Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature…

Explanation

For a closed vessel, the volume is constant. According to the ideal gas law (\(PV=nRT\)), at constant volume, pressure is directly proportional to temperature in Kelvin (\(P\propto T\)).

Therefore, the fractional change is:

\[ \frac{\Delta P}{P} = \frac{\Delta T}{T} \]

Given the values from the problem:

Percentage change in pressure: \(\frac{\Delta P}{P}=0.4%=\frac{0.4}{100}\)

Change in temperature: \(\Delta T=1^\circ \text{C}=1\text{ K}\) (Note: A change of \(1^\circ \text{C}\) is exactly equal to a change of \(1\text{ K}\))

Substituting these values into the equation:

\[ \frac{0.4}{100} = \frac{1}{T} \] \[ T = \frac{100}{0.4} \] \[ T = 250\text{ K} \]

Correct Option: C