Thermodynamics-- gas problem?

Can you explain how to solve this? I am very confused! Problem 4-3. A piston-cylinder device contains 0.8 kg of nitrogen initially at 100 kPa and 27oC. The gas is now compressed slowly in a polytropic process during which PV1.3 = constant until the volume is reduced by one-half. Calculate the work done and... show more Can you explain how to solve this? I am very confused!

Problem 4-3.

A piston-cylinder device contains 0.8 kg of nitrogen initially at 100 kPa and 27oC. The gas is now compressed slowly in a polytropic process during which PV1.3 = constant until the volume is reduced by one-half. Calculate the work done and the heat transfer for this process.

(Answers: 54.8 kJ, 13.6 kJ)

Here I tried to use the relation W=(P2V2-P1V1/(1-n)). I solved for V1 using PV=nRT and got .696, and used P1V1=P2V2 to find P2, for which I got 50. Plugging all these values into my work equation yielded 174000 J which is of course wildly offbase. How should I be solving this?

Thanks!
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