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.
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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.
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