question_answer

In an experiment, the specific heats of some inert gases (at ordinary temperatures) are measured to be as follows:  

Gas	Atomic mass \[(u)\]	Specific heat (cal\[{{\mathbf{g}}^{\mathbf{-1}}}{{\mathbf{K}}^{\mathbf{-1}}}\])
Helium	4.00	0.748
Neon	20.18	0.147
Argon	39.94	0.0760
Krypton	83.80	0.0358
Xenon	131.3	0.0226

  Try to discover a regularity in the data and explain it on the basis of kinetic energy.             

Answer:

                Molar specific heat \[=\] Atomic mass \[\times \] specific heat

Gas	Molar specific heat
Helium	\[4.00\times 0.748=2.992\] \[\text{cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}\]
Neon	\[20.18\times 0.147=2.966\]\[\text{cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}\]
Argon	\[39.94\times 0.0760=3.035\]\[\text{cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}\]
Krypton	\[83.80\times 0.0358=3.000\]\[\text{cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}\]
Xenon	\[131.3\times 0.0226=2.967\]\[\text{cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}\]

 Thus the molar specific heat of each gas is nearly\[\text{3 cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}.\] It should be so on the basis of kinetic theory of gases according to which for a monoatomic gas, \[{{C}_{V}}=\frac{3}{2}R=\frac{3}{2}\times 2\,cal\,mo{{l}^{-1}}{{K}^{-1}}\] \[=3\,cal\,mo{{l}^{-1}}\,{{K}^{-1}}.\]