A) \[\frac{{{P}_{1}}}{{{T}_{1}}{{d}_{1}}}=\frac{{{P}_{2}}}{{{T}_{2}}{{d}_{2}}}\]
B) \[\frac{{{P}_{1}}{{T}_{1}}}{{{d}_{1}}}=\frac{{{P}_{2}}{{d}_{1}}}{{{d}_{2}}}\]
C) \[\frac{{{P}_{1}}{{d}_{2}}}{{{T}_{2}}}=\frac{{{P}_{2}}{{d}_{1}}}{{{T}_{1}}}\]
D) \[\frac{{{P}_{1}}{{d}_{1}}}{{{T}_{1}}}=\frac{{{P}_{1}}{{d}_{2}}}{{{T}_{2}}}\]
Correct Answer: A
Solution :
Gas equation is \[\frac{PV}{T}=cons\tan t=R\] or \[\frac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\] If m is the mass of a gas and \[{{d}_{1}}\]and \[{{d}_{2}}\]are its density at absolute temperature \[{{T}_{1}}K\]and \[{{T}_{2}}K,\]then \[{{V}_{1}}=m/{{d}_{1}}\]and \[{{V}_{2}}=m/{{d}_{2}}\] \[\therefore \] \[\frac{{{P}_{1}}}{{{T}_{1}}}\left ( \frac{m}{{{d}_{1}}} \right)=\frac{{{P}_{2}}}{{{T}_{2}}}\left( \frac{m}{{{d}_{2}}} \right)\] \[\frac{{{P}_{1}}}{{{T}_{1}}{{d}_{1}}}=\frac{{{P}_{2}}}{{{T}_{2}}{{d}_{2}}}\]
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