Question

A car tyre is filled with nitrogen gas at 35 psi at 27$^\circ$C. It will burst if pressure exceeds 40 psi. The temperature in $^\circ$C at which the car tyre will burst is ___________

Hint:

Always use Absolute Temperature (Kelvin) in gas law calculations. A small error in Kelvin becomes a significant error in Celsius.

Answer 1

Correct Answer: 70

Step 1: Volume is constant ($V_1 = V_2$). Use Gay-Lussac's Law: $P_1/T_1 = P_2/T_2$.
Step 2: Convert initial temperature to Kelvin: $T_1 = 27 + 273 = 300$ K.
Step 3: Substitute values: $35 / 300 = 40 / T_2$.
Step 4: $T_2 = (40 \times 300) / 35 = 12000 / 35 \approx 342.85$ K.
Step 5: Convert back to Celsius: $t_2 = 342.85 - 273 = 69.85^\circ\text{C} \approx 70^\circ\text{C}$.