Question

The volume of a gas in a container at a constant temperature varies inversely as the pressure. The volume is 23 cubic centimeters at a pressure of 9 pounds. Use a

proportion to find the pressure when the volume is 44 cubic centimeters.
pounds.

Answer 1

Using Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, the pressure when the volume is 44 cubic centimeters can be found to be approximately 4.7 pounds.

Step-by-step explanation:

The student's question involves the concept that the volume of a gas at a constant temperature is inversely proportional to its pressure. This is one of the gas laws known as Boyle's Law, which is a part of high school physics. To find the pressure when the volume is 44 cubic centimeters, we can set up a proportion using the initial conditions (23 cc and 9 pounds) and the final condition (44 cc and the unknown pressure).

From Boyle's Law, we know that P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. With the values provided:

9 pounds * 23 cc = P2 * 44 cc

After rearranging and solving for P2, we find that:

P2 = (9 pounds * 23 cc) / 44 cc

P2 = 207 / 44

P2 = 4.7 pounds (rounded to one decimal place)

Thus, the final pressure when the volume is 44 cubic centimeters will be approximately 4.7 pounds at constant temperature.

Answer 2

`4.70\ lb/cm^2`

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`yx=k` or
`y=k/x`

Let

y -----> the volume of a gas in cubic centimeters

x ----> the pressure in lb/cm^2

we have

For y=23, x=9

Find the value of k

`k=yx` ----->
`k=23(9)=207`

so

The equation that represent the proportion is

`yx=207`

For y=44

substitute in the equation and solve for x

`44x=207`

`x=4.70\ lb/cm^2`