Question

the volume of a gas in a container varies inversely as the pressure on the gas. if a gas has a volume of 242 cubic inches under a pressure of 5 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? round your answer to the nearest integer if necessary.

Explanation:

Step1: Establish inverse - variation formula

The inverse - variation formula is $V=\frac{k}{P}$, where $V$ is volume, $P$ is pressure, and $k$ is a constant. We know that when $V = 242$ and $P = 5$, we can find $k$. Substitute these values into the formula: $242=\frac{k}{5}$.

Step2: Solve for the constant $k$

Multiply both sides of the equation $242=\frac{k}{5}$ by 5 to get $k = 242\times5=1210$.

Step3: Find the new volume

Now that we know $k = 1210$ and the new pressure $P = 7$, we substitute into the formula $V=\frac{k}{P}$. So $V=\frac{1210}{7}\approx173$.

Answer:

173