Question

For a fixed amount of gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. The function v=18000/p relates the volume in cubic inches and pressure in pounds per square inch of a gas. What is the volume when the pressure is 900 pounds per square inch?

Answer 1

Answer:

Volume of the gas is 20 cubic inches.

Step-by-step explanation:

Inverse proportion: Let x and y be two quantities are said to be inverse proportion or inversely proportional if one quantity increases at the same rate the other decreases.

$x \propto \frac{1}{y}$ or

$x = \frac{k}{y}$ ⇒$k =xy$   where k is constant.

Since, it is given that the volume of gas is inversely propotional to its pressure.

Given the function:  

$v = \frac{18000}{p}$           ......[1] ; where volume in cubic inches and pressure in pounds per square.

To find the volume in cubic inches.

The pressure (p) = 900 pounds per square inch.

Substitute the value of p in [1];

$v = \frac{18000}{900}= 20 in^3$

Therefore, the volume(v) = 20 cubic inches when the pressure is 900 pounds per square inch.

Answer 2

The volume when the pressure is 900 pounds per square inch is $20 in^3.$

What is proportionality?

proportionality can be explained as equality between two ratios, it gives relationship that is always in the same ratio.

We were given the function as$v= \frac{18000}{p}$

But the pressure is given as pressure (p) = 900 pounds per square inch.

We can get volume, if we substitute "p" as;

$v=\frac{18000}{p}$

$V= \frac{18000}{900} =20 in^3.$

Hence, the volume when the pressure is 900 pounds per square inch is $20 in^3.$

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