Question

The volume V of a gas has an indirect variation with pressure P on it. If the volume is $120$ $c{m}^3$ under pressure of $23$ $\frac{kg}{c{m}^2}$, what pressure has to be applied to have a volume of $80c{m}^3$ ?

• A. $34.5\frac{kg}{c{m}^2}$
• B. $417.3\frac{kg}{c{m}^2}$
• C. $54.5\frac{kg}{c{m}^2}$
• D. $420.3\frac{kg}{c{m}^2}$

Answer 1

The correct option is A $34.5\frac{kg}{c{m}^2}$

For, indirect type of variation,

$k=x\times y$

Here let's consider $x=$ Volume of the gas and $y=$ Pressure applied on it.

So, $k=120\times 23=2760$

Now, solving for the unknown, we have $x=80$ and $k=x\times y$
Therefore, $y=\frac{k}{x}=\frac{2760}{80}=34.5$

Which means, to have a volume of $80c{m}^3$ the a pressure of $34.5\frac{kg}{c{m}^2}$ must be applied on the gas.

Option (a.) is correct.