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Pressure Air Tyre

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Pressure Air Tyre


1. **State the problem:** We are given a volume of air in a tyre: $4000$ cm$^3$. We need to calculate the pressure $p$ in Pascals (Pa). 2. **Assume ideal gas behavior and apply Boyle's Law:** If no temperature change or other conditions are given, assume constant temperature. Boyle's Law states: $$p_1V_1 = p_2V_2$$ 3. Given: - Initial volume $V_1 = 2750$ cm$^3$ - Initial pressure $p_1$: not specified, but likely atmospheric pressure $101325$ Pa if initial is assumed normal. - Final volume $V_2 = 4000$ cm$^3$ - Final pressure $p_2 = p$ (what we want) 4. Rearranging for pressure: $$p_2 = p_1 \times \frac{V_1}{V_2}$$ 5. Substitute known values: $$p = 101325 \times \frac{2750}{4000}$$ 6. Calculate: $$p = 101325 \times 0.6875 = 69655.469$$ Pa **Answer:** The pressure of the air in the tyre is approximately $69655$ Pa.