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MHT CET · Physics · Kinetic Theory of Gases

Which one of the following is NOT a correct expression for an ideal gas?
\(\left[\mathrm{C}_{\mathrm{p}}=\right.\) Molar specific heat of a gas at constant pressure,
\(\mathrm{C}_{\mathrm{V}}=\) Molar specific heat of a gas at constant volume,
\(\gamma=\) Ratio of two specific heats of a gas, \(\mathrm{R}=\) Universal gas
constant]

  1. A \(\mathrm{C}_{\mathrm{v}}=\mathrm{C}_{\mathrm{p}}+\mathrm{R}\)
  2. B \(\mathrm{R}=\mathrm{C}_{\mathrm{V}}(\gamma-1)\)
  3. C \(\frac{\mathrm{C}_{\mathrm{v}}}{\mathrm{C}_{\mathrm{p}}}=\frac{1}{\gamma}\)
  4. D \(\mathrm{R}=\frac{\mathrm{C}_{\mathrm{p}}(\gamma-1)}{\gamma}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{C}_{\mathrm{v}}=\mathrm{C}_{\mathrm{p}}+\mathrm{R}\)

Step-by-step Solution

Detailed explanation

\(C_P\) and \(C_V\) are related as: \(C_P=C_V+R\) Hence expression in (A) is not correct.