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.