Polytrope A mathematical model of an inhomogeneous, compressible configuration in equilibrium under its own gravitation in which the relation between the pressure and the density satisfies the relation p = K(n+1)/n, where K is a constant and n is the polytropic index. [H76] Polytropic Index (n) The polytropic index may have any value from zero (uniform density throughout) to 5 (entire mass concentrated at the center). A polytropic index of 1.5 corresponds to a fully degenerate, nonrelativistic electron gas; it also describes a perfect-gas star in convective equilibrium. (See also Polytrope) [H76]
good question, well, if you look for this on the internet, all you can get is a short definition related to a mathematical formula: PV*exp(K) = constant (unfortunately, I did it many times) . Maybe a good book can help you, however...
A polytropic process is any process in which the specific heat of the gas remains constant. By this defination, all five thermodynamic processes are polytropic. Generally the term polytropic is only applied to those processes whose path falls between those of the isothermal and adiabatic processes. In other words, any expansion process in which the energy to do the work of expansion is supplied partly from the surroundings and partly from the gas within the system will follow a path that falls between those of isothermal and adiabatic. Try following this by ploting a PV diagram and you'll see the results.
I suggest "Principles of refrigeration" by R.J. Dosset. And... "Introduction to chemical Engineering Thermodynamics", by Van Ness, Smith et al.
and... this is not an appropiate forum to ask this question, search the web, there are lots of students discussing many subjects like one this you just posted.