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

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: