Question

The pressure of a vessel is inversely proportional to the cube of its temperature. If the pressure of the vessel is 8 Bar when the temperature of the vessel is 2 Kelvin. Find the pressure when the temperature of the vessel is 4 Kelvin.

• A. 1 Bar
• B. 0.5 Bar
• C. 2 Bar
• D. 4 Bar

Answer 1

The correct option is A 1 Bar

Given, the pressure (P) of a vessel is inversely proportional to the cube of its temperature (T).
$\Rightarrow P\propto \frac{1}{T^3}$
Let the constant of variation be k.
$\Rightarrow P=\frac{k}{T^3}$
$\Rightarrow P{T}^3=k$
Given, at P = 8 Bar, T = 2 Kelvin.
So, $k=P{T}^3=\left(8\right)\left(2^3\right)=64$
$\Rightarrow P=\frac{64}{T^3}$
Hence, the pressure (P) when the temperature of the vessel is 4 Kelvin $=\frac{64}{T^3}=\frac{64}{4^3}=1Bar.$