A car tyre is filled with nitrogen gas at 35 psi at 27°C. It will burst if pressure exceeds 40 psi. The temperature in °C at which the car tyre will burst is ______ (Rounded-off to the nearest integer)

The tyre contains nitrogen gas at a fixed volume, so we can apply Gay-Lussac's Law, which states that at constant volume, $$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$.

The initial conditions are $$P_1 = 35$$ psi and $$T_1 = 27°C = 27 + 273 = 300$$ K. The tyre bursts when $$P_2 = 40$$ psi, and we need to find $$T_2$$.

Substituting into the equation: $$\frac{35}{300} = \frac{40}{T_2}$$

Solving for $$T_2$$: $$T_2 = \frac{40 \times 300}{35} = \frac{12000}{35} = 342.86 \text{ K}$$

Converting to Celsius: $$T_2 = 342.86 - 273 = 69.86°C \approx 70°C$$

The temperature at which the car tyre will burst is $$\mathbf{70}$$°C.