Equation of polytropic process in terms of pressure and temperature is p1−nTn=const.
Writing this explicitly for initial and final state, obtain p11−nT1n=p21−nT2n, from where (p2p1)1−n=(T1T2)n, or p2p1=(p2T1p1T2)n. Using last equation, n=log(p2T1p1T2)p2p1≈−6.7.
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