Question

The volume of a gas in a container varies inversely with the pressure on the gas. If a gas has a volume of 450 cubic inches under a pressure of 3 pounds per square inch, what will be its volume if the pressure is increased to 5 pounds per square inch

Answer 1

Answer: $270\ in.^3$

Step-by-step explanation:

Given

Volume of a gas varies inversely with pressure i.e.

$V\propto \dfrac{1}{P}\\\\PV=\text{constant}$

Initially, $V_1=450\ in.^3,P_1=3\ psi$

Then, pressure increases to $P_2=5\ psi$

$\therefore P_1V_1=P_2V_2\\\Rightarrow 3\times 450=5\times V_2\\\Rightarrow V_2=3\times 90\\\Rightarrow V_2=270\ in.^3$

Thus, volume decreases to $270\ in.^3$.