Question

The pressure of a vessel is directly proportional to the square of its volume. If the pressure of the vessel is 5 Bar when the volume of the vessel is 2 Litres.Find the pressure when the volume of the vessel is 1 Litre.

• A. 1.25 Bar
• B. 0.25 Bar
• C. 6.25 Bar
• D. 5 Bar

Answer 1

The correct option is A 1.25 Bar

Given, the pressure (P) of a vessel is directly proportional to the square of its volume (V).
$\Rightarrow P\propto V^2$
Let the constant of variation be k.
$\Rightarrow P=k{V}^2$
Given, at P = 5 Bar, V = 2 Litres.
So, $k=\frac{P}{V}=\frac{5}{2^2}=\frac{5}{4}=1.25$
$\Rightarrow P=1.25V^2$
Hence, the pressure (P) when the volume of the vessel is 1 Litre = $1.25V^2=1.25\left(1^2\right)=1.25Bar.$