Question 11.15:
Heat must be supplied to increase the temperature of these gases. This increases the average energy of all the modes of motion. Hence, the molar specific heat of diatomic gases is more than that of monatomic gases.
If only rotational mode of motion is considered, then the molar specific heat of a diatomic gas = (5/2)R
= (5/2) X 1.98 = 4.95 cal mol-1 K-1
With the exception of chlorine, all the observations in the given table agree with (5/2)R.
This is because at room temperature, chlorine also has vibrational modes of motion besides rotational and translational modes of motion.
Given
below are observations on molar specific heats at room temperature of
some common gases.
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?
|
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
|
Solution:
The
gases listed in the given table are diatomic. Besides the
translational degree of freedom, they have other degrees of freedom
(modes of motion).Heat must be supplied to increase the temperature of these gases. This increases the average energy of all the modes of motion. Hence, the molar specific heat of diatomic gases is more than that of monatomic gases.
If only rotational mode of motion is considered, then the molar specific heat of a diatomic gas = (5/2)R
= (5/2) X 1.98 = 4.95 cal mol-1 K-1
With the exception of chlorine, all the observations in the given table agree with (5/2)R.
This is because at room temperature, chlorine also has vibrational modes of motion besides rotational and translational modes of motion.
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