When a gas filled in a closed vessel is heated by raising the temperature by $$1°$$C, its pressure increases by $$0.4\%$$. The initial temperature of the gas is ______ K.

Temperature increase: $$\Delta T = 1°$$ C $$= 1$$ K

Pressure increase: $$0.4\%$$

For a gas at constant volume:

$$\frac{P}{T} = \text{constant}$$

If the temperature increases from $$T$$ to $$T + 1$$:

$$\frac{P_1}{T} = \frac{P_2}{T + 1}$$

$$P_2 = P_1 \times \frac{T + 1}{T} = P_1\left(1 + \frac{1}{T}\right)$$

The percentage increase in pressure:

$$\frac{P_2 - P_1}{P_1} \times 100 = \frac{1}{T} \times 100 = 0.4\%$$

$$\frac{100}{T} = 0.4$$

$$T = \frac{100}{0.4} = 250 \text{ K}$$

Hence, the initial temperature of the gas is 250 K.