Question

The pressure of a vessel is directly proportional to the cube of its volume. If the pressure of the vessel is 125 Bar when the volume of the vessel is 5 Litres.Find the pressure when the volume of the vessel is 2 Litres.

• A. 8 Bar
• B. 5 Bar
• C. 16 Bar
• D. 22 Bar

Answer 1

The correct option is A 8 Bar

Given, the pressure (P) of a vessel is directly proportional to the cube of its volume (V).
$\Rightarrow P\propto V^3$
Let the constant of variation be k.
$\Rightarrow P=k{V}^3$
Given, at P = 125 Bar, V = 5 Litres.
So, $k=\frac{P}{V^3}=\frac{125}{5^3}=\frac{125}{125}=1$
$\Rightarrow P=V^3$
Hence, the pressure (P) when the volume of the vessel is 2 Litres = $V^3=\left(2^3\right)=8Bar.$