Answer to Question #306300 in Physics for Phil

Question

4.5m of air a gauge pressure 46.kPa undergoes an isothermal expansion to where the gauge pressure drops to 13.kPa. Calculate the final volume in m3

Answer 1

Assuming air to be ideal gas and applying Boyle–Mariotte law, have:

$$p_1V_1 = p_2V_2$$

where $p_1 = 46kPa, p_2 = 13kPa$ are initial and final pressure respectively, and $V_1 = 4.5m^3, V_2$ are initial and final volumes. Expressing $V_2$, obtain:

$$V_2 = \dfrac{p_1V_1}{p_2} = \dfrac{46kPa\cdot 4.5m^3}{13kPa} \approx 16m^3$$

Answer. 16m^3.