Question

The pressure of a vessel is inversely proportional to its temperature. If the pressure of the vessel is 5 Bar when the temperature of the vessel is 10 Kelvin.Find the pressure when the temperature of the vessel is 20 Kelvin.

• A. 2.5 Bar
• B. 5 Bar
• C. 10 Bar
• D. 7.5 Bar

Answer 1

The correct option is A 2.5 Bar

Given, the pressure (P) of a vessel is inversely proportional to the its temperature (T).
$\Rightarrow P\propto \frac{1}{T}$
Let the constant of variation be k.
$\Rightarrow P=\frac{k}{T}$
$\Rightarrow PT=k$
Given, at P = 5 Bar, T = 10 Kelvin.
So, k = PT = (5)(10) = 50
$\Rightarrow P=\frac{50}{T}$
Hence, the pressure (P) when the temperature of the vessel is 20 Kelvin $=\frac{50}{T}=\frac{50}{20}=2.5Bar.$