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Qmechanic
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Irreversible process involving temperature change

I do get a sense of how intermediate states cannot be defined if pressure and/or volume are changed suddenly, but what if it is the temperature that is being changed suddenly? For instance, what I if I take a closed container full of hot gas and put it in a freezer? My intuition leads me to believe that temperature change is a very continuous process and hence every intermediate state can be plotted on an isochoric curve. But theoretically, I know that since it is not a quasi-static process, it must have undefined intermediate states. Which one is it?