What is the volume in cubic inches?
According to Boyle’s law, the volume of a gas, at a constant temperature, varies inversely with pressure applied to it. If the volume of a gas is 120 cubic inches when the pressure is 30 pounds per square inch, find the volume in cubic inches when the pressure is 40 pounds per square inch.
The volume of a gas varies inversely with the pressure applied.
Let us denote volume as V and the pressure applied as P.
Now as they are inversely related. V = k/P
Now for a pressure of 30 pounds per square inch, the volume is 120 cubic inch.
=> 120 = k / 30
=> k = 120*30 = 3600
So we have the relation between volume and pressure as V = 3600/P
For P = 40 pounds per square inch, V = 3600 / 40 = 90.
Therefore the volume is 90 cubic inches.
At a constant temperature the volume V is inversely proportional to pressure P.
=> P = K/V, where K is the constant of proportion.
Or PV = K.
Given P = 30 pounds / c i, when V = 120 sq i.
SO PV = K gives: 30*120 p/ in = K. So K = 3600 P/in.
Therefore the volume of the gas when P = 40 p/ sq in, is given by: 40*V = K = 3600p/in.
V = 3600/40 = 90 P/ sq in.
Therefore the volume of the gas when pressure = 40p/sq in is 90 Pounds/Sq in or 90 cubic inches.