Question

A graph is plotted between $\log V$ and $\log T$ for 2 $mol$ of gas at constant pressure of 0.0821 $atm$. $V$ and $T$ are in $L$ and $K$. Which of the following statements are correct?

$I.$ The curve is straight line with slope -1.
$II.$ The curve is straight line with slope $+1$.
$III.$ The intercept on $Y$-axis is equal to 2.
$IV.$ The intercept on $Y$-axis is equal to 0.3010.

• A. $I,II$
• B. $III,IV$
• C. $II,IV$
• D. $I,III$

Answer 1

The correct option is C $II,IV$

$PV=nRT$ or $\log V=\log T+\log \frac{nR}{P}$

Comparing the above equation with $Y=mX+C$

$Slope=m=\tan \theta =\tan {45}^{\circ }=1$

$Intercept=C=\log \frac{nR}{P}=\log \left[\frac{2\times 0.0821}{0.0821}\right]=0.3010$
$II$ & $IV$ are correct.
Hence the correct option is C.