In a cylinder sealed with a piston, you rapidly compress 3.00 L of N2 gas initially at

Question:

In a cylinder sealed with a piston, you rapidly compress 3.00 L of N2 gas initially at 1.00 atm pressure and 0.00oC to half its original volume. Assume the N2 behaves like an ideal gas.
(a) Calculate the final temperature and pressure of the gas.
(b) If you now cool the gas back to 0.00°C without changing the pressure, what is its final volume?