Thermal Properties of Matter

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Question : 15
Total: 22
Given below are observations on molar specific heats at room temperature of some common gases.
 Gas  Molar specific heat (CV)(calmol1K1)
 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 fromthese for monatomic gases. Typically, molar specific heat of a monatomicgas is 2.92calmol1K1. Explain this difference. What can you infer from the somewhat larger (than the rest) value for chlorine?
Solution:  
The gas which are listed in the above table are diatomic gases and not mono-atomic gases. For diatomic gases, molar specific heat =
5
2
R
=
5
2
×1.98
=4.95
which agrees fairly well with all observations listed in the table except for chlorine. A monoatomic gas molecule has only the translational motion. A diatomic gas molecule, apart from translation motion, the vibrational as well as rotational motion is also possible.
Therefore, to raise the temperature of 1 mole of a diatomic gas through 1°C, heat is to be supplied to increase not only translational energy but also rotational and vibrational energies. Hence, molar specific heat of a diatomic gas is greater than that for monoatomic gas. The higher value of molar specific heat of chlorine as compared to hydrogen, nitrogen, oxygen etc. shows that for chlorine molecule, at room temperature vibrational motion also occurs along with translational and rotational motions, whereas other diatomic molecules at room temperature usually have rotational motion apart from their translation motion. This is the reason that chlorine has somewhat larger value of molar specific heat.
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