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If a gas expands irreversibly and adiabatically from $(V_i, p_f+const)$ to $(V_f,p_f)$ will the internal energy change?

I have two thoughts: 1) Yes because $\Delta E= \Delta Q + \Delta W$ always holds

2) No, because theres still the same amount of particles vibrating around.

Can someone clarify this and why internal energy changes for some processes but not for others.

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No, because theres still the same amount of particles vibrating around.

How fast the particles are moving around that actually matters not the number of particles.

Ans will be yes. The system has done some work on the sorrounding (or work is done on the system) but no heat is added to the system(as adiabatic process) so the internal energy will now change according 1st law of thermodynamics.

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