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 |
Answer:
Molar specific heat \[=\] Atomic mass \[\times \] specific heat
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, \[{{C}_{V}}=\frac{3}{2}R=\frac{3}{2}\times 2\,cal\,mo{{l}^{-1}}{{K}^{-1}}\] \[=3\,cal\,mo{{l}^{-1}}\,{{K}^{-1}}.\]
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
\[131.3\times 0.0226=2.967\]\[\text{cal mo}{{\text{l}}^{\text{-1}}}{{\text{K}}^{\text{-1}}}\]
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