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My Chemistry textbook says that in free expansion there is no external pressure and thus the change in internal energy of the system is equal to the heat that we supply to it.

But i think that the only way to apply heat to a system is to make the external molecules loose their kinetic energy to the molecules of the system. ( NOTE - I am not talking about increasing the heat by adding radiant energy to the system )

If the external molecules loose some of their KE then they must exert a force on the system and thus the external pressure must not be equal to zero!

Is this correct? If not, then please tell me where I am wrong.

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  • $\begingroup$ So you are talking about conduction of heat to a fluid? $\endgroup$
    – Steeven
    Dec 17, 2016 at 11:56
  • $\begingroup$ @Steeven In general, this happens. Well to be precise, I was reading about gases when this doubt popped up in my head. $\endgroup$
    – Aaryan Dewan
    Dec 17, 2016 at 11:58
  • $\begingroup$ No external pressure practically means no material surrounding it. So the statement is itself assuming only heating from radiation. So, unless I misunderstood your question, the answer would be "yes". $\endgroup$
    – Steeven
    Dec 17, 2016 at 12:00
  • $\begingroup$ @Steeven , So in free expansion is there no way to increase the temperature of a system except by providing it some heat through radiations ? $\endgroup$
    – Aaryan Dewan
    Dec 17, 2016 at 12:04
  • $\begingroup$ If free expansion means no external pressure, then there is no "touching" surrounding material. Conduction or convection is not possible. $\endgroup$
    – Steeven
    Dec 17, 2016 at 12:12

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If no external pressure means no material surrounding it, the statement is itself assuming only heating from radiation. So, unless I misunderstood your question, the answer would be "yes".

With no "touching" surrounding material, conduction or convection is not possible.

In a comment @ChesterMiller points out that a gas can be kept in a container with a free direction to expand along (as with a free piston). Here there is free expansion but possibly conduction as well.

To your question in this case, the "collisions" between more energitic molecules in the container wall with the gas molucules does indeed provide tiny pressure on the gas. It will most likely be negligible, but your thinking is strictly correct. In text-books I've been using, such container (and piston) is usually described as thermally insulating.

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  • $\begingroup$ This is incorrect. You can have zero external pressure over part of the boundary where the motion is occurring (e.g., a massless frictionless piston with vacuum outside the cylinder) while you are applying conductive heat through the rigid walls of the cylinder (say by means of an electrical heater in contact with the cylinder). $\endgroup$
    – Chet Miller
    Dec 17, 2016 at 13:41
  • $\begingroup$ @ChesterMiller Yes, of course. AaryanDeWan see this comment. I am adding it to the question accordingly. $\endgroup$
    – Steeven
    Dec 17, 2016 at 13:57
  • $\begingroup$ @Steeven , What do you mean by conduction here? Heat going out of the system into the vacuum as the piston goes up? $\endgroup$
    – Aaryan Dewan
    Dec 20, 2016 at 10:19
  • $\begingroup$ @AaryanDewan What I mean by conduction? I you heat up the surrounding container, the container walls in contact will transfer heat to the gas as the walls interfaces. $\endgroup$
    – Steeven
    Dec 20, 2016 at 11:39
  • $\begingroup$ How can you heat the surrounding if there is vacuum outside? ( NO radiation here ) $\endgroup$
    – Aaryan Dewan
    Dec 20, 2016 at 14:04

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