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Q. Pressure versus temperature graph of an ideal gas is shown, The density of gas at point $A$ is $\rho _{0}$ then the density of gas at point $B$ would be
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NTA AbhyasNTA Abhyas 2022

Solution:

If mass of a gas is constant then there is variation in density of gas with the variation of temperature and pressure because the molar volume of the gas goes on changing because $\rho =\frac{M}{V}$
We know, from Ideal gas law $p=\frac{ρRT}{M}$
For point $A$ , $p=\frac{\rho _{0} RT_{0}}{M}$ $\Rightarrow M=\frac{\rho _{0} RT_{0}}{p}$ ...(i)
For point $B$ , $3p=\frac{ρR \left(\right. 2 T_{0} \left.\right)}{M}=\frac{ρR \left(\right. 2 T_{0} \left.\right)}{\left(\rho \right)_{0} \left(RT\right)_{0}}\times p$ [By Eq. (i)]
$\Rightarrow \, \rho =\frac{3 \rho _{0}}{2}$