From the graph, we can see that slope of straight line with temperature

T₁ is greater than slope of straight line with temperature T_2.

Slope of straight line is given as:

Slope =

In our graph, slope is

where P=pressure

= density of gas

So, ratio for T₁ is more than T_2.

Rms speed of gas is given as

where R=gas constant whose value is 8.31 J/mol K.

T=temperature of gas.

M= molar mass of molecule of gas

We also know that ideal gas equation is

PV=nRT

Where V= volume of gas

R=gas constant

T=temperature

N=number of moles of gas

So, we can write .

Putting the value of RT in equation (i),we get

nM= total mass of gas ‘m’

and density =

Putting the value of density in equation (ii)_, we get

Since ratio for T₁ is more than T₂ therefore rms speed for ideal gas at temperature T₁ is more than temperature T₂. And if rms speed is more for temperature T₁ then T₁ > T₂ from formula

v_rms =