Question

In the process $PV=$ constant, pressure $\left(P\right)$ versus density $\left(\rho \right)$ graph of an ideal gas is

• A. a straight line parallel to $P$ - axis
• B. a straight line parallel to $\rho$ - axis
• C. a straight line passing through origin
• D. a parabola

Answer 1

The correct option is C a straight line passing through origin

Given:
$PV=$ constant
$\Rightarrow T=$ constant $[\because PV=nRT\text{for ideal gas}]$
We know that,
$PM=\rho RT$
$\Rightarrow P=\frac{RT}{M}\rho$ ........(1)
On comparing (1) with the equation of straight line , $y=mx+c$,
where $y=P$ & $x=\rho$
$\text{Slope}m=\frac{RT}{M}$ which is positive
and $\text{y-intercept}c=0$

As y-intercept is zero and slope is positive , the straight line passes through the origin with positive slope.