Question

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure. What can be inferred about relation between $ {{p}_{1}} $ and $ {{P}_{2}} $ ?

• A. $ {{p}_{1}}>{{p}_{2}} $
• B. $ {{p}_{1}}={{p}_{2}} $
• C. $ {{p}_{1}}<{{p}_{2}} $
• D. data is insufficient

Answer 1

Answer: (A)

$ pV=nRT\Rightarrow V=\left( \frac{nR}{p} \right)T $ Slope of the $ V-T $ graph, $ m=\frac{dV}{dT}=\frac{nR}{p} $ $ \Rightarrow $ $ m\propto \frac{1}{p} $ [ $ \therefore $ $ nR= $ constant] Or $ p\propto \frac{1}{m} $ Hence, $ \frac{{{p}_{2}}}{{{p}_{1}}}=\frac{{{m}_{1}}}{{{m}_{2}}}<1 $ where, $ {{m}_{1}} $ is slope of the graph corresponding of $ {{p}_{1}} $ and similarly $ {{m}_{2}} $ is slope corresponding to $ \Rightarrow $ $ {{p}_{2}}<{{p}_{1}}\,or\,\,{{p}_{1}}>{{p}_{2}} $