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 ___________
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Always use Absolute Temperature (Kelvin) in gas law calculations. A small error in Kelvin becomes a significant error in Celsius.
To solve the problem, we must use the ideal gas law in its simplified form under different conditions known as Gay-Lussac's law, which relates pressure and temperature for a gas at constant volume: P₁/T₁ = P₂/T₂. Here, pressures (P₁ and P₂) are measured in psi, and temperatures (T₁ and T₂) must be in Kelvin. Step 1: Convert the initial temperature from Celsius to Kelvin. T₁ = 27°C + 273.15 = 300.15 K Step 2: Set the known pressures and temperatures in the formula. P₁ = 35 psi, P₂ = 40 psi, T₁ = 300.15 K Step 3: Solve for the temperature at which the tyre bursts (T₂). Rearranging the formula gives: T₂ = (P₂ × T₁) / P₁ T₂ = (40 psi × 300.15 K) / 35 psi T₂ = 343.03 K Step 4: Convert final T₂ back to Celsius. T₂ = 343.03 K - 273.15 = 69.88°C
Therefore, the temperature at which the car tyre will burst is approximately 70°C. This value falls within the specified range of 70,70°C.
