Answer to Question #86924 in Molecular Physics | Thermodynamics for mayra

Question

If temperature does not change, Boyle’s law can be applied to a gas. Imagine a little container filled with some gas and a moveable piston on top. By pushing the piston down, the gas gets compressed and its pressure increases. The piston’s weight is very small, so by just “sitting” on the gas it does not really do much to it, and the gas maintains normal atmospheric pressure (101,325 Pa) at a volume of about 1 liter (0.001 m3). Let’s say the container’s wall is very thin and can stand an overpressure of max. 151,325 Pa. To what volume in m^3 would you have to compress the gas to make that happen? (Write the number only in the form #x10^(-#) (mind the parantheses and the minus sign in the 10-power), that is, 1 significant figure)

Answer 1

Boyle’s law

$$P_1\times V_1 = P_2\times V_2$$

$P_1 = 101,325 Pa$

$V_1 = 0.001 m^3$

$P_2 = 151,325 Pa$

$$101,325 Pa \times 0.001 m^3 = 151,325 Pa \times V_2$$

$$V_2 = 7\times 10^{-4} m^3$$

Answer: $7\times 10^{-4} m^3$