Question

The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 173 cubic inches under a pressure of 4 pounds per square inch, what will be its volume if the pressure is increased to 5 pounds per square inch? (Round off your answer to the nearest integer.)

Answer 1

9 pounds per square inch

Explanation:

Let V = the gas' volume and P = its pressure. The volume of a gas in a container varies inversely with the pressure on the gas:

V = k/P

where k is a constant. To find the value of k, plug in the one known point, V = 390 cubic inches when P = 7 pounds per square inch and solve for k:

V = k/p

390 = k/7

390*7 = k

2730 = k

The full equation, then, is:

V = 2730/P

To find the volume when P = 9 pounds per square inch:

V = 2730/9 = _____ cubic inches

Answer 2

The volume of the gas will be 138 cubic inches the pressure is increased to 5 pounds per square inch.

Explanation:

Given: Volume of a gas in a container is inversely proportional to the pressure on the gas.

`Volume(V)\propto (1)/(Pressure(P))`

`PV=constant`

`P_1V_1=P_2V_2`

Given :

`P_1=4 pounds/inch^2,V_1=173 inches^3`

`P_2=5 pounds/inch^2,V_2=?`

`P_1V_1=P_2V_2`

`V_2=(P_1V_1)/(P_2)`

`=(4 pounds/inch^2* 173 inches^3)/(5 pounds/inch^2)`

`V_2=138.4 inch^3\approx 138 inch^3`

The volume of the gas will be 138 cubic inches the pressure is increased to 5 pounds per square inch.