Question

TABLE 3-3 Gas He Ne 1.659 2.521.519 1.001 1.64 1.67 1.68 1.66 2.52 1.5091.008 Kr Xe 1.4103.422.438 0.9995 1.401 3.522.504 1.004 1.404 3.502.448 1.005 1.4043.502.488 1.005 1.4003.522.512 1.005 1.36 H2 CO NO Cl2 1.09 4.12 3.02 1.304 4.40 3.38 1.31 CO21 NH3 1.027 1.06 4.48 3.42 C4H1o0 1.0816.615.4 1.23

The measured data were at temperatures near room temperature.

For diatomic molecules, I know how to calculate the value of r, Cp/R, Cv/R, (Cp-Cv)/R.

I confused why value of Cl2 has a gap with others diatomic molecules value (r, Cp/R, Cv/R, (Cp-Cv)/R) in experimental.

Thanks!

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Answer 1

In general while calculating heat capacity we assume that molucule stays in lowest vibrational energy state because spacing of vibration energy level is large so there will not be any contribution of vibrational degree of freedom in specific heat. However, as per quantum harmonic oscillator approximation, spacing of quantum vibrational energy levels are inversely proportional to reduced mass of atoms in diatomic molecule. Hence, in heavier molecules like chlorine Cl2, energy spacing becomes small and higher vibration energy levels can be occupied even at low temperature. As a result we have to add vibrational degree of freedom as well in case of chlorine specific heat. That is why specific heat of chlorine is higher

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