Question

The slope of the graph between $\log P$ and $\log V$ at constant temperature for a given mass of a gas is:

• A. $+1$
• B. $-1$
• C. $\frac{1}{T}$
• D. $\frac{1}{n}$

Answer 1

The correct option is B $-1$

The gas equation is given by, $PV=nRT$

Taking log on both side, $logPV=lognRT$

By expanding,

$logP+logV=log\left(nRT\right)$

$logP=(-1)logV+log\left(nRT\right)$

When the temperature is constant, mass remains constant hence mole is constant, it means $nRT$ is constant.

So, $log\left(nRT\right)$ is constant

$logP=(-1)logV+log\left(nRT\right)$

This equation follows as,$Y=Mx+C$

Where, $y=logP$ $x=logV$

$c=log\left(nRT\right)$ and $m=-1$

Here m is the slope of the equation.

So, slope = $-1$

Hence, option B is correct.