Polytropic Process

Any thermodynamic process, represented by a Gas Equation in terms of product of powers of parameters {P, V, T} equated to a constant is called a polytropic process.

For example-

(P^3)(V^5)=constant

(P^-1)(V^-3)(T^6)=constant

(P)(V^gamma)=constant...(yes, even the adiabatic one)

P=constant

V=constant, and so on

now, i take a general process (P^a)(T^b)=constant, or equivalently, (P)(T^b/a)=constant, calculate

1)molar heat capacity in terms of Cv, R, a, and b

2)coefficient of volume expansion in terms of instantaneous temperature T, a, and b

3)bulk modulus in terms of instantaneous pressure P, a, and b

and

4)learn if possible..(the resemblance in the 3 is uncanny, and always saves up maths and calculations worth 2 mins during the exam, a double treat if this equation comes in a paragraph!)

now, if someone comes up with a process (P^l)(V^m)(T^n)=constant, use the ideal gas equation to convert it in the form (P^a)(T^b)=constant, and then use the formulae we learnt :-)

-Sambhav