/2mv^2
2000 = mv^2
2000 = (2)v^2
1000 = v^2
v = 31m/s

You can see they have identical energy by having the same temperature, yet they have different velocities because of different masses.

#### physics junkie

10+ Year Member
5+ Year Member
ditto. Energy is not based on mass, only velocity.
Energy is based on both mass and velocity. It's units are (mass)(velocity)^2.

#### Kaustikos

##### Archerize It
Gold Donor
10+ Year Member
Energy is based on both mass and velocity. It's units are (mass)(velocity)^2.
average kinetic energy.

you knew what i meant.

#### physics junkie

10+ Year Member
5+ Year Member
average kinetic energy.

you knew what i meant.
I actually didn't know what you meant and still had to think about it for a minute. Average kinetic energy for a single type of gas would only depend on the velocity of each particle since 'm' would be the same for each particle. The example given was two gases mixing so I was thinking differently.

#### Kaustikos

##### Archerize It
Gold Donor
10+ Year Member
I actually didn't know what you meant and still had to think about it for a minute. Average kinetic energy for a single type of gas would only depend on the velocity of each particle since 'm' would be the same for each particle. The example given was two gases mixing so I was thinking differently.
oops. meant to put a " ".

And I should clarify yet again.

The average kinetic energy of a sample gas is measured/determined by temperature.

#### Zerconia2921

10+ Year Member
Ok so there was a problem I did while practicing that explained this but I have literally thousands of problems and I cant find that specific one, so bear with me. I cant exactly remember if the gases were in mixture or separated, for the 1st scenario lets say they were a mixture of non ideal gases at the same temperature, if gas A is heavier than gas B which one will have the greater kinetic energy? I know that Gas B will have a higher average speed than A but will A have a higher Kinetic Energy because of its larger mass? Or will B have a higher Kinetic energy due to the relation of KE=1/2mv^2 since V will be much higher in B? In the 2nd scenario lets say the non ideal gases were separated how do my questions apply to this case. I would really appreciate anyones helps, I know in non ideal gases it might depend on what the gases are and how different the speeds are but in general would you think the heavier mass would have a higher KE or the lighter gas would? Thanks
hmm i would think the ligher the gas the faster it will move.

#### BlackSails

10+ Year Member
You can see they have identical energy by having the same temperature, yet they have different velocities because of different masses.
Identical kinetic energy. If one gas is diatomic and the other is triatomic, then the triatomic gas will have more bending and stretching modes in which energy will be partioned. Im only mentioning this because the OP asked about real gases, not the ideal gas. For ideal gases, this doesnt matter.

#### Premed Worrier

10+ Year Member
5+ Year Member
isn't there also a couple equations relating kinetic energy to gasses that are independent of mass?

i.e.
KE=3/2*kT
KE=3/2*RT

I am pretty sure that this applies to the energy question. After this, the velocity can be figured out with the translational motion equation. just a thought...

#### BlackSails

10+ Year Member
isn't there also a couple equations relating kinetic energy to gasses that are independent of mass?
Only for the ideal gas, the OP asked about non ideal gases.

#### andafoo

##### Andy
10+ Year Member
They both have identical energy because they have identical temperature. Temperature is a measure of average kinetic energy. Let's say they both have, oh I don't know, 1000 joules of energy.

Kinetic energy is 1/2mv^2

So you should see if 1000 = 1/2mv^2
The heavier gas will have a lower velocity by virtue of having higher mass. The lighter gas will have a higher velocity by virtue of having a lower mass. They have the same energy, they're just traveling at different speeds.

Let's say that Gas A weighs "20kg"... keep in mind these are arbitrary numbers and would be nowhere near what's real, but I'm doing it to just simplify my explanation
1000 = 1/2mv^2
2000 = mv^2
2000 = (20)v^2
100 = v^2
v = 10m/s

Let's say that Gas B weighs "2kg"... keep in mind these are arbitrary numbers and would be nowhere near what's real, but I'm doing it to just simplify my explanation
1000 = 1/2mv^2
2000 = mv^2
2000 = (2)v^2
1000 = v^2
v = 31m/s

You can see they have identical energy by having the same temperature, yet they have different velocities because of different masses.