Question 36: Thermodynamics & KTG

Question

The figure shows graphs of pressure (p) versus density (d) for an ideal gas at two temperatures T
1
and T
2
, then
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1ls1lp12u/9733ffc6-fbf4-4d69-9a10-3fe28b99e4ae/4cfda560-c01d-11ee-a44e-4fd06148d0b3/file-6y3zli1ls1lp12v.png?format=png)

Accepted Answer

From Ideal gas equation,
$pV = nnT = {{mRT} \over M}$
$n = {{Molar\,mass\,(m)} \over {Molecular\,weight\,(M)}}$
Here, n = number of moles, R = Gas constant, V = volume
$ \Rightarrow {{pV} \over m} = {{RT} \over M}$
$ \Rightarrow {p \over {(m/V)}} = {{RT} \over M}$
${p \over d} = {{RT} \over m}$ [$\because$ ${m \over v} = d$]
$ \Rightarrow {p \over d} \propto T$
$\Rightarrow$ Slope of p versus d graph $\propto$ T
Since, slope is less for the gas at temperature T
1
.
Therefore, T
1
< T
2

Answer

T
1
> T
2

Answer

T
1
< T
2

Answer

T
1
= T
2

Answer

None of these

Thermodynamics & KTG

The figure shows graphs of pressure (p) versus density (d) for an ideal gas at two temperatures T 1 and T 2 , then

Choose the correct answer: