A) \[8.0\,J{{K}^{-1}}mo{{l}^{-1}}\]
B) \[7.5\,\,J{{K}^{-1}}mo{{l}^{-1}}\]
C) \[7.0\,\,J{{K}^{-1}}mo{{l}^{-1}}\]
D) \[8.5\,\,J{{K}^{-1}}mo{{l}^{-1}}\]
Correct Answer: A
Solution :
| Given, \[M=4\,gm,V=22.4\,L,{{C}_{v}}=5\,J{{K}^{-1}}mo{{l}^{-1}}\] |
| \[{{V}_{\text{sound}}}=952m/s,{{C}_{p}}=?\] |
| As. velocity of sound, \[{{V}_{sound}}=\sqrt{\frac{\gamma PV}{My}}\] |
| \[\Rightarrow \] \[\gamma =\frac{M}{pV}v_{sound}^{2}=\frac{{{C}_{p}}}{{{C}_{v}}}\] |
| so heat capacity at constant pressure, |
| \[{{C}_{p}}={{C}_{v}}\left[ \frac{M}{pV} \right]v_{sound}^{2}=5\left[ \frac{4\times {{10}^{-3}}}{{{10}^{5}}\times 22.4\times {{10}^{-3}}} \right]{{(952)}^{3}}\] \[=\frac{20}{22.4}\times {{(952)}^{2}}\times {{10}^{-5}}\] |
| \[=809.200\times {{10}^{-5}}\,=8.09\,\,J/mol\,K\] |
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