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Q.
The density of air at N.T.P. is 1.293 gm/lit. If the pressure is tripled keeping its temperature constant its density becomes
Thermal Properties of Matter
Solution:
First we derive an expression for density of a gas.
Density $=\frac{\operatorname{mass}( w )}{\operatorname{volume}( V )}$
but we know that PV = nRT
now $n =\frac{ w }{ M }$ where $M$ is molecular weight
So, $PV =\frac{ w }{ M } RT$
this gives $\frac{ w }{ V }=\frac{ PM }{ RT }=$ density $= d$
Clearly at a constant temperature,
$
\frac{ d _{1}}{ P _{1}}=\frac{ d _{2}}{ P _{2}}
$
so since pressure is tripled, density also triples new density $=$ old density $x_{3}$
$=1.293 \times 3$
$=3.87 gm / ltr$