Question

Equation of a gas in terms of pressure (P), absolute temperature, (T) and density (rf) is:

• 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}}} $

Answer 1

Answer: (A)

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}}} $