The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $220 \mathrm{~cm}^{3}$ under a pressure of $18 \mathrm{~kg} / \mathrm{cm}^{2}$. What will be its volume under a pressure of $30 \mathrm{~kg} / \mathrm{cm}^{2}$ ?
A) $367 \mathrm{~cm}^{3}$
B) $132 \mathrm{~cm}^{3}$
C) $145 \mathrm{~cm}^{3}$
D) $385 \mathrm{~cm}^{3}$

Question

Quizplus · Accepted Answer

The volume of a gas varies inversely with the pressure, which means $V \propto \frac{1}{P}$ or $VP = k$ (a constant). Given $V_1 = 220 \, \text{cm}^3$ and $P_1 = 18 \, \text{kg/cm}^2$, we find $k = 220 \times 18$. For $P_2 = 30 \, \text{kg/cm}^2$, using $V_2P_2 = k$, we solve for $V_2 = \frac{k}{P_2} = \frac{220 \times 18}{30} = 132 \, \text{cm}^3$.

The Volume VVV Of a Gas Varies Inversely as the Pressure PPP

The Volume $V$ Of a Gas Varies Inversely as the Pressure $P$