(Solved): (10 points) Suppose we use a movable piston to confine a sample of nitrogen gas in a cylinder. The ...

(10 points) Suppose we use a movable piston to confine a sample of nitrogen gas in a cylinder. The cylinder is immersed in ice water, so the gas initially has a temperature of \( 0^{\circ} \mathrm{C} \). (1) You fairly rapidly compress the gas, a diabatically decreasing its volume by a factor-of 2.)(2) You hold the piston still until the gas has cooled again to \( 0^{\circ} \mathrm{C} \), and then (3) you allow the gas to expand slowly to its original volume while allowing plenty of time for heat to move out of or into the gas (so that its temperature remains very close to \( 0^{\circ} \mathrm{C} \) ). If \( 85 \mathrm{~g} \) of ice was melted during the second step of the cycle, how much work energy did you put into the gas during the first step? Describe your reasoning. (Hint: I suggest that you first draw a PV diagram. Also, it only looks as if you do not have enough information to solve this problem. If you find yourself doing lots of calculations, stop and think about it some more.)