A bicycle tyre is filled with air having pressure of $$270$$ kPa at $$27°$$C. The approximate pressure of the air in the tyre when the temperature increases to $$36°$$C is

We need to find the pressure of air in the tyre when the temperature increases from $$27°$$C to $$36°$$C.

Initial pressure: $$P_1 = 270$$ kPa

Initial temperature: $$T_1 = 27°C = 300$$ K

Final temperature: $$T_2 = 36°C = 309$$ K

Using Gay-Lussac's Law: (pressure is directly proportional to temperature at constant volume):

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

Solving for $$P_2$$:

$$P_2 = P_1 \times \frac{T_2}{T_1} = 270 \times \frac{309}{300}$$

$$P_2 = 270 \times 1.03 = 278.1$$ kPa

The approximate pressure of air in the tyre is $$278$$ kPa.

The correct answer is Option 3: $$278$$ kPa.