[puppypower]

There is also a consideration called heat capacity. Heat capacity is the measure of the amount of energy a substance can absorb, per uint of temperature change. Something with high heat capacity will not get as hot, as something with low heat capacity, for the same energy input. Heat capacity is often measure as the heat absorbed per gram of material to raise it one degree celsius.

 Water has an unusually heat capacity and boiling point, for a molecule so small in size. If you compare water; H2O, to methane; CH4 and ammonia; NH3, which all have the same molecular weights, water is in a different category. Water has more ways to tie up energy, so the temperature rise per unit of energy input is much lower. Temperature appears to be connected to saturation of available energy states, with some materials having more states needing saturation.

The greenhouse affect is based on CO2 and H2O having higher heat capacity than the rest of the gases in the atmosphere. Once these big dogs are saturated, any excess energy given off will heat the rest of the gases to a higher temperature.

[Bored chemist]

There is also a consideration called heat capacity.

Did you think you were adding anything by saying that?

The grown ups have been discussing heat capacity in this thread for a while.

But since their Molar heat capacities are different

the only contributions to the heat capacity are translation and rotation.

the calculated heat capacities under those conditions are 2.5kT and 3 kT

Let's consider the molar heat capacities of noble gases

If you compare water; H2O, to methane; CH4 and ammonia; NH3, which all have the same molecular weights,

In the very real sense that 18, 16 and 17 are the same number.
Did you consider not posting tosh?

The greenhouse affect is based on CO2 and H2O having higher heat capacity than the rest of the gases in the atmosphere.

No, it is not.
that's utter hogwash.

Water has more ways to tie up energy, so the temperature rise per unit of energy input is much lower.

Since the thread is talking about the vapour phase that's simply wrong (water vapour has a lower heat capacity)  and complicatedly wrong ammonia has more ways to distribute the energy).
More interestingly, it's wrong for liquid phase material too.
Water at the BP 4.1813 j/g/k
liquid ammonia 4.700 j/g/k

(from wiki)
https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities

So, as one might expect from a fool who believes in homoeopathy, you are wrong on essentially every "point" you have made.

[hamdani yusuf (OP)]

Their temperatures are almost entirely determined by their average translational motion.
Increasing one mole of Helium by 1 Kelvin increases its internal energy by 20.78 Joule. Since the kinetic energy is ½mv², the average velocity of Helium atoms would increase by √(2 * 20.78 / 4 * 1000) = 101.93 m/s
For Radon, the internal energy will increase by 20.786 Joule.
The average atom velocity would increase by √(2 * 20.786 / 222 * 1000) = 13.68 m/s

By contrasting those average speed values I was trying to figure out if they have anything to do with thermal radiation of gases, which are significantly different than black body radiation. Let's say those noble gases are contained in spherical containers with the same volume. With higher average speed, the gas particles would bounce more often with container wall, hence producing higher frequency of radiation, even though their temperatures are the same. I wonder if there are experimental evidence regarding this issue.

[Bored chemist]

It will make a difference to this
https://en.wikipedia.org/wiki/Spectral_line#Broadening_due_to_local_effects

At high enough temperatures and pressures the light emitted will be pretty close to black body radiation.

https://en.wikipedia.org/wiki/Xenon_arc_lamp

[hamdani yusuf (OP)]

Let's consider the molar heat capacities of noble gases which are almost uniform and very close to 21 J/(mol.K).
But their atomic mass are very different, (4 for Helium and 222 for Radon)
Their densities also vary significantly (0.1786 g/L for Helium and 9.73 g/L for Radon).

Their temperatures are almost entirely determined by their average translational motion.
Increasing one mole of Helium by 1 Kelvin increases its internal energy by 20.78 Joule. Since the kinetic energy is ½mv², the average velocity of Helium atoms would increase by √(2 * 20.78 / 4 * 1000) = 101.93 m/s
For Radon, the internal energy will increase by 20.786 Joule.
The average atom velocity would increase by √(2 * 20.786 / 222 * 1000) = 13.68 m/s

From those results, we can infer that temperature is proportional to particle's mass and square of particle's speed. From previous information we also obtain that different type of motions contribute differently to the temperature of a system. Thus,
T=C.∑m.v_n².ε_n
where
C is a proportionality constant.
m is particle's mass
v_n is particle's speed in corresponding degree of freedom.
ε_n is effectiveness of each degree of freedom to affect system's temperature.

[Bored chemist]

The equipartition principle says that all degrees of freedom are as good as eachother.
Quantum mechanics modifies that  and considers how likely it is that a given degree of freedom is actually excited.

we can infer that temperature is proportional to particle's mass and square of particle's speed.

For a given number of gas molecules and a given energy- which is a rather odd set of data to have.

[hamdani yusuf (OP)]

This is from Wikipedia:
https://en.wikipedia.org/wiki/Equipartition_theorem#History

The equipartition of kinetic energy was proposed initially in 1843, and more correctly in 1845, by John James Waterston.[15] In 1859, James Clerk Maxwell argued that the kinetic heat energy of a gas is equally divided between linear and rotational energy.[16] In 1876, Ludwig Boltzmann expanded on this principle by showing that the average energy was divided equally among all the independent components of motion in a system.[17][18] Boltzmann applied the equipartition theorem to provide a theoretical explanation of the Dulong–Petit law for the specific heat capacities of solids.

The history of the equipartition theorem is intertwined with that of specific heat capacity, both of which were studied in the 19th century. In 1819, the French physicists Pierre Louis Dulong and Alexis Thérèse Petit discovered that the specific heat capacities of solid elements at room temperature were inversely proportional to the atomic weight of the element.[20] Their law was used for many years as a technique for measuring atomic weights.[11] However, subsequent studies by James Dewar and Heinrich Friedrich Weber showed that this Dulong–Petit law holds only at high temperatures;[21] at lower temperatures, or for exceptionally hard solids such as diamond, the specific heat capacity was lower.[22]

Experimental observations of the specific heat capacities of gases also raised concerns about the validity of the equipartition theorem. The theorem predicts that the molar heat capacity of simple monatomic gases should be roughly 3 cal/(mol·K), whereas that of diatomic gases should be roughly 7 cal/(mol·K). Experiments confirmed the former prediction,[3] but found that molar heat capacities of diatomic gases were typically about 5 cal/(mol·K),[23] and fell to about 3 cal/(mol·K) at very low temperatures.[24] Maxwell noted in 1875 that the disagreement between experiment and the equipartition theorem was much worse than even these numbers suggest;[25] since atoms have internal parts, heat energy should go into the motion of these internal parts, making the predicted specific heats of monatomic and diatomic gases much higher than 3 cal/(mol·K) and 7 cal/(mol·K), respectively.

A third discrepancy concerned the specific heat of metals.[26] According to the classical Drude model, metallic electrons act as a nearly ideal gas, and so they should contribute (3/2) NekB to the heat capacity by the equipartition theorem, where Ne is the number of electrons. Experimentally, however, electrons contribute little to the heat capacity: the molar heat capacities of many conductors and insulators are nearly the same.[26]

Several explanations of equipartition's failure to account for molar heat capacities were proposed. Boltzmann defended the derivation of his equipartition theorem as correct, but suggested that gases might not be in thermal equilibrium because of their interactions with the aether.[27] Lord Kelvin suggested that the derivation of the equipartition theorem must be incorrect, since it disagreed with experiment, but was unable to show how.[28] In 1900 Lord Rayleigh instead put forward a more radical view that the equipartition theorem and the experimental assumption of thermal equilibrium were both correct; to reconcile them, he noted the need for a new principle that would provide an "escape from the destructive simplicity" of the equipartition theorem.[29] Albert Einstein provided that escape, by showing in 1906 that these anomalies in the specific heat were due to quantum effects, specifically the quantization of energy in the elastic modes of the solid.[30] Einstein used the failure of equipartition to argue for the need of a new quantum theory of matter.[11] Nernst's 1910 measurements of specific heats at low temperatures[31] supported Einstein's theory, and led to the widespread acceptance of quantum theory among physicists.[32]

I find these data surprising.
https://en.wikipedia.org/wiki/Deuterium#Data_for_elemental_deuterium

Specific heat capacity at constant pressure cp: Gas: 5200 J/(kg·K)

Since molecular weight is 4 g/mol, molar heat capacity of deuterium is
5200 * 4 / 1000 = 20.8 J/(mol·K)

https://en.wikipedia.org/wiki/Hydrogen

Molar heat capacity   (H2) 28.836 J/(mol·K)

Since molecular weight is 2 g/mol, specific heat capacity of hydrogen is 28.836 * 1000 / 2 = 14418 J/(kg·K), which is much bigger than deuterium.

Molar heat capacity of deuterium is significantly different than hydrogen. It's surprising because in case of noble gases, different atomic masses don't seem to affect molar heat capacity.

[Bored chemist]

Were they measured at the same temperature?
There's also this complication.
https://en.wikipedia.org/wiki/Spin_isomers_of_hydrogen

[hamdani yusuf (OP)]

Wikipedia doesn't clearly mention that

Data for elemental deuterium
Formula: D2 or 2
1H
2

Density: 0.180 kg/m3 at STP (0 °C, 101.325 kPa).
Atomic weight: 2.0141017926 u.
Mean abundance in ocean water (from VSMOW) 155.76 ± 0.1 ppm (a ratio of 1 part per approximately 6420 parts), that is, about 0.015% of the atoms in a sample (by number, not weight)
Data at approximately 18 K for D2 (triple point):

Density:
Liquid: 162.4 kg/m3
Gas: 0.452 kg/m3
Viscosity: 12.6 μPa·s at 300 K (gas phase)
Specific heat capacity at constant pressure cp:
Solid: 2950 J/(kg·K)
Gas: 5200 J/(kg·K)

The data is either at triple point or STP.

[alancalverd]

Noble gases are monatomic, so essentially billiard balls, whereas H2 and D2 are dumbell molecules with all sorts of ways of storing and exchanging energy.

[hamdani yusuf (OP)]

https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782390&Mask=1#Thermo-Gas
https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782390&Mask=1&Type=JANAFG&Table=on#JANAFG

At 300K, the molar heat capacity of deuterium is 29.19 J/(mol*K)
At 300K, the molar heat capacity of hydrogen is 28.85 J/(mol*K)
At 300K, the molar heat capacity of helium is 20.79 J/(mol*K)

https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Mask=1&Type=JANAFG&Table=on#JANAFG
https://webbook.nist.gov/cgi/cbook.cgi?ID=C7440597&Mask=1&Type=JANAFG&Table=on#JANAFG

[alancalverd]

And there you have it. Most of the kinetic energy is in "billiard ball" kinetics, but where you have a simple diatomic molecule like H2 or D2, there are additional rotational and stretching modes that increase molar heat capacity, and in the case of a "bent" molecule like H2O there are umpteen more bending and asymmetric stretching modes available, even without temporary polymerisation at low temperatures.

[Bored chemist]

Noble gases are monatomic, so essentially billiard balls, whereas H2 and D2 are dumbell molecules with all sorts of six ways of storing and exchanging energy.

Three translations, a vibrational mode and two (degenerate) rotational ones.

and in the case of a "bent" molecule like H2O there are umpteen is one more bending and asymmetric stretching rotational  modes available

[Bored chemist]

https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782390&Mask=1#Thermo-Gas
https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782390&Mask=1&Type=JANAFG&Table=on#JANAFG

At 300K, the molar heat capacity of deuterium is 29.19 J/(mol*K)
At 300K, the molar heat capacity of hydrogen is 28.85 J/(mol*K)
At 300K, the molar heat capacity of helium is 20.79 J/(mol*K)

https://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Mask=1&Type=JANAFG&Table=on#JANAFG
https://webbook.nist.gov/cgi/cbook.cgi?ID=C7440597&Mask=1&Type=JANAFG&Table=on#JANAFG

For helium, only the translational modes exist, so it has the lowest heat capacity of these gases. (And the same as neon, argon etc)

At 300K there's enough energy to excite the translational and rotational modes, but barely enough to excite the vibrational one.
However, the energy needed to excite the vibration in deuterium is a bit lower because the vibrational frequency is lower (the spring is pretty nearly the same, but the masses are larger).
So slightly more energy goes into getting the molecule vibrating, That's why D2 has a slightly greater  heat capacity.

[alancalverd]

http://www.chem.ucla.edu/~harding/IGOC/A/asymmetric_stretching.html#:~:text=Asymmetric%20stretching%3A%20Simultaneous%20vibration%20of%20two%20bonds%2C%20with,is%20contracting.%20Asymmetric%20bond%20stretching%20in%20water%20.

is a nice illustration of a phenomenon that occurs in Cambridge and Los Angeles, but not in Oxford, apparently 

[Bored chemist]

http://www.chem.ucla.edu/~harding/IGOC/A/asymmetric_stretching.html#:~:text=Asymmetric%20stretching%3A%20Simultaneous%20vibration%20of%20two%20bonds%2C%20with,is%20contracting.%20Asymmetric%20bond%20stretching%20in%20water%20.

is a nice illustration of a phenomenon that occurs in Cambridge and Los Angeles, but not in Oxford, apparently 

Are you saying that you think that Cantabrian diatomics like H2 and D2 have an asymmetric stretch, or do you think that linear molecules can't?

The only change that being bent or linear makes is the removal of the rotational energy about the linear axis.
So

in the case of a "bent" molecule like H2O there  is one more  rotational  modes available

compared to a bent  but otherwise similar molecule.

There are two approaches to this, in one case you count the atoms, multiply by 3 and then subtract 5 or 6 (depending on whether it's linear or not).
https://en.wikipedia.org/wiki/Molecular_vibration

In the other approach, you count the spectroscopists writing the posts.

[alancalverd]

Are you saying that you think that Cantabrian diatomics like H2 and D2 have an asymmetric stretch, or do you think that linear molecules can't?

The only change that being bent or linear makes is the removal of the rotational energy about the linear axis.

My original statement referred explicitly to H2O, which seems to have the same properties at UCLA as in Cantab. I can't imagine an asymmetric stretch in a diatomic molecule, but then I'm not a chemist!   There being no suitable emoticon, semper lingua in buccam, socius.

[Bored chemist]

My original statement referred explicitly to H2O,

And it has 1 more mode than CO2 (where the difference is that the molecule is linear rather than bent), or 4 more modes than H2.
Yet you talked about

umpteen more bending and asymmetric stretching modes available,

What's your idea of the cut off for calling something "umpteen"?
Is it 1,2,3 or 4?

[Bored chemist]

semper lingua in buccam, socius.

My Latin is practically non existent but Google thinks you said "Always tongue into my head member".
I suggest you 

[alancalverd]

Tongue in cheek, buddy.