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  1. If I have a Number of gas molecules in a container each having some velocity $v(i)$, what would be the $K.E$ of the gas?

    Will it be the sum of kinetic energies of the individual particles or will it be $\frac{1}{2}mv^2$ where $v$ is the velocity of the center of mass? My book says we have to use the center of mass velocity but according to me the center of mass should stay at rest since there are no external forces (inter molecular attraction if exists is an internal force ) $$$$

  2. What if the container is moving too? What will be the kinetic energy of the gas?

    The sum of K.E's of particles (their velocity somehow calculated by adding the velocity of the container) or by using the velocity of the center of mass. If in the second case both the ways give the same answer please explain me how. And should we include the macroscopic K.E also in the Internal Energy or not $$$$

  3. Please explain which way is the correct and also explain why the other method is wrong.

Edit This is after @sammygerbil last comment Please refer to my last comment in which I quote Feynman

Feynman writes enter image description here


marked as duplicate by AccidentalFourierTransform, sammy gerbil, heather, David Hammen, Kyle Kanos Feb 19 '17 at 14:53

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    $\begingroup$ I think you are failing to distinguish between temperature and kinetic energy. Temperature is related to the random component of KE. See also Do temperature and kinetic energy depend on overall motion? and How does temperature relate to the kinetic energy of molecules? $\endgroup$ – sammy gerbil Feb 18 '17 at 16:08
  • $\begingroup$ @sammygerbil Ok , I sort of understand you. But if we just look at the above question seeing the mechanics point of view and neglecting the thermodynamic one. If atoms are replaced with many big balls then what is the K.E of the system ? Is it the addition of the k.e of different balls ( using their separate velocities) or is K.E of the sysmtem found out by using Center of Mass Velocity because I think the center of mass should remain at rest ( imagine the box to be very very large so that balls can move considerable distances keeping com at rest since no external force)? $\endgroup$ – E2n Feb 18 '17 at 16:18
  • $\begingroup$ @sammygerbil And if we keep this all mechanics point of view what will be the answer to 2nd question ? $\endgroup$ – E2n Feb 18 '17 at 16:18
  • $\begingroup$ You tagged the question as thermodynamics, which implies you are asking about thermal motion and temperature. Outside of that context you have to be clear what you are asking, and which frame of reference you are measuring from. If you are only interested in bulk motion you use the motion of the CM (rest frame). If only interested in internal energy you use the random motion excluding CM motion (CM frame). If you want total KE it is the sum of the two, which is the total KE of all particles (rest frame). There is no standard definition which says one is correct and the others are not. $\endgroup$ – sammy gerbil Feb 18 '17 at 16:30
  • $\begingroup$ @sammygerbil Actually I couldn't understand wholly what you are saying.If I just want the total K.E of the system ( total energy of the system) , I need to sum the kinetic energies of all the parts ( if I am seeing only the mechanics part ) , because the COM as it is stays at rest . Is that right I guess it should be right because that is why we have Moment of Inertia ! ? $\endgroup$ – E2n Feb 18 '17 at 16:48