Which of the following formulae is wrong?

  • A
    $C_V = \frac{R}{\gamma - 1}$
  • B
    $C_P = \frac{\gamma R}{\gamma - 1}$
  • C
    $C_P / C_V = \gamma$
  • D
    $C_P - C_V = 2R$

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The graph of specific heat at constant volume $(C_v)$ for a monoatomic gas with respect to temperature $(T)$ is:

The ratio of the specific heats $\frac{C_p}{C_v} = \gamma$ in terms of degrees of freedom $(n)$ is given by

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The specific heat capacities of an ideal gas at constant pressure and at constant volume are $620 \ J \ kg^{-1} \ K^{-1}$ and $420 \ J \ kg^{-1} \ K^{-1}$ respectively. The density of the gas at $STP$ is approximately, (in $kg \ m^{-3}$)

Given below are observations on molar specific heats at room temperature of some common gases.
Gas Molar specific heat $(C_v)$ $(cal\, mol^{-1}\, K^{-1})$
Hydrogen $4.87$
Nitrogen $4.97$
Oxygen $5.02$
Nitric oxide $4.99$
Carbon monoxide $5.01$
Chlorine $6.17$

The measured molar specific heats of these gases are markedly different from those for monatomic gases. Typically,molar specific heat of a monatomic gas is $2.92 \; cal/mol\; K$. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?

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