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  4. At 10° C the value of the density of a fixed mass of an ideal gas divided by it pressure is x. At 110° C this ratio is

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Q. At $10^{\circ} C $ the value of the density of a fixed mass of an ideal gas divided by it pressure is $x$. At $110^{\circ} C $ this ratio is

AIPMTAIPMT 2008Thermodynamics

Solution:

Mass of the gas $=m$.
At a fixed temperature and pressure, volume is fixed.
Density of the gas $\rho=\frac{m}{V} $
$\Rightarrow \frac{m}{V . P}=\frac{m}{n R T}=x$
$\therefore \times T=$ constant.
At $10^{\circ} C$ i.e., $283 K , \times T=\times 283 K$
At $110^{\circ} C, x T=x^{\prime} 383 K$
$\Rightarrow x^{\prime}=\frac{283}{383} x$