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Q.
At $10^{\circ}$ C the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$ . At $110^{\circ}$C this ratio is:
Kinetic Theory
Solution:
Let the mass of the gas be m.
At a fixed temperature and pressure, volume is fixed.
Density of the gas, $\rho = \frac{m}{V} $
Now $\frac{\rho}{P} = \frac{m}{PV} = \frac{m}{nRT} $
$\Rightarrow \frac{m}{nRT} = x$ (By question)
$ \Rightarrow xT = \text{constant} \Rightarrow x_{1}T_{1} = x_{2} T_{2} $
$\Rightarrow x_{2} \Rightarrow \frac{x_{1}T_{1}}{T_{2}} = \frac{283}{383} x \begin{bmatrix}\therefore &&\\ T_{1}&=&283K\\T_{2}&=&383K\end{bmatrix}$