MHT CET · Physics · Kinetic Theory of Gases
The molar specific heat at constant pressure of an ideal gas is \(\frac{7}{2} R\). The gas is made up of molecules which are ( \(R\) is the universal gas constant)
- A Polyatomic
- B triatomic
- C monoatomic
- D diatomic
Answer & Solution
Correct Answer
(D) diatomic
Step-by-step Solution
Detailed explanation
Given: \(C_P=\frac{7}{2} R\), and \(C_P-C_V=R\)
\(\therefore C_V=C_P-R=\frac{7}{2} R-R=\frac{5}{2} R\)
\(\therefore \gamma=\frac{C_P}{C_V}=\frac{\frac{7}{2}}{\frac{5}{2}}=\frac{7}{5}\) which matches the \(\gamma_{\text {diatomic }}=\frac{7}{5}\)
\(\therefore\) The gas consists of diatomic molecules!
\(\therefore C_V=C_P-R=\frac{7}{2} R-R=\frac{5}{2} R\)
\(\therefore \gamma=\frac{C_P}{C_V}=\frac{\frac{7}{2}}{\frac{5}{2}}=\frac{7}{5}\) which matches the \(\gamma_{\text {diatomic }}=\frac{7}{5}\)
\(\therefore\) The gas consists of diatomic molecules!
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