An ideal monatomic gas at 300 k expands adiabatically and reversibly to twice its volume. what is its final temperature?

In an adiabatic process, the following relationship holds:

where T is the gas temperature, V is the volume and  is the adiabatic index, which is equal to  for a monoatomic gas.

We can re-write the equation as

where the labels 1,2 refer to the initial and final conditions of the gas.
Let's rewrite it for , the final temperature:


We can now substitute the initial temperature, T1=300 K, and , because the final volume is twice the initial one. So we find the value of the final temperature:

Ithink they do have the same properties just in less quantities i think