Does a heavier gas lose heat faster than a lighter gas

[morrobay]

Consider two gases, Hydrogen H2 and Neon Ne. in separate containers.
Hydrogen molecular weight=2.02 velocity= 1838m/sec K.E. = 3370 j/mole
Neon molecular weight=20.1 velocity= 584m/sec K.E. =3420 j/mole
Given pV=nRT at t=0 record the temperatures of the two gases.
At t=1,t=2,t=3... would you expect Neon to lose heat faster that Hydrogen,
since the kinetic energy imparted to container walls during collisions is greater with Neon than with Hydrogen ?
Or would you expect Hydrogen to lose heat faster since the collision frequency with container wall is higher with velocity.

 

[sophiecentaur]

Classically, the rate of heat transfer just depends upon temperature difference. If the two gases are at the same temperature then the heat transfer rate should be the same.
In your microscopic scenario, the heavier atoms are going slower - so they will strike the wall less frequently - there is your compensating factor to keep the heat transfer rates the same.

 

[Driftwood1]

Q= mCpDT = UADT

The driving force is the temperature differential.

The other factor is the heat capacity Cp, which is obviously different for the 2 gases


Now you can also look at the heat transfer coefficents at the vessel wall. Remember the temperature differential is across the vessel wall (plus the boundary films/regions etc) - ie the environment. So the determination of the overall heat transfer coefficient (U) is needed.

Lets look at a vessel that has walls equal to the exterior temperature - ie DT=0. Teh gas itself is also in thermal equilibrium with the vessel walls and exterior. The heat transfer rate becomes zero and so the temperature of the gases do not change with time.

If you have the same NUMBER of H2 and Ne atoms in each vessel, with the same temperature differential, then the loss of heat by the gases will be dictated by the heat capacity values.

(should however determine the value of U in each case which will take into account the gas properties and what's actually occruing at the boundary)

You can estimate the Molar heat capacity at constant volume (Cv,m) of monatomic noble gases such Neon by the equation Cv,m = 1.5R. Good agreement for noble gases

For diatomic gases such Hydrogen Cv,m = 2.5R.

So the heat capacity ratio for the 2 gases is approx [H2/Ne] = 5/3

So the amount of heat loss for hydrogen will be about 5/3 times that of Neon if the DT is the same for both vessels and the number of atoms is the vessel is the same

 

[nasu]

Consider two gases, Hydrogen H2 and Neon Ne. in separate containers.
Hydrogen molecular weight=2.02 velocity= 1838m/sec K.E. = 3370 j/mole
Neon molecular weight=20.1 velocity= 584m/sec K.E. =3420 j/mole
Given pV=nRT at t=0 record the temperatures of the two gases.
At t=1,t=2,t=3... would you expect Neon to lose heat faster that Hydrogen,
since the kinetic energy imparted to container walls during collisions is greater with Neon than with Hydrogen ?
Or would you expect Hydrogen to lose heat faster since the collision frequency with container wall is higher with velocity.

I think you may have a problem with your values of kinetic energies.
Assuming ideal gas model, the ratio between the average KE of diatomic hydrogen molecule and that of monoatomic neon should be 5/3.
The average KE actualy does not depend on mass. You can just calculate it as
KE= i/2 KB T
where KB is Boltzman constant, T is kelvin temperature and i is 3 for monoatomic and 5 for diatomic molecules.
This is the value per particle. If you multiply by Avogadro number you'll have it per mol.

As for the rest of the question, you need to specify what parameter(s) are the same.
Is the density of the gases the same, for example? Or they have the same volume?

 

[morrobay]

The values for the two gases are at standard temperature and pressure:
273 Kevin and 1 atm for one mole of gas with vol 22.4 liters.
The relative density 10/1 Ne/H2
My values for KE= 1/2Mv^2
H2=3412 j/mole
Ne=3427 j/mole
These are very close to the values in the original post that are from the chapter:
Kinetic Theory of Gases -1 Physics, Halliday Resnick (quote from chapter) Notice that although the average speeds of different gases varies consideably at the same temperature, the kinetic energy per mole is nearly the same for all gases at the same temperature.
And with 1/2Mv^2=3/2RT the translational KE is proportional to temp.
For the specific heat of monatomic gas ,Neon = 3cal/mole (K)
For the diatomic gas, Hydrogen=5cal/mole (K) both values for constant vol.
So if both gases lose 5cal/mole then the Hydrogen temperature decreases 1 deg. K
and the Neon temp decreases 1.6 deg K.
Its understood that at the same temperatures hydrogen contains more heat.
And if both gases have a temperature decrease of 1 deg K hydrogen loses 5 cal/mole
and neon loses 3 cal/mole.
So Ill re ask the question : Could you expect both gases to transfer the same amount of calories
at the same rate and that then neon would show a larger temp decrease in an equal time interval ?

note - I put in that quote on KE/mole because that was questioned in post #4

 

[sophiecentaur]

"the kinetic energy per mole is nearly the same for all gases at the same temperature"
Isn't that pretty intuitive because temperature is the mean KE per molecule and there are the same number of molecule in a mole.

 

[nasu]

Looking back to your post, I think you are interested, for some reason, in translational degrees of freedom (translation kinetic energy) only.
In this case both gases should have the same value, according to the ideal gas model.
KE=3/2 kB T
You don't need to go through calculating the speed and then use it to calculate the kinetic energy. It just add up errors.

However the total internal energy per mole is not the same and as a consequence the gases have different values for their specific heats, as you show in your post above. This is not a consequence of one molecule being heavier. If you compare Helium with Xenon, they have the same average kinetic energy per mole even though Helium is much more lighter.

Regarding the speed of the global cooling of the gas, it depends on the thermal conductivity of the gases and on the amount of gas, between other things. Maybe you can make the problem more specific by assuming identical containers filled with the same amount of gas (same number of moles or same mass?) in the same initial conditions (pressure and temperature).
See how the thermal conductivity depends on the gas. For ideal gas you can find a quite simple formula, and the fact that it is related to heat capacity.
So the gas with larger heat capacity has larger conductivity.

 

[morrobay]

I just put in a specific numerical problem on the cooling rates of Hydrogen and Neon gases.
From 300 Kevin---> 120Kevin in the introductory physics/homework-coursework section.
So far no replies ? I sure would like to see someone check it out for correctness.