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, \[M=4gm,V=22.4L,{{C}_{v}}=5J{{K}^{-1}}mo{{l}^{-1}}\] \[{{V}_{sound}}=952m/s,{{C}_{p}}=?\] 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, \[{{C}_{p}}={{C}_{v}}\left[ \frac{M}{pV} \right]v_{sound}^{2}=5\left[ \frac{4\times {{10}^{-3}}}{{{10}^{5}}\times 22.4\times {{10}^{-3}}} \right]{{(952)}^{3}}\]\[=\frac{20}{22.4}\times {{(952)}^{2}}\times {{10}^{-5}}\] \[=809.200\times {{10}^{-5}}\,=8.09\,\,J/mol\,K\].
You need to login to perform this action.
You will be redirected in
3 sec
