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There is also a consideration called heat capacity.
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,
The greenhouse affect is based on CO2 and H2O having higher heat capacity than the rest of the gases in the atmosphere.
Water has more ways to tie up energy, so the temperature rise per unit of energy input is much lower.
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/sFor 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
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/sFor 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
we can infer that temperature is proportional to particle's mass and square of particle's speed.
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]
Specific heat capacity at constant pressure cp: Gas: 5200 J/(kg·K)
Molar heat capacity (H2) 28.836 J/(mol·K)
Data for elemental deuteriumFormula: D2 or 21H2Density: 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/m3Gas: 0.452 kg/m3Viscosity: 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)
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.
and in the case of a "bent" molecule like H2O there are umpteen is one more bending and asymmetric stretching rotational modes available
https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782390&Mask=1#Thermo-Gashttps://webbook.nist.gov/cgi/cbook.cgi?ID=C7782390&Mask=1&Type=JANAFG&Table=on#JANAFGAt 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#JANAFGhttps://webbook.nist.gov/cgi/cbook.cgi?ID=C7440597&Mask=1&Type=JANAFG&Table=on#JANAFG
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
in the case of a "bent" molecule like H2O there is one more rotational modes available
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,
umpteen more bending and asymmetric stretching modes available,
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