Question

Give the derivation of “polytropic process”.

$\mathsf{How, C = C_v + \frac{R}{1 - n}?}$​

Answer 1

⭐《ANSWER》

$\huge\mathfrak{\underline {\underline\pink {ANSWER}}}$

↪Actually welcome to the concept of the THERMODYNAMICS

↪Basically here , we are going through a QUASI STATIC ADIABATIC REVERSIBLE PROCESS ,

↪The above Concept is only applicable for the IDEAL GASES AND REVERSIBLE IN NATURE ,

↪Now here , we know that ,

↪as Given in the THERMODYNAMICS ,

↪Molar Heat Capacity is Total heat I.e. ,

↪C = Heat at constant pressure + Heat at constant volume

↪so we get as ,

↪C = Cp + Cv____(3)

↪so we get as ,

〽C = Cp + Cv

↪now from the Thermodynamic relations , we know that ,

〽Cp/Cv = n _____(1)

↪and also ,

〽Cp - Cv = R ________(2)

↪so solving these both we get as ,

↪Cv = Cp/n

↪so we substitute it in ____eqn (2)

↪==》 Cp - Cp/n = R

↪so we get as ,

↪Cp = R/1-n

↪now we substitute in eqn (3)

↪we get as ,

⭐C = Cv + R/1-n

Answer 2

Answer:-

C = Cp + Cv

C = Cp + Cv

Cp/Cv = n Eqation(1)

Cp - Cv = R Equation(2)

Cv = Cp/n

From equation (1) and (2)

Cp - Cp/n = R

Cp = R/1-n

C = Cv + R/1-n