Question

the volume of a gas in a container varies inversely with the pressure on the gas. if a gas has a volume of 460 cubic inches under a pressure of 10 pounds per square inch, what will be its volume if the pressure is increased to 19 pounds per square inch?

Answer 1

242.1 in^3

Explanation:

The combined gas law can be used to predict the changes in pressure, P, volume, V, and temperature, T:

P1V1/T1 = P2V2/T2 where 1 and 2 represent the initial (1) and final (2) states.

We are told:

V1 = 460 in^3

P2 = 10 psi

V2 = Unknown

P2 = 19 psi

No mention is made of temperature, so we must assume there is no change and T1 = T2

Rearrange the combined gas law to solve for V2, the new, and unknown, volume.

P1V1/T1 = P2V2/T2

P2V2/T2 = P1V1/T1

(P2V2/T2)*(T2/P2) = P1V1/T1*(T2/P2) [Multiply both sides by (T2/P2)]

V2 = V1*(T2/T1)*(P1/P2)

Since T2 = T1, this reduces to:

V2 = V1*(P1/P2)

Enter the data:

V2 = (460 in^3)*(10psi/19psi)

V2 = (460 in^3)*(0.526)

V2 = 242.1 in^3