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I was wondering if you could help me, I think I may have some concepts wrong or incomplete.

## Homework Statement

We have an adiabatic cylinder of volume ##V_1## filled with a gas of pressure ##p_1## and temperature ##T_1## in thermal equilibrium, closed with a piston. All of a suden we rise the pressure on the outside to ##p_2>p_1##, so the cylinder compress in a non reversible way. What is the change in entropy and temperature of the system?

## Homework Equations

## The Attempt at a Solution

All right, first of all, we are told that the cylinder is adiabatic, so ##\Delta Q=0## right? But change of entropy is defined as ##\Delta S=T \Delta Q##, so according to that definition it should also be 0. But that sounds strange, since it's an irreversible process. I guess that definition of entropy does not apply to irreversible process, which one would apply and why?

Assuming that ##\Delta Q=0## we have

##\Delta U=c_v (T_2-T_1)=-p_2 (V_2-V_1)=-p_2 nR(\frac{T_2}{p_2}-\frac{T_1}{p_1})##

And from that equation we could get ##T_2## and thus ##\Delta U##. Is this right?

Thank you very much