JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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) :
- A \(n = \frac{{{C_p} - C}}{{C - {C_V}}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\)
- B \(\;n = \frac{{C - {C_V}}}{{C - {C_p}}}\)
- C \(\;n = \frac{{{C_p}}}{{{C_V}}}\)
- D \(\;n = \frac{{C - {C_p}}}{{C - {C_V}}}\)
Answer & Solution
Correct Answer
(D) \(\;n = \frac{{C - {C_p}}}{{C - {C_V}}}\)
Step-by-step Solution
Detailed explanation
For a polytropic process \(C = {C_V} + \frac{R}{{1 - n}}\) \(\therefore C - {C_V} = \frac{R}{{1 - n}}\) \(\therefore 1 - n = \frac{R}{{C - {C_V}}}\) \(\therefore 1 - \frac{R}{{C - {C_V}}} = n\)…
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