# What is the temperature at which the motion of particles theoretically ceases?

I think that you will have to tell us that one........

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The temperature at which the motion of particles theoretically ceases is

At this temperature, both the enthalpy (heat content) and entropy (state of randomness or disorder) approach zero. Effectively, the molecules of the gas are slowing down towards being motionless.

Absolute zero also describes a gas reaching a temperature from which no more heat can be removed. Experiments have shown that molecules continue to vibrate at absolute zero.

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ATOMIC MOTION AT 0 K

In regards to atoms, yes, the motion of particles will stop at

When we consider non-interacting atoms in the classical limit, the equipartition theorem gives for the *average per-particle kinetic energy*:

#<< K_(avg,"trans") >> -= K_(avg,"trans")/N = 3/2 k_BT# , in#"J/particle"# where the

#3# comes from the three cartesian directions (#x,y,z# ),#N# is the number of particles,#k_B# is the Boltzmann constant, and#T# is the temperature in#"K"# .MOLECULAR MOTION AT 0 K

Molecules, on the other hand, have chemical bonds, which obviously means they can stretch and/or bend. To a first-order approximation, neglecting rotation at

#"0 K"# (which is entirely valid), they can be modeled by the simple harmonic oscillator system, with energy

#E_(upsilon) = hnu(upsilon + 1/2) = ℏ omega (upsilon + 1/2)# ,where

#upsilon# is the vibrational quantum number,#h# is Planck's constant, and#nu# is the fundamental vibrational frequency in#"s"^(-1)# .

#omega# is the angular frequency, or#2pinu# , and#ℏ = h//2pi# is the reduced Planck's constant.

At

#"0 K"# , everything is in its ground state, and the vibrational ground state has#upsilon = 0# , so

#E_0 = hnu(0 + 1/2) = 1/2hnu# and all molecules continue to vibrate in their ground state at

#"0 K"# .

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Absolute zero.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- At NTP, what is the mass of #"22.4 L"# of nitrogen gas?
- What is the ideal gas law constant?
- If the initial temperature of an ideal gas at 2.250 atm is 62.00 #"^o#C, what final temperature would cause the pressure to be reduced to 1.500 atm?
- A 153.5 mL volume of gas is measured at 71.1#"^o#C. If the pressure remains unchanged, what is the volume of the gas at standard temperature?
- What volume is occupied by a #5.0*g# mass of ammonia that is placed in a piston and allowed to expand against a pressure of #740*mm*Hg# at a temperature of #50# #""^@C#?

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