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Q. 11.15  Given below are observations on molar specific heats at room temperature of some common gases.

                    Gas                                    Molar specific heat (Cv )

                                                                    (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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Monoatomic gases have only translational degree of freedom but diatomic gases have rotational degrees of freedom as well. The temperature increases with increase in the spontaneity of motion in all degrees. Therefore to increase the temperature of diatomic gases more energy is required than that required to increase the temperature of monoatomic gases by the same value owing to higher degrees of freedom in diatomic gases.

If we only consider rotational modes of freedom the molar specific heat of the diatomic gases would be given as

\\c=\frac{fR}{2}\\ c=\frac{5}{2}\times 1.92\\ c=4.95\ cal\ mol^{-1}\ K^{-1}

The number of degrees of freedom = 5 (3 translational and 2 rotational)

The values given in the table are more or less in accordance with the above calculated one. The larger deviation from the calculated value in the case of chlorine is because of the presence of vibrational motion as well.

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Sayak

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