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I have a box filled with a gas ( a real gas , cannot be approximated to a ideal gas) in which the molecules are jiggling. This box is in a gravitational field and an electric field and has a piston over it. The piston is not diathermal and the gas is somehow doing work on the piston. Together with this , the box is moving in the gravitational field as well as the electric field and there is an external force on the box which is continuously accelerating it. Moreover outside the box there is some medium which is applying a non conservative force on the box as it moves ( friction ).

What would be the 1st law in this case for the entire box piston system. I am not asking for a solution ( it might not be possible ). I am asking what the general equation of the 1st law would become ( just the terms that would be added ) due to gravitational , electric and non conservative force effect. What shall be the energy Conservation equation in the above

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Well, the complete form of the first law of thermodynamics (that is sometimes overlooked) is $$\Delta E=Q-W$$where $$E=U+(KE)+(PE)$$ Also, in this equation, W includes piston work, frictional work, work related to an electric field, etc. The system, according to your description includes the solid box and its contents (the gas). Actually, the electric field could be lumped in with the PE or it could be included separately in the work. But the PE would usually be considered to include gravitational.

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  • $\begingroup$ Thanks I was in search for the answer since weeks. The problem that I had was that U (internal energy) , according to wikipedia does not depend on external fields ( electric or any other ). So please just tell whether what I have understood from your answer is correct ! The U term in your equation accounts for the internal energy ( depending on only internal forces and accounting for the K.E due to random motion of molecules which the gives the gas its temperature) . I am continuing in the comment (just a second) $\endgroup$
    – Shashaank
    Feb 26 '17 at 12:29
  • $\begingroup$ Continued- The KE and PE terms include the kinetic and the potential energy of the system due to its movement in the field ( electric gravitational ). For W you have explained already. Now if this is right , then first of all due to Movement of the system in the field and due to the continued work done by the external force its PE and KE will continuously change . How to represent that ?Thanks $\endgroup$
    – Shashaank
    Feb 26 '17 at 12:34
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    $\begingroup$ Well, to determine the changes in KE and PE, you usually also have to use Newton's 2nd law (unless you are provided with more specific details on the initial and final states of the system). $\endgroup$ Feb 26 '17 at 12:39
  • $\begingroup$ So at any instant of time where I know the values of P.E & Ke the equation is the above one ? Besides that + W would be equally right ? And just one last thing . Wouldn't the KE term and PE term have any effect on U ( relative motion for K.E polarization effects for P.E ) ? In that way U would depend on external field but wiki media says it doesn't ? $\endgroup$
    – Shashaank
    Feb 26 '17 at 12:43
  • $\begingroup$ I don't have experience with applying this in situations where there is an electric field or a magnetic field, but my inclination would be to include molecular polarization effects in the internal energy. I might also add that, if the final state of the system is not an equilibrium state (such that the KE , pressure, temperature, etc. of the gas is changing), you would supplement this with consideration of the fluid mechanics of the gas (including viscous effects and turbulence). $\endgroup$ Feb 26 '17 at 13:02

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