A) \[15.2\,\,kg\]
B) \[3.7\,\,kg\]
C) \[zero\]
D) \[7.5\,\,kg\]
Correct Answer: D
Solution :
Initial mass of the gas\[{{m}_{1}}=10\,\,kg\] Initial pressure\[{{P}_{1}}=10\,\,N/{{m}^{2}}\] Final pressure\[{{P}_{2}}=2.5\times {{10}^{6}}\,\,N/{{m}^{2}}\] According the kinetic theory of gases \[PV=\frac{1}{3}m{{c}^{-2}}\] or \[P\propto m\] Hence, \[\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{M}_{1}}}{{{M}_{2}}}\] or \[\frac{{{10}^{7}}}{2.5\times {{10}^{6}}}=\frac{10}{{{m}^{2}}}\] or \[{{m}_{2}}=2.5\,\,kg\] Hence, the quantity of gas taken out from the cylinder is \[={{m}_{1}}-{{m}_{2}}=10-2.5=7.5\,\,kg\]
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