thermodynamics - How to calculate the final temperature of a gas when it undergoes adiabatic expansion?

The question is as follows:

A sample of $\pu{4.0 moles}$ of a gas ($C_{v,m} = \pu{21 J mol-1 K-1}$) has an initial pressure of $\pu{304.4 kPa}$ and an initial volume of $\pu{20 dm3}$ at $\pu{270 K}$. It undergoes an adiabatic expansion against a constant external pressure of $\pu{79.8 kPa}$, until the volume has increased by a factor of $3$. Calculate the final temperature.

I have calculated: $Q = 0$ and $w = \pu{-3192 J}$ and change in internal energy $=\Delta U = \pu{-31922 J}$.

The next question is to calculate the final temperature of the gas. However, I am unsure on how to calculate this. Originally I thought as $Q=0$, then the final temperature would be the same as the initial temperature. However, I have realized this is incorrect.