I have a metal tin full of xenon, with a volume of 600cm3 at 20 celcius. I need to work out what will happen if I cool the tin to -40 celcius. I need to work out the new volume of the tin at this cooler temperature.

Firstly I need to decide whether the process is isothermal, isochoric or adiabatic.

My own conclusion is that the process cannot be isochoric because in an isochoric process the volume of the closed system remains constant.

In an isothermal process the temperature remains constant, and clearly here we also have a change of temperature. Hence I suspect it cannot be isothermal.

By process of elimination I am left with adiabatic, but I'd just like a helpful explanation as to why so, as my book isn't very comprehensive.

Please be patient with me, I'm a junior in high school taking early AP's and physics is still quite new to me.

Thank you

Why would the volume change?

You have a tin, unless you have extremely low pressure you aren't going to change the volume appreciably; the tin wont change size much when cooling.

Obviously it's not isothermal; the temperature is what we know changes.

We are now left with adibatic or isochoric process to choose between.

I have no reason to assume the volume of the tin changed; besides the fact that you stated that (which I'm interpreting as a misunderstanding). On the other hand, going from 20C to -40C likely involved heat transfer.

Therefore it's not adibatic, making it isochoric.

Adiabatic mean no heat transfert and it is a way of approximation behavior for part of ideal gazes. It is about the opposite of isothermal because in most cases, to be isothermal mean to had or take off heat or order to maintain temperature. Heat is internal energy as well as kinetic and potential are mecanical energies.