JEE Mains · Physics · STD 11 - Kinetic theory of gases
- JEE Mains 2016
- Hard
- MCQ
An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity \(C\) remains constant. If during this process the relation of pressure \(P\) and volume \(V\) is given by \(PV^n =\) constant, then n is given by (Here \(C_p\) and \(C_v\) are molar specific heat at constant pressure and constant volume, respectively) :
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(\;n = \frac{{C - {C_p}}}{{C - {C_V}}}\)
Step-by-step Solution
Detailed explanation
For a polytropic process
\(C = {C_V} + \frac{R}{{1 - n}}\) \(\therefore C - {C_V} = \frac{R}{{1 - n}}\)
\(\therefore 1 - n = \frac{R}{{C - {C_V}}}\) \(\therefore 1 - \frac{R}{{C - {C_V}}} = n\)
\(\therefore n = \frac{{C - {C_V} - R}}{{C - {C_V}}} = \frac{{C - {C_V} - {C_P} + {C_V}}}{{C - {C_V}}}\)
\( = \frac{{C - {C_P}}}{{C - {C_V}}}\left( {{C_P} - {C_{V = R}}} \right)\)
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