In this scenario, we're dealing with an isochoric process, meaning the volume of the gas remains constant. For an ideal gas in an isochoric process, the pressure ( P ) is directly proportional to the temperature ( T ) in Kelvin.

The relationship can be expressed as:

Given the percentage increase in pressure is when the temperature is increased by , we can use the relationship:

Substituting the given values into the equation, we have:

Solving for , we find:

Therefore, the initial temperature of the gas in the vessel must be 250 K.