Question

A graph between pressure, $P$ (along $y$ -axis) and absolute temperature, $T$ (along $x$-axis) for equal moles of two gases has been drawn. Given that volume of second gas is more than volume of first gas. Which of the following statements in correct ?

• A. Slope of gas $(1)$ is less than gas $(2)$
• B. Slope of gas $(1)$ is more than gas $(2)$
• C. Both have same slopes
• D. None of these

Answer 1

Answer: (B)

According to ideal gas equation
$PV = nRT$
or $\frac{P}{T}=\frac{nR}{V}$
$\frac{P}{T} $ represents slope of the graph
As the no. of moles are the same for the two gases
$\therefore \, \frac{P}{T} \propto \frac{1}{V}$
$\because\, V_{2} >\,V_{1}$ (Given)
$\therefore \, \left(Slope\right)_{2} <\, \left(Slope\right)_{1}$
or $\left(Slope\right)_{1}>\, \left(Slope\right)_{2}$