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## Definition of first law of thermodynamics

 Quote by Outrageous So it is the internal energy for the adiabatic process remains same, then it has nothing to do with the kinetic energy and potential energy? Is that mean the kinetic energy will not necessary remain constant?
Internal energy a system is the sum of the kinetic and potential energy of the system. For a system undergoing an adiabatic expansion in which work is done by the system, there must be a reduction in kinetic + potential energy of the system. For an ideal gas, potential energy does not exist - internal energy is all kinetic. So the kinetic energy and temperature would decrease.

 But that book say, The total work is the same in all adiabatic processes between any two equilibrium states having the same kinetic and potential energy.
The statement is rather poorly worded, in my view. It does sound like they are saying that the kinetic and potential energy of the beginning and end states are the same. But if that were the case, it seems to me that there would be no change in internal energy. So the statement would be meaningless. So I conclude that the statement is intended to mean what I said in my earlier post.

AM

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 Quote by DrDu For example?
I was thinking about two states in which V is the same for each state but P and T differ: eg for an ideal gas where: State 1 = (P0,T0,V0); State 2 = (3P0, 3T0, V0)

But, I suppose you could adiabatically compress and then allow adiabatic free expansion back to the original volume to reach the final state. There is certainly no reversible adiabatic path between the two states.

AM

The total work is the same in all adiabatic processes between any two equilibrium states having the same kinetic and potential energy.

 Quote by Andrew Mason It means that if you take two adiabatic processes, one between state I1 and F1 and the other between I2 and F2, the work done on/by the system will be the same IF the internal energy of the system at I1 and at I2 are the same AND the internal energy of the system at F1 and F2 are the same. AM
Understand already . Thank you

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 Quote by Andrew Mason But, I suppose you could adiabatically compress and then allow adiabatic free expansion back to the original volume to reach the final state. There is certainly no reversible adiabatic path between the two states. AM
Yes, that's one possibility. But remember that you could also add work stirring or with an immersion heater (The latter can be made arbitrarily small or you can use a spark gap in the gas. So it can be viewed at as part of the system. )

 But remember that you could also add work stirring or with an immersion heater (The latter can be made arbitrarily small or you can use a spark gap in the gas. So it can be viewed at as part of the system. )
Yes indeed you can always change any system to a different one and perform pretty well any change you wish.

That does not make it possible for the original system (or impossible either).

 Recognitions: Science Advisor At least stirring is discussed e.g. in Max Planck's Thermodynamik at length as an example of how to do irreversible work and the idea goes back at least to the canon drilling experiments of Lord Rumford.