From the last equation, , so we have to find . From the first equation, . By taking root of degree n of both sides, you can find .The pressure, p, and volume, V, of a gas undergoing a polytropic process are related by the equation:

p1V1n = p2V2n

where n is the polytropic index.

Ifp1V1/ T1 = p2V2/ T2

determine and expression for p1 in terms of p2 , T1, T2 and n

A remark concerning notation. As is standard, use * for multiplication (it can be omitted in certain cases like 3x) and ^ for exponentiation. Otherwise, it is not clear if your p1V1n means or .