Question

The pressure of a vessel is inversely proportional to the square of its temperature. If the pressure of the vessel is 2 Bar when the temperature of the vessel is 5 Kelvin. Find the pressure when the temperature of the vessel is 10 Kelvin.

• A. 0.5 Bar
• B. 1 Bar
• C. 5 Bar
• D. 10 Bar

Answer 1

The correct option is A 0.5 Bar

Given, the pressure (P) of a vessel is inversely proportional to the square of its temperature (T).
$\Rightarrow P\propto \frac{1}{T^2}$
Let the constant of variation be k.
$\Rightarrow P=\frac{k}{T^2}$
$\Rightarrow P{T}^2=k$
Given, at P = 2 Bar, T = 5 Kelvin.
$So,k=P{T}^2=\left(2\right)\left(5^2\right)=50$
$\Rightarrow P=\frac{50}{T^2}$
Hence, the pressure (P) when the temperature of the vessel is 10 Kelvin $=\frac{50}{T^2}=\frac{50}{{10}^2}=0.5Bar.$