We now know the initial and final pressures, the inital temperature and the ratio of initial to final volumes.
Since we consider Helium to act as an ideal gas (it is very close to one actually), we can use the equation of state for an ideal gas to find the final temperature.
We start by stating the equation of state for an ideal gas and plugging in the initial and final values to get two equations:
Since the number of moles never change, and R is just a constant, we can equate the unknows in the following way:
Solve for the final temperature and plug in the values:
