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

Answer:

9 pounds per square inch

Step-by-step 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

Answer:

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

Step-by-step explanation:

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

$Volume(V)\propto \frac{1}{Pressure(P)}$

$PV=constant$

$P_1V_1=P_2V_2$

Given :

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

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

$P_1V_1=P_2V_2$

$V_2=\frac{P_1V_1}{P_2}$

$=\frac{4 pounds/inch^2\times 173 inches^3}{5 pounds/inch^2}$

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

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